thesis all chapters en 26 october 06

Mach Jacobi

Archimedes

Taylor Bernoulli

Venturi

Hardy Cross Pitot

Darcy

Newton

Fourier

Gauss

Lagrange

Weisbach

Euler

Reynolds

Laplace

Pascal

Use of Hydraulic Modeling andSimulation Software to Optimize the

Operation of Water Distribution Networks

Thesis submitted byEmad Shudifat

In Fulfillment of the Requirements forthe Degree of Doctor of Philosophy at:

French Institute of Forestry, Agricultural andEnvironmental Engineering( ENGREF-Montpellier- France )

January 03, 2007

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i

This PhD thesis submitted by:

Emad Shudifat

In Fulfillment of the Requirements for the Degree of Doctor of Philosophy at:

French Institute of Forestry, Agricultural, and Environmental Engineering ( ENGREF- Montpellier - France )

And it was orally defended in public on January 03, 2007 in the front of the following committee:

- Chairperson / Président : - Supervisor / Directeur de thèse : - Reviewer / Rapporteur : - Examiner / Examinateur : - Invitee / Invité :

École Nationale Du Génie Rural Des Eaux et Des Forêts ENGREF – Montpellier

Société Du Canal De Provence SCP – Aix En Provence

MREA Mission Régionale Eau-Agriculture MREA – Amman – Jordanie

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Acknowledgements Traditionally, acknowledgement is addressed only to persons whom

we have met in person and who helped us to carry out our research work. But my first, and most earnest, acknowledgment must go to all scientists in mathematics, in physics, and in hydraulics, such whom appear on the cover page of this work, whom I did not meet in person but I will be ever respectful for them and for their scientific heritage that they left behind since hundreds and thousands of years, and this precious heritage is the core of this thesis.

The greatest acknowledgement is addressed to MREA (Mission Régionale Eaux-Agriculture, French Embassy-Amman-Jordan). I would not have been able to accomplish or even start this thesis without the support of MREA; in particular Mr. Rémy Courcier and Mlle. Alice Arrighi de Casanova who have been instrumental in ensuring my academic, professional, financial, and moral well being, and they deserve far more credit than I can ever give them.

This work has been carried out during the years 2003–2006 at Canal de Provence Company in France (SCP). I wish to heartily thank the former for providing excellent facilities for both research and studying. I have always considered it a privilege to have had the opportunity of pursuing my Ph.D. at SCP. The time I have spent at the Engineering Division of SCP has been very fruitful, extremely enriching. I want especially to thank M. Pierre Rousset, M. Bruno Grawitz, M. Frédéric Bonnadier, M. Franck Sanfilippo, and M. Georges Favreau for having always been there for me and helped in most variable matters. Although I will not be able to acknowledge all the people who have directly or indirectly helped me during my work at SCP.

I would like to gratefully acknowledge the supervision of my advisor Dr. Pierre-Olivier Malaterre during this work. He has given me constant advice throughout this study and his encouraging comments have been most valuable for me. I would also thank him for the reviewing of this thesis with great effort.

I would also like to acknowledge Dr. Alain Delacourt who deserves particular credit for his careful support and who started me on the path I traveled during this thesis, and for his assistance with all types of administrative problems - at all times. He has always treated me with trust – and with patience, too.

I also owe a huge debt of gratitude to Dr. Bogumil Ulanicki, Dr. Bryan Coulbeck, Dr. Peter Bounds and other friends from Water Software Systems at De Montfort University, located in Leicester City in England, who were instrumental in the success of my two visits to their university. They are acknowledged for numerous stimulating and relevant discussions,

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and general advices throughout this study and teaching me how to use their software FINESSE.

I want to thank several people from Agricultural and Environmental Engineering Research Institute (Cemagref-Bordeaux) for the time that they spent for me and for receiving me for one week to carry out some relevant research work.

Dr. Jacques Sau, from University of Lyon I, is acknowledged for his contribution and for interesting towards my studies. Many thanks go also to the committee members.

Far too many people to mention individually have assisted in so many ways during my work. They all have my sincere gratitude.

I am grateful to all my friends from Aix-En-Provence and Montpellier Cities for being the surrogate family during the four years I stayed in France and for their continued moral support there after. “My Tunisians brothers” are especially thanked for the warm atmosphere.

A penultimate and sincere thank-you goes to my wonderful family. I am very grateful to both of my parents for their love, support, and belief in me, and never once complaining about how infrequently I visit in Jordan while I was working on this study here in France.

My final, and most heartfelt, acknowledgment must go to “my wife” whom I never even met nor found and, if she has been with me, she would surely have had a knack for boosting my morale during rough times, and she would have been acknowledged for her understanding, endless patience and encouragement when it is most required. Her support, encouragement, and companionship would have turned my journey through this thesis into a pleasure. For all that, and for being everything I am not, she has my everlasting love, and I dedicate this thesis to her.

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Abstract The two major contradictory objectives of the operation management

of the water supply systems are security of water supply and minimizing the water production and transportation costs. Optimization tools can help to achieve these objectives. The efficient operation of water supply systems is a fundamental issue for extending the system’s service life as much as possible. Efficient operation requires knowledge of the system, supported by necessary tools that play essential roles in the management optimization of water supply systems. These tools are: modeling and simulation, calibration, demand prediction, and SCADA system. In general, these four mainstays represent the fundamental elements in the management optimization problem of an existing water supply system, and they constitute the core of this thesis.

Besides, this thesis, carried out at the Canal de Provence Company (French: Société du Canal de Provence, SCP), shows a case-study for a particular SCP’s water supply network, constituting the water supply system “Les Laures - Trapan - La Môle” composed of the main supply pipe of the same name and the sets of the derived storage tanks. This unit is commonly called “Toulon Est”, where a development program is proposed upon the decision of SCP to improve safety and reliability of the water supplying service for the eastern zone of the region of Toulon City. The program includes the construction of a reversible pump-turbine plant which will be installed close to a dam called Trapan, of 2 Mm3 (million cubic meter) in volume, and the construction of a new water tank at Col Gratteloup. We will highlight in this thesis the problems of the optimization and the management of the “Toulon Est” system, the Trapan dam and the future pump-turbine plant.

For many years, design and projects have used computer modeling programs, a trend that has been amplified by the development of computer-assisted drawing and design. FINESSE, acronym of “Fully Integrated Network Editing, Simulation, and Scheduling Environment”, a software of modeling and “On Line” and “Real Time” simulation, developed by De Montfort University (DMU-UK), enables the user to determine an optimal operating schedule for pumps and valves for the whole operating horizon (typically 24 hours). This software is the modeling and scheduling tools that will be used in this research work.

v

Thesis objectives and organization

The objective of the thesis is to study the theoretical and practical problems related to the use of computer simulation models and softwares to optimize the operation of the pressurized water distribution and irrigation networks. The theoretical bases of these softwares will be analyzed, and the complementary modules necessary to their practical use will be developed to meet the needs listed and expressed by the services of networks management and operation. Moreover, we will highlight the problems of the optimization of the management of the “Toulon Est” hydraulic system and also Trapan dam and the future pump-turbine plant. Yet, we will recall these objectives later.

In order to cover the major elements that play very important and critical roles in the modeling and optimizing the operation and management of pressurized water systems this thesis is organized in eleven chapters:

1. Chapter N° 1:

This chapter is an introduction to the water distribution and management challenges and solutions where certain concepts are presented such as, Water Utility Production Management System, Information Technology (IT), Computer Integrated Manufacturing and Engineering (CIME).

2. Chapter N° 2:

In this chapter the thesis problematic, methodology, and objectives are presented. The Canal de Provence Company and the eastern branch of Toulon City’s network are also presented here.

3. Chapter N° 3:

This chapter is an introduction to the water distribution systems hydraulic, modeling, and simulation. Their basics concepts, methodologies and applications will be discussed.

4. Chapter N°4:

This chapter relates to the first mainstay of the optimization and management of water networks that is the modeling softwares available in the market, and also the softwares already used at SCP, and their applications.

5. Chapter N°5:

This chapter is about the fundamental numerical methods for solving water pipe networks problem.

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6. Chapter N°6: This chapter is an introduction to SCADA system, the second

mainstay of the optimization and management of water networks, and its role and its integration in the “Real Time” modeling and simulation of the water networks. The operation of SCADA system of SCP also will be described. 7. Chapter N°7:

This chapter approaches the third mainstay of the optimization of water networks; the process of the calibration of the hydraulic parameters of the model: roughness and demand factor. The calibration of “Toulon Est” network also will be presented. 8. Chapter N°8:

This chapter approaches the fourth mainstay of the optimization and management of water networks; demand prediction. The theoretical base of FINESSE module of demand prediction will be explained in detail and the SCP’s demand prediction technique too. 9. Chapter N°9:

This chapter is concerned with the optimization of water distribution network where the optimization terminologies, applications, and methods will be presented, and the optimization method implemented in FINESSE will be presented too. 10. Chapter N°10:

In this chapter the “Toulon Est” development program and the reversible pump-turbine plant of Trapan dam and its optimization will be covered.

11. Chapter N°11:

The last part of the thesis, it is the conclusions section where the personal achievements, the objectives fulfillment and the future work proposed are included.

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Acronyms

- ACF : Autocorrelation Function

- AIC : Aikake Information Criterion

- ANN : Artificial Neural Networks

- AR : AutoRegressive

- ARIMA : AutoRegressive Integrated Moving-Average

- ASCII : American Standard Code for Information Interchange

- BFM : Branch Flow Model

- CAD : Computer Aided Design

- CEMAGREF : Agricultural and Environmental Engineering Research Institute-France

- CEO : Compagnie d’Eau et d’Ozone (English: Water and Ozone Company)

- CGTC : Centre Général de Télé-Control (English: Control Central)

- CIME : Computer Integrated Manufacturing and Engineering

- CONOPT : Non-linear programming solver

- CRE : Centre Régional d’Exploitation (English: Regional Operating Room)

- CSV : Comma Separated Value file format

- DAE : Differential Algebraic Equation

- DES : Double-Exponential Smoothing

- DMU : De Montfort University

- DP : Dynamic Programming

- EDF : Électricité De France (English: France’s Electricity Company)

- EPS : Extended- Period Simulations

- ES : Evolutionary Strategy

- FAC : Free Available Chlorine

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- FCV : Flow Control Valve

- FEM : Finite Element methods

- FFT : Fast-Fourier-Transform

- FINESSE : Fully Integrated Network Editing, Simulation and Scheduling Environment Software

- FPE : Final Prediction Error

- GA : Genetic Algorithm

- GAMS : General Algebraic Modeling System

- GIDAP : Graphical Interactive Demand Analysis and Prediction

- GINAS : Graphical and Interactive program for Network Analysis and Simulation for water distribution system

- GIS : Geographical Information System

- GRG : Generalized Reduced Gradient

- GSM : Global System for Mobile Communication

- GUI : Graphical User Interface

- HGL : Hydraulic Gradient Line

- HW : Holt-Winters method

- IEEE : Institute of Electrical and Electronics Engineers

- IP : Integer Programming problem

- IT : Information Technology

- LFM : Loop Flow Model

- LP : Linear Programming

- LTCCP : Long Term Council Community Plan

- MA : Moving-Average

- MAE : Mean Absolute Error

- MIP : Mixed Integer Programming problem

- MM : Mixed Model

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- MMI/HMI : Man Machine Interface/Human Machine Interface

- MRPE : Mean Relative Percentage Error

- MSE : Mean Squared Error

- MUX : Multiplexing

- NAS : Network Analysis Software

- NGF : Nivellement Général de la France (English: French National Levelling)

- NLP : Non-Linear Programming

- NM : Nodal Model

- NPSHa : Available Net Positive Suction Head

- NPSHr : Required Net Positive Suction Head

- NRV : Non-Return Valve

- PACA : Provence-Alpes-Côte d’Azur

- PACF : Partial Autocorrelation Function

- PCV : Pressure Control Valve

- PRV : Pressure Reducing Valve

- PSV : Pressure Sustaining Valve

- RMINLP : Relaxed Mixed Integer Nonlinear Programming

- RT : Remote Transmission

- RTU : Remote Terminal Units

- SBB : Simple Branch and Bound algorithm

- SCADA : Supervisory Control And Data Acquisition

- SCE : Shuffled Complex Evolution

- SCP : Société du Canal de Provence (English: Canal de Provence Company)

- SES : Single-Exponential Smoothing

- SIDECM : Syndicat Intercommunal de Distribution d’Eau de la Corniche des Maures (English: Water Distributing Association of La Corniche des Maures)

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- TCV : Throttle Control Valve

- TES : Triple-Exponential Smoothing

- UK : United Kingdome

- VMS : Virtual Memory System operating system

- WAN : Wide Area Network

- WDMs : Water Distribution Models

- WDS : Water Distribution System

- WMA : Weighted Moving Average

- WSS : Water Software Systems

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Table of Contents

Acknowledgements......................................................................................ii Abstract ....................................................................................................... iv Acronyms ...................................................................................................vii Table of Contents .......................................................................................xi List of Figures ............................................................................................ xv List of Tables............................................................................................xvii CHAPTER 1 ................................................................................................. 1

1. Water Distribution and Management Challenges and Solutions ... 1 1.1 Introduction................................................................................................... 1 1.2 Water utility production management system .............................................. 6 1.3 Information integration technology in water utilities ................................... 8 1.4 Computer Integrated Manufacturing and Engineering, CIME ................... 10 1.5 Management and operational control of water supply and distribution

systems........................................................................................................ 13 1.6 Use computer model of water network systems ......................................... 15

CHAPTER 2 ............................................................................................... 18

2. Thesis Problematic and Objectives .................................................. 18 2.1 Canal de Provence Company and needs for modeling tools ...................... 18 2.2 Thesis objectives......................................................................................... 20 2.3 Presentation of Canal de Provence Company (SCP) .................................. 22 2.4 Presentation of the “Toulon Est” water supply network............................. 25 2.5 Description of the existing hydraulic system of “Toulon East” ................. 25 2.6 Operation and hydraulic management ........................................................ 31 2.7 Water demand of the zone “Toulon Est” .................................................... 32 2.8 Development program of the zone “Toulon Est” ....................................... 33

CHAPTER 3 ............................................................................................... 34

3. Water Distribution Network System Hydraulics and Modeling .. 34 3.1 Anatomy of water distribution network system.......................................... 34

3.1.1 Source of water ................................................................................... 34 3.1.2 Customers of water ............................................................................. 34 3.1.3 Transport facilities .............................................................................. 35 3.1.4 System configurations......................................................................... 35 3.1.5 Solving network problems .................................................................. 37

3.2 Water distribution network system simulation ........................................... 37 3.3 Water distribution network system modeling............................................. 38

3.3.1 Application of models......................................................................... 38 3.3.2 Modeling process................................................................................ 40 3.3.3 Network model elements .................................................................... 43 3.3.4 Water quality modeling ...................................................................... 44 3.3.5 Model simplification (skeletonisation) ............................................... 44 3.3.6 Model calibration................................................................................ 45 3.3.7 Model maintenance............................................................................. 46

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3.4 Network water consumption....................................................................... 46 3.5 Network system security............................................................................. 47 3.6 Using SCADA system for hydraulic modeling .......................................... 49 3.7 Network optimization ................................................................................. 49

CHAPTER 4 ............................................................................................... 50

4. Pressurized Water Network Modeling and Simulation Softwares50 4.1 Introduction................................................................................................. 50 4.2 Market study for water distribution modeling softwares............................ 51

4.2.1 Market study aims............................................................................... 51 4.2.2 Market studies tasks............................................................................ 52

4.3 Identifying and analyzing competitor products .......................................... 53 4.3.1 Final product list ................................................................................. 53 4.3.2 Sources of Information ....................................................................... 53 4.3.3 Product information ............................................................................ 54 4.3.4 Omitted products................................................................................. 56 4.3.5 Developer information........................................................................ 59 4.3.6 Criteria ................................................................................................ 61

4.4 General conclusions.................................................................................... 68 4.5 Water distribution networks simulation and modeling softwares at the SCP. .................................................................................................................... 69 4.6 FINESSE..................................................................................................... 70 4.7 EPANET Software...................................................................................... 76

CHAPTER 5 ............................................................................................... 78

5. Methods for Solving Water Pipe Networks Problem..................... 78 5.1 Introduction................................................................................................. 78 5.2 Conceptual model of a water network ........................................................ 79 5.3 Fundamental mathematical model .............................................................. 80 5.4 Theoretical properties of the mathematical model ..................................... 88 5.5 Numerical methods ..................................................................................... 89

5.5.1 Hardy-Cross method ........................................................................... 89 5.5.2 Newton-Raphson method ................................................................... 90 5.5.3 Linear Theory method ........................................................................ 90 5.5.4 Finite Element Methods...................................................................... 90 5.5.5 Linear Graph theory............................................................................ 91

5.6 Extended-period simulation........................................................................ 91 5.7 FINESSE simulator (GINAS)..................................................................... 92

CHAPTER 6 ............................................................................................... 94

6. Role of SCADA System for Real Time Hydraulic Simulation ...... 94 6.1 Objectives of SCADA systems for water distribution network.................. 94 6.2 Components of a SCADA system .............................................................. 96 6.3 Data acquisition mechanisms...................................................................... 97 6.4 Types of SCADA data and SCADA data format ....................................... 98 6.5 Handling of data during SCADA failures and processing of data from the

field ............................................................................................................. 98 6.6 Responding to data problems and verifying data validity .......................... 99 6.7 Integrating SCADA systems and hydraulic models ................................. 100

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6.8 Description of SCADA systems at SCP (Canivet, 2002) ......................... 102 6.8.1 The equipments of the supervisor system......................................... 102 6.8.2 Description of the measuring chain of SCP...................................... 103 6.8.3 The measurements acquisition in real-time ...................................... 107 6.8.4 Measurements conciliation technique............................................... 108

6.9 Establishing link between FINESSE SCADA Gateway and CGTC supervisor.................................................................................................. 108

CHAPTER 7 ............................................................................................. 112

7. Calibration of Pipe Network Hydraulic Model ............................ 112 7.1 Introduction............................................................................................... 112 7.2 Calibration approach................................................................................. 113 7.3 Calibration methods.................................................................................. 116 7.4 State estimation of water network ............................................................ 119 7.5 Observability and identifiability of water network................................... 120 7.6 Problem formulation for network calibration ........................................... 121 7.7 FINESSE for automatic network calibration ............................................ 123 7.8 Calibrating “Toulon Est” network ............................................................ 124

7.8.1 “EPAXL Calibrator” approach ......................................................... 124 7.8.2 Schematic diagram of the mainline of “Toulon Est” network.......... 127 7.8.3 Part#1: Single-period calibration ...................................................... 129 7.8.4 SCP’s Maintenance Division calibration tests.................................. 130 7.8.5 EPAXL Calibrator results ................................................................. 132 7.8.6 Calibration results discussion ........................................................... 134 7.8.7 Part#2: Extended-period calibration ................................................. 142 7.8.8 Continuity equation........................................................................... 142 7.8.9 Extended-period calibration approach .............................................. 143

7.9 General discussion and conclusion ........................................................... 156 CHAPTER 8 ............................................................................................. 159

8. Demand Prediction .......................................................................... 159 8.1 Introduction............................................................................................... 159 8.2 Water demand prediction.......................................................................... 159 8.3 Prediction methodology and techniques ................................................... 164 8.4 Time series methods ................................................................................. 166

8.4.1 Autocorrelation function (ACF) and partial autocorrelation function (PACF).............................................................................................. 167

8.4.2 Simple autoregressive models .......................................................... 168 8.4.3 Simple moving-average models........................................................ 169 8.4.4 Simple Box-Jenkins ARMA model .................................................. 170 8.4.5 ARIMA model .................................................................................. 171 8.4.6 Box-Jenkins Model Identification .................................................... 171 8.4.7 Smoothing methods .......................................................................... 173

8.5 Evaluating the accuracy of forecasting..................................................... 175 8.6 Forecasting softwares ............................................................................... 176 8.7 Water demand prediction technique at SCP ............................................. 178 8.8 Daily demand prediction technique implemented in FINESSE software. 181 8.9 Comparison between short-term water demand forecasting techniques for

water supply networks - case study : “Toulon Est” network system........ 186

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8.9.1 Approach........................................................................................... 186 8.9.2 Comparison of the prediction results ................................................ 197 8.9.3 Conclusion ........................................................................................ 205

CHAPTER 9 ............................................................................................. 206

9. Optimization of Water Distribution Networks............................. 206 9.1 Introduction............................................................................................... 206 9.2 Optimization terminology......................................................................... 207 9.3 The Optimization process ......................................................................... 208 9.4 Water distribution networks optimization ................................................ 209 9.5 Applications of optimization in water distribution networks ................... 211 9.6 Optimization methods............................................................................... 212 9.7 FINESSE scheduler for optimal operational scheduling .......................... 216

9.7.1 Mathematical principles and problem formulation........................... 216 9.7.2 Transformation of the network scheduling problem into a non-linear

programming problem ...................................................................... 219 9.7.3 The equation-oriented programming language................................. 220 9.7.4 Selection of a starting point .............................................................. 222 9.7.5 Continuous relaxation of the network scheduling problem.............. 222 9.7.6 Solution approaches to integer programming problems (IP)............ 224 9.7.7 Discretization by post-processing of continuous solution ................ 229 9.7.8 Remarks on GAMS/CONOPT Solver for optimal operational

scheduling ......................................................................................... 237 CHAPTER 10 ........................................................................................... 241

10. Development Program and the Reversible Pump-Turbine Plant of Trapan Dam..................................................................................... 241

10.1 Introduction............................................................................................... 241 10.2 Optimization of pumping stations at SCP................................................. 242 10.3 The Pump – Turbine plant of Trapan........................................................ 243 10.4 Gratteloup water tank................................................................................ 246 10.5 Piping and fittings..................................................................................... 246 10.6 Electrical equipments................................................................................ 251 10.7 Operating points of pump-turbine plant.................................................... 251 10.8 NPSH (Net Positive Suction Head) .......................................................... 261 10.9 Reversible pump-turbine plant: operation principles and scenarios......... 262 10.10 Reversible pump-turbine plant scheduling using FINESSE Pump Scheduler

(CONOPT/GAMS) .................................................................................. 269 10.10.1 Pump-mode................................................................................... 272 10.10.2 Turbine-mode................................................................................ 274

CHAPTER 11 ........................................................................................... 277

11. Summary and Conclusions ........................................................... 277 11.1 Summary................................................................................................... 277 11.2 General conclusions.................................................................................. 278

References................................................................................................. 281

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List of Figures

Figure 1.1 : Production management system.................................................................... 7 Figure 1.2 : WaterCIME methodology ........................................................................... 11 Figure 1.3 : CIME pyramid............................................................................................. 12 Figure 1.4 : Mainstays of optimization........................................................................... 17 Figure 2.1 : General sight of Canal de Provence ............................................................ 24 Figure 2.2 : General sight of “Toulon Est” water supply network ................................. 25 Figure 2.3 : Point A – Les Laures................................................................................... 26 Figure 2.4 : Point C – Pierrascas tank............................................................................. 27 Figure 2.5 : Point F – Fenouillet tank ............................................................................. 27 Figure 2.6 : Point G – Mont Redon tank......................................................................... 28 Figure 2.7 : Point H – Golf Hôtel tank ........................................................................... 28 Figure 2.8 : Point M – La Môle ...................................................................................... 28 Figure 2.9 : Hydraulic profile of Toulon Est network .................................................... 29 Figure 2.10 : Point T – Trapan dam................................................................................ 30 Figure 3.1 : Looped and branched networks................................................................... 36 Figure 3.2 : Looped and branched networks after network failure................................. 36 Figure 3.3 : Major points of vulnerability in a water supply system.............................. 47 Figure 4.1 : FINESSE architecture ................................................................................. 71 Figure 4.2 : FINESSE interface ...................................................................................... 76 Figure 5.1 : Conceptual model........................................................................................ 79 Figure 6.1 : Generic SCADA system network ............................................................... 97 Figure 6.2 : Architecture of SCADA communication at SCP ...................................... 104 Figure 6.3 : Schema of data conciliation algorithm...................................................... 109 Figure 6.4 : “Telemetric Link” between FINESSE and CGTC/SCP supervisor ......... 111 Figure 7.1 : Calibration approach for pipe roughness .................................................. 128 Figure 7.2 : Schematic diagram of the mainline of “Toulon Est” network .................. 129 Figure 7.3 : ε_values computed by EPAXL ................................................................. 134 Figure 7.4 : Differences between ε_values of Test#1 and Test#2 ................................ 136 Figure 7.5 : Differences between ε_values of SCP and EPAXL.................................. 138 Figure 7.6 : Difference between measured and simulated pressures –Test#1 .............. 140 Figure 7.7 : Difference between measured and simulated pressures –Test#2 .............. 141 Figure 7.8 : Hourly total water demand – Toulon Est, Year 2005 ............................... 143 Figure 7.9 : Differences between system inflows and outflows ................................... 143 Figure 7.10 : Colebrook vs. simplified friction factor equations.................................. 144 Figure 7.11 : hf vs. Q2 for Pipe A-B ............................................................................. 145 Figure 7.12 : hf vs. Q2 for Pipe B-C ............................................................................. 146 Figure 7.13 : hf vs. Q2 for Pipe C-E ............................................................................. 146 Figure 7.14 : hf vs. Q2 for Pipe E-F.............................................................................. 147 Figure 7.15 : hf vs. Q2 for Pipe F-G ............................................................................. 147 Figure 7.16 : hf vs. Q2 for Pipe G-H............................................................................. 148 Figure 7.17 : hf vs. Q2 for Pipe H-K............................................................................. 148 Figure 7.18 : Measured and simulated pressures at Point B ......................................... 152 Figure 7.19 : Measured and simulated pressures at Point C......................................... 152 Figure 7.20 : Measured and simulated pressures at Point E ......................................... 153 Figure 7.21 : Measured and simulated pressures at Point F ......................................... 153 Figure 7.22 : Measured and simulated pressures at Point G ........................................ 154 Figure 7.23 : Measured and simulated pressures at Point H ........................................ 154 Figure 7.24 : Measured and simulated pressures at Point K ........................................ 155

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Figure 7.25 : Calculated delta’s values (Δ)................................................................... 155 Figure 7.26 : Comparison between the ε_values .......................................................... 156 Figure 8.1 : Example of demand prediction at SCP – Toulon Est – 2006.................... 180 Figure 8.2 : GIPAD’s demand prediction stages .......................................................... 182 Figure 8.3 : Example of original vs. smoothed demand - Year 2002 ........................... 187 Figure 8.4 : Measured demand and the periodogram ................................................... 188 Figure 8.5 : Autocorrelation function of demand series ............................................... 193 Figure 8.6 : Autocorrelation and partial autocorrelation functions, 2002 .................... 194 Figure 8.7 : Autocorrelation and partial autocorrelation functions, 2003 .................... 195 Figure 8.8 : Autocorrelation function of residual ......................................................... 196 Figure 8.9 : Prediction methods comparison – Year 2002 ........................................... 199 Figure 8.10 : Prediction methods comparison – Year 2003 ......................................... 200 Figure 8.11 : Prediction methods comparison – July 31, 2003..................................... 201 Figure 8.12 : Measured and predicted demand (July 31, 2003) ................................... 202 Figure 8.13 : Prediction methods comparison – Year 2004 ......................................... 203 Figure 8.14 : Prediction methods comparison – Year 2005 ......................................... 204 Figure 9.1 : Optimization process................................................................................. 207 Figure 9.2 : Discretization by valve aperture adjustment ............................................. 230 Figure 9.3 : Valve adjustment approach ....................................................................... 231 Figure 9.4 : Discretization by pump speed adjustment................................................. 232 Figure 9.5 : Pump speed adjustment approach ............................................................. 234 Figure 9.6 : Timestep adjustment approach.................................................................. 236 Figure 9.7 : Network configuration example 1............................................................. 237 Figure 9.8 : Network configuration example 2............................................................. 238 Figure 10.1 : Hydraulic characteristics of the pump - turbine unit............................... 245 Figure 10.2 : Hydraulic profile of Toulon Est network ................................................ 248 Figure 10.3 : 900mm-pipeline profile connecting the station to Trapan ...................... 249 Figure 10.4 : 700mm-pipeline profile connecting the station and the supply pipe ...... 249 Figure 10.5 : General view of the project ..................................................................... 250 Figure 10.6 : Turbine operating points ......................................................................... 253 Figure 10.7 : Operation of the Trapan pumping station at different conditions ........... 260 Figure 10.8 : NPSH – Toulon Est pumping station ...................................................... 262 Figure 10.9 : FINESSE model for “Toulon Est” .......................................................... 271 Figure 10.10 : Pumping and turbining in the same time............................................... 271 Figure 10.11 : Toulon Est in pump-mode under normal operation .............................. 273 Figure 10.12 : Pump control – Pump optimal continuous solution .............................. 273 Figure 10.13 : Toulon Est in turbine-mode under normal operation ............................ 275 Figure 10.14 : Toulon Est in turbine-mode and water tanks between Les Laures and Trapan are not isolated.................................................................................................. 276

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List of Tables

Table 2.1 : Characteristics of the submain pipelines ...................................................... 27 Table 3.1 : Types of problems that could be analyzed by modeling .............................. 39 Table 3.2 : Network Data................................................................................................ 42 Table 3.3 : Demand Data ................................................................................................ 43 Table 3.4 : Operational Data........................................................................................... 43 Table 3.5 : Common network modeling elements.......................................................... 43 Table 4.1 : General software information and features .................................................. 69 Table 7.1 : Description of hydraulic measurements of “Toulon Est”........................... 129 Table 7.2 : Flow measurements during Test#1_SCP.................................................... 130 Table 7.3 : Calibration results for Test#1_SCP ............................................................ 131 Table 7.4 : Flow measurements during Test#2_SCP.................................................... 131 Table 7.5 : Calibration results for Test#2_SCP ............................................................ 131 Table 7.6 : Calibration results for Test#1_EPAXL ...................................................... 133 Table 7.7 : Calibration results for Test#2_EPAXL ...................................................... 133 Table 7.8 : Calibration results for Test#1 and Test#2_EPAXL................................... 134 Table 7.9 : Differences between ε_SCP#1 and ε_SCP#2............................................. 135 Table 7.10 : Differences between ε_ EPAXL#1 and ε_ EPAXL#2 ............................. 136 Table 7.11 : Difference between ε_SCP#1 and ε_EPAXL#1....................................... 137 Table 7.12 : Difference between ε_SCP#2 and ε_EPAXL#2....................................... 137 Table 7.13 : Difference between measured and simulated pressures –Test#1 ............. 140 Table 7.14 : Difference between measured and simulated pressures –Test#2 ............. 141 Table 7.15 : Results for linear regression parameters estimation - 2005...................... 145 Table 7.16 : Calibration results for equation inversion ................................................ 150 Table 7.17 : Results for EPAXL Calibrator - 2005 ...................................................... 151 Table 7.18 : Summary of ε_values for calibration 2005 and 2006.............................. 156 Table 8.1 : Alpha setting for SES ................................................................................. 190 Table 8.2 : Alpha setting for TES ................................................................................. 191 Table 8.3 : Parameter estimation .................................................................................. 197 Table 8.4 : Results - 2002 ............................................................................................. 199 Table 8.5 : Results - 2003 ............................................................................................. 200 Table 8.6 : Results - July 31, 2003 ............................................................................... 201 Table 8.7 : Results - 2004 ............................................................................................. 203 Table 8.8 : Results - 2005 ............................................................................................. 204 Table 10.1 : Optimal operating points .......................................................................... 244 Table 10.2 : Pumping to Les Laures ............................................................................ 255 Table 10.3 : Pumping to Les Laures ............................................................................ 255 Table 10.4 : Pumping to Gratteloup............................................................................. 257 Table 10.5 : Pumping to Gratteloup............................................................................. 257 Table 10.6 : Pumping to Golf Hôtel ............................................................................ 259 Table 10.7 : Pumping to Golf Hôtel ............................................................................ 259 Table 10.8 : 2005 Summer Demand for Toulon Est..................................................... 272 Table 10.9 : EDF Electricity tariff (€/kWhr) ................................................................ 272

1. CHAPTER 1 : Water Distribution and Management Challenges and Solutions

1

CHAPTER 1

1. Water Distribution and Management Challenges and Solutions

1.1 Introduction Human life, as with all animal and plant life on the planet, is

dependent upon water. Not only do we need water to grow our food, generate our power and run our industries, but we need it as a basic part of our daily lives; our bodies need to ingest water every day to continue functioning. Communities and individuals can exist without many things if they have to; they can be deprived of comfort, of shelter, even of food for a period, but they can not be deprived of water and survive for more than a few days. Because of the intimate relationship between water and life, water is woven into the fabric of all cultures, religions and societies in many ways (Gleick, 1999).

Water and civilization, two terms historically associated. The first civilizations appeared by the big rivers (Gleick, 1999). The flowing waters of the Euphrates, the Nile, the Indus and the Yangtze were silent witnesses of the human settlements along their banks and the flourishing of their culture. They switched from subsistence agriculture to organized farming in a short time. Water can be social, economic, private and public good. Water is important to the process of economic development improving both individual and social well being. It is essential for life and health and has cultural and religious significance (Suleiman, 2002).

Access to basic water requirements is a fundamental right implicitly supported by international law, declarations and state practices. This right is even more basic than other explicit human rights as can be seen by its recognition in some local traditional laws or religious norm (Gleick, 1999). The holly Quran for instance, says that “And we made from water every living thing”. This forthright statement explicitly correlates water with life (Suleiman, 2002).

The world-wide consumption of the last century has increased seven folds. In the last half of the XX century the answer to this increase in the demand was basically the construction of more and larger hydraulic infrastructures, especially reservoirs and canals for deviating rivers. More


2

than 85% of the 40,000 reservoirs built in the world have been constructed in the last 35 years (Pérez, 2003). Such engineering works have guaranteed the supply of water to great urban and rural areas but have, in the opinion of ecologists, led to the degradation of the fluvial deltas and increased the risk of extinction of some species in wetland areas.

Nobody can ignore the fact that it is not possible to satisfy a demand without limit with a permanent increase of the offer of a commodity that has ecological, physical and economic limitations. As the most accessible sources of water are exhausted new resources are obtained in an increasingly complicated and hence more expensive way. This leads to a worse quality of the resource and the necessity of a new culture of water usage based on a more rational and sustainable use of this valuable resource (Pérez, 2003).

The challenge is to spend less and more efficiently. To guarantee a sufficient supply of water does not in itself suffice to solve the distribution problems. It is necessary to continue conserving water. This is a broad concept that includes all those techniques orientated to help in the saving and better management of this liquid (UNICEF, 2000).

Such techniques include the modernization and rehabilitation of the networks to minimize leakage. This is a problem that affects not only the urban centers where 30% of the water that enters the network does not get to its destiny at the consumption points but also the watering infrastructures. Installation of low consumption devices nowadays allows savings of 50% without losing quality in the service. There are models of taps, showers and toilets with such improved efficiency. Wastewater can be reused after a good process of depuration. Education campaigns are crucial for saving water and the introduction of new tariffs can stimulate such savings (UNICEF, 2000). The contamination of both surface water (rivers become increasingly polluted as they pass by cities and industrial areas) and ground water (polluted by nitrates, heavy metals and organic components and affected by salinization) should be reduced.

Water provision can not be separated from two other inter-related factors - sanitation and health. This is because one of the primary causes of contamination of water is the inadequate or improper disposal of human (and animal) excreta. This often leads to a cycle of infection and contamination that remains one of the leading causes of illness and death in the developing world.

Drinking water quality is not an objective any more but an obligation (Pérez, 2003). Access to clean water is fundamental to survival and critical for reducing the prevalence of many water related diseases. For centuries, Europe had to cope with plagues and epidemics unaware of their origin. In 1854 in London, during a cholera epidemic, Dr John Snow discovered that the means of dissemination of this disease was water. He treated the water


3

with chlorine and it eradicated the disease. After this experience the temporary treatment of water with chlorine began, first in the United Kingdom and afterwards in the United States becoming generalized at the beginning of the 20th century. It brought about the reduction of diseases such as Hepatitis A, Cholera and Typhus. The purification of water with chlorine has been the sanitary measure that has saved most lives in the last century.

In addition, the provision of safe drinking water and proper sanitation has the greatest overall impact upon national development and public health. 1.1 billion people in the world are still without some form of improved water supply, 2.4 billion live without adequate sanitation and 5 million people a year, of mostly children under age 5, die from illnesses linked to unsafe water, unclean domestic environments and improper sanitation (UNICEF, 2000).

The modern treatment stations use slow filtration systems that reproduce the conditions of the riverbeds. The European legislation defines three types of water depending on which treatment it undergoes. This ranges from the simplest physical treatment and disinfecting to the most sophisticated physical and chemical treatment and disinfecting. Now in the quick filtration plants water undergoes treatment that includes different phases: caption, mixing with coagulating and reactive substances, decantation and sand separation, flocculation, sedimentation, filtration, and disinfecting. This procedure may last five hours and some new tools have been added. These technologies allow the fulfillment of the quality standards. Active carbon (produced by the combustion in special and controlled conditions of organic substances) that presents a big exposed area can trap by absorption suspended particles and dissolved substances. The disinfecting process using Ozone is very efficient but is more expensive than the use of chlorine. Inverse osmosis uses membranes to separate dissolved salts. In general solar technologies applied to the purification of water are only useful for water with low contamination.

Desalination of water is the other choice to increase the availability of water instead of reusing residual water. It is a perfectly viable solution from a technological point of view. The problem is the high cost of the technology. Nevertheless the latest advances in this technology and the introduction of inverse osmosis have decreased the energetic cost. The cost seems to be decreasing and the supporters of this technology believe that soon this water will be cheaper. On the other hand the energy needed is a great drawback for obtaining a sustainable supply of water by this method.

Although the chemical purification methodologies guarantee that the water that comes from the taps is all right from the sanitary point of view in the last few years the consumption of bottled water has increased spectacularly. This happens despite consumers having to pay between 500


4

and 1,000 times more for this water than that in the public network, and that in more than 50% of cases this bottled water has the same quality as the tap water except for some salts and aggregated minerals. Consumption of bottled water increases in the world by 7% each year (WHO, 2001). The reason has to be found in the fact that consumers do not like tap water, sometimes because it has a disagreeable taste or odor or sometimes because it can appear white color.

Aware of this problem the distribution companies have started plans to determine and increase the quality of the water offered to their customers. For example the Societat General d’Aigües de Barcelona (Agbar), in collaboration with the French Society Lyonaise des Eaux and the North American Water Works Association Research, has developed a system to quantify the color, taste and odor of the drinking water. If there is any case in which one of these characteristics becomes unpleasant the causes are discovered and corrected. For this purpose there are some professionals that can detect 30 different tastes and smells in the water like the ones who work with wine. Typical tastes of chlorine, humid soil, metallic, cooked vegetable or the classical acid, sweet, salt and bitter can define the water. After the taste process the chemical analysis allows the detection of substances that produce such problems and the water can be treated adequately.

Unlike other sectors, water sector is the closest approximation to the ideal “natural monopoly” of economic texts (OECD, 1998). The required infrastructure is costly and specialized. Therefore, duplication by potential competitors would be prohibitive. As a consequence, one can not count on competition to maintain reasonable prices and levels of services. Although privatization does not work magic in the public area, experience has approved that it is quite successful in those industries where technology is flexible in the sense of permitting multicompany use of facilities. In the water sector, the natural monopoly problem has not been overcome and unless, there is a competitive market, private sector involvement will not be able to offer the potential efficiency gains.

Actually what is apparent after all these facts is that the water that is consumed is cheap but the solutions to guarantee its availability and quality are not. The reality is that water is a limited resource and should be treated not just as a social commodity, but an economical one too. Citizens should use water in the most efficient way and pay for the real cost of this precious resource. The Worldwatch Institute estimates that only 15% of the real cost is paid, a fact which does not encourage water conservation (Suleiman, 2002).

Careful usage as recommended by experts should be supported by different initiatives. Specific legislation and recommendations for the population about this necessity would help avoid wastage. The adoption of


5

financial incentives would stimulate the substitution (for uses that do not require high quality water) of the potable water with that coming from the regeneration of residual waters. The objective of these programs would be the adjustment of the resource to the demands in order to liberate high quality flows to the most appropriate uses. It is not sensible to use potable water to water the plants, wash the car, or clean the streets.

Managing water as economic good means that water will be allocated among competitive users in a way that maximize the net benefit from the amount of water (OECD, 1998). As a result, the cost of water should consider the full economic cost including the opportunity cost. This may cause poor people to be priced out of the market leaving them without adequate social good. The recognition of the economic character of the water was associated with the existence of the water market but, it has not been clear so far how practically, to achieve the rights balance between managing water as both a social and economic good.

International human rights law recognizes that without access to adequate water, it is not possible to attain many other explicit rights, such as life, health, education, gender equity, and adequate standards of livings. Some women in Ghana have correlated lack of water with lack of dignity and even sometimes violence in the home under the growing emphasis on the market to manage water supply, certainly, and if the market fail to provide the water basic requirements, it is the responsibility of the state to meet these needs under the human right agreements. At the World Water Forum in The Hague, it was the subject of heated debate, with the World Bank and the water companies seeking to have it declared as a human need that is not semantic. If water is a human need, it can be provided by the private sector while if it is a human right, it can not be sold. Water is not simply a handout or a market commodity that can be priced through contractual agreement. A human rights perspective demands authentic popular consultation and participation in decisions affecting the production and distribution of water (UNICEF, 2000).

The problem outlined in the previous paragraphs affects all of society. Some of the solutions suggested so far depend on the customers, others depend on the governments, and some depend on production companies and some on the distribution companies. Distribution of water also presents some challenges. Distribution has improved in the last century although it existed in ancient civilizations.

The quality control of the water that flows through the network is an obligation nowadays. The physical conditions of the water offered to the customers are an objective of all the distribution companies. It is necessary to assure a pressure of water and a reliability of the service so that people, industry, hostelry, hospitals and all of society can trust in a basic service. Another important aspect already mentioned is the huge quantity of water


6

that disappears in the network before it reaches its target. A knowledge allowing an understanding of what happens in a water

utility is indispensable for any quality certification, as the quality concept has more to do with the reliability of the data and assertion than to improve an unknown level. This knowledge is useful to correct any failure in the process or to improve its functioning. This knowledge is provided by control and supervision of the process. In a distribution network such supervision uses the data-loggers distributed in the network where the communications are often by radio due to the remote location of these measures, informatics applications that show the working state of the network, and some decision tools, depending on the water utility, that help the human operators. Control and supervision of processes are part of the Water Utility Production Management System described hereafter.

1.2 Water utility production management system The term “water utility” covers all forms of organization directly

responsible for managing parts of water cycle (WaterCIME, 1994). The term “production management” system covers the engineering activities required to run a water system. Examples of such activities include operational control, maintenance and planning design and construction (Figure 1.1). The activities include tasks which are automated and/or performed by people. The European Union contains diversity of organizational types and national legal frameworks. Despite this diversity, the essential missions of water utilities are similar, and it is not surprising that similar categories of activities are found in every water utility, for example, operational control, planning design and construction, maintenance, water quality analysis, finance, personnel management, costumer services, etc (Eureau, 1993).

The existence of common objectives and activities creates the possibility of generalized methods of analyzing utilities, just as there are generalized methods for analyzing hydraulic networks. In the ideal utility, its mission decomposed into hierarchy of objectives with corresponding activities which co-operate to achieve the utility’s objectives.

The management of water system can be characterized as a process control and transport problem. Water management systems typically consist of distributed structures and works, having relatively high levels of instrumentations, controls and automation, which are interconnected by transport networks having lower levels. Dynamic information is exchanged with the water system via the supervisory system. The water system is also described by more or less static information in asset databases. An operator’s view of the water system is usually limited to this information


7

(WaterCIME, 1995). Some of the problems associated with water utility production

management system are:

1. Information distributed in time, space and according to the departmental and hierarchical organization.

2. Information may be inconsistent, out of date and inaccessible. 3. The net effect of the complex mixture of human and automated

activities, each having localized objectives, is not generally efficient overall.

4. There are difficulties in communication owing to different protocol and understanding.

5. Much staff-time is spent on data gathering, checking and processing.

6. It is difficult to understand the overall effect of introducing reorganized and new systems.

Figure 1.1 : Production management system Therefore, organizing and improving production management system

is a complex and challenging task, because it is often complex with many activities distributed in time and space. Activities are also distributed across department and the management hierarchy. Activities can be viewed as information producers and costumers. Information must be exchanged for the utility to work in an efficient and coordinated way. Also, information is distributed and exists in different paper-based and computerized forms. However, the water utilities are trying to achieve greater efficiencies from

Planning Design and

Construction

Water Utility Production Management System

Operational Control

Maintenance

Customer Services


8

the use of complex and more integrated Information Technology Systems IT (WaterCIME, 1995). The role of Information Integration is to enable and make utility activities more efficient.

1.3 Information integration technology in water utilities As mentioned here above, Information is distributed across a water

utility in different departments and geographical locations. It is also distributed vertically according to management level (Buxton, 1996). This distribution, and the use of different computer and paper-based information systems cause difficulties when ensuring that shared information is up to date, correct and consistent. Different activities require and produce information in different forms.

In general, information is aggregated and abstracted through the different management levels, requiring information processing, much of which is trivial and repetitive. Much staff-time is spent on relatively simple data acquisition, gathering, checking and processing tasks, which is time consuming, costly and reduce the time available for data analysis. Many of these data processing tasks could be automated. The degree of automation is a matter of utility management strategy. Some activities can be fully or partially automated (Rance, 1999).

However, computers are unable to abstract and conceptualize and can not handle incomplete and ill-defined description, and some activities can not be automated. A computerized system stores and manipulates data. It carries out many complex tasks and accurately executes complex formally-specified procedures such as calculating the optimal schedule for a supply network. A computer can perform a number of unrelated tasks simultaneously which a single person would find impossible. In particular, a computer has an extensive and accurate short-term and long-term memory. Data storage and access is currently the major role in water utilities which are commissioning large information management systems such as Geographical Information System (GIS). Communication networks provide the ability to exchange and share information quickly across a distributed utility. Placing existing utility information into a common data store can impose formal constraints, such as the identification of unique name for certain items in order to access the data store effectively.

Information integration means the consistent linking of computer systems, its general objective is to provide timely, reliable and relevant information to perform activities and make decisions. This usually involves the use of digital computer systems which is the dominant technology for information storage, retrieval and processing. However, the efficient exploitation of this technology requires the use of systematic analytical and


9

planning methods. The main problems in achieving information integration arise from organizational complexity, organizational change, and in managing the introduction of new technology and existing systems (Brunel Uni., 1997).

In practice, information integration often occurs gradually by evolution under the pressure of different forces. Competition and regulatory pressures drive water companies to address particular aspects of the business such as asset management, leakage reduction, and costumer service. Computer technology develops rapidly and offers new tools for companies to improve efficiency. There are different levels of integration and different interpretations of integration (Rance, 1999):

1. Separate databases and applications implemented to support specific aspect of the business such as asset management, operational control, and customer service. Examples include Geographical Information System (GIS), Supervisory Control And Data Acquisition (SCADA), Asset maintenance databases, and customer billing system. Many companies are implementing such databases as the primary source of information about these aspects of the business. The philosophy is to assemble all relevant information about a particular aspect in one database, and thereafter to maintain and use this database as the primary source of information.

2. Interconnected databases and applications are required by some

activities. For example, the management of leakage requires information which is typically stored in the asset and operational control databases. Some companies have developed specialized software interfaces to extract and process the required information, and to exchange it across computer networks. Such interfaces are specialized to the requirements of a particular activity. There are standards and products which facilitate the development of such interfaces.

3. The company – wide integration of information system requires a

systematic analytical approach and planning method. Information integration proceeds through the theoretical analysis of the operation of a company and the development of a migration plan which takes into account the investment in existing systems and the improvement opportunity within the company. Such an approach can lead to the improvement in the operation of the company as a whole. It may involve changing some working practices.


10

Most companies have achieved successes at level 1 and 2. Although, coherent plans and policies toward fully integrated information systems are uncommon in the water industry at present, many companies are now considering the issue. The task of designing an information integration system is quite complex and time consuming process. This has led some manufacturing industries (which have activities and products families in common with water utilities) to develop general models or references as guides that defines a general methodology for information integration problem, and for developing and trying out practical, open and evolutionary solutions. This subject had been studied during a European project called “WaterCIME” (1995). “WaterCIME” project consortium consists of, Alcatel TITN Answare (France), AspenTech-CIMTECH (Belgium), Daimler-Benz Aerospace (Germany), De Montfort University (UK), Instituut voor Agrotechnologisch Onderzoek (Netherlands), Bremer Entsorgungs-Betriebe (Germany), Société Canal de Provence (France), and the Société Wallonne des Distribution d’Eau (Belgium). It belongs to the European research program ESPRIT relating to information technologies. It has for the base the concept CIME “Computer Integrated Manufacturing and Engineering” that already largely used in other industrial field. The consortium of

1.4 Computer Integrated Manufacturing and Engineering, CIME

Much work has been performed on the cooperation of computer-based engineering activities in the manufacturing industry. The task of designing a computer integrated manufacturing system is complex and time consuming (WaterCIME, 1995). The CIME methodology, developed by some manufacturing industries, helps to plan, design and operate manufacturing enterprise, and it is particularly suited to engineering organizations. CIME models are verbal and graphical descriptions of the overall process of CIME development and implementation. Also, water utilities share some common problems with electrical power and gas industries. Results arising from these industries are also relevant to water industry. The CIME concepts were adapted to the water domain (WaterCIME, 1995).

The mission of WaterCIME project is to develop open water management systems. As a step toward achieving this, the consortium of this project developed the WaterCIME methodology. It was developed from the experience of the partners and drawing from working manufacturing industries to address the problem of information integration in “water production management systems”, a term used to cover the activities required to run a water system. Four groups of activities are


11

identified in the production management system: operational control, maintenance, planning design and construction, and costumer services. The groups include tasks which are automated and/or performed by people. The methodology treats activities as information procedures and consumers. Hierarchical models of the system are built; the modeling enables the rational identification of improvement opportunities. The outputs of the methodology include models of the existing and improved company, and a migration plan and cost/benefit analysis (WaterCIME, 1995).

The essence of the methodology is to produce a full model of the existing production management system, called “As-Is” model. The model building process reveals potential improvement to the system. This and other knowledge is used to construct another full model capturing the improvement opportunities, called “To-Be” model. The CIME methodology is supported by the Reference Model (Figure 1.2) which is a generalized example used to help derive the specific models. The Reference Model includes the following sub-models, providing successive layers of abstraction:

1. Reference Objectives and Constrain Model. 2. Reference Decision Model. 3. Reference Information Model. 4. Reference Information System.

The Reference Objective and Constrain Model describe general

water utility objectives. These are transformed into the Reference Decision Model, which is hierarchical model of activities and associated information flows between the activities. The information flows are decomposed into an object-oriented data model called the Reference Information Model. This model aggregates these data objects and utility functions into the elements of a computerized information system.

Figure 1.2 : WaterCIME methodology Generally speaking, any production management system can be

divided into management levels, each level bringing together distinct

AS-IS Utility

TO-BE Utility

Real Organization

WaterCIME Methodology

Step by Step Approach

Assess

ReferenceModel

As Is Model

To Be Model Plan


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elements so as to form a homogenous whole containing the same functionality. This division is commonly called the CIME pyramid (Figure 1.3).

The means brought into operation at each of the levels of the CIME pyramid are different. At each level, there are functions some of which are executed using software.

Figure 1.3 : CIME pyramid Level 0 - Sensors/Actuators

Contains the whole of the sensors and actuators. It is the one closet

to the process, the function of this level enables the development of the process to be followed and guided. At this level, process information is taken up toward level 1. Typically, we will find at this level motors, pressure sensors, and meters…

Level 1- Process Control

Corresponds to the management of the part of a facility (pumping

station, reservoir, water tower…). At this level we find a control and operating system of the programmable automatic device type piloting the facility in real time. The absence of permanent communications between this level and the upper levels, means that interesting information is temporary stored with a view to its future repatriation.

Level 2- Process Supervision

This level manages a group of equipments which has to ensure a

Sensors / Actuators

Company Management

Factory Management

Process Management

Process Supervision

Process Control

Level 0

Level 1

Level 2

Level 3

Level 4

Level 5


13

function or a group of clearly defined functions, such as pumping and storage. It is in charge of the management of alarms, monitoring of the process through animated supervision screen, filling of process data, creation of production reports, and the transmission of input or orders to level-1 equipment. It corresponds to process daily management activities. The geographical dispersion of facilities requires the use of commutated or digital telephone networks or radio network, such as GSM, in order to exchange information between level 1 and 2.

Level 3- Process Management

This level is entrusted with the consistent management of a group of

interconnected facilities or networks. Simulation and process optimization as well as the quality follow-up of the product, are carried out at this level.

Level 4- Factory Management

Corresponds to the management of a group of geographically close

networks but not necessary interconnected. This is the role of a company regional management. At this level, process maintenance planning, spare part and store management are worked out.

Level 5- Overall Company Management

This level is a general management level. It is the level where

decisions are made so as to improve the use of the system. This level needs information from facilities and networks, but also additional information concerning the topology of the process, human and technical resources, sales data, etc (WaterCIME, 1995).

1.5 Management and operational control of water supply and distribution systems

Water is linked to life and human activities from many angles and

using drinking water has become a commonplace for each of us (Brunel University, 1997). Water flows as soon as we open the tap, as naturally as if it is spurting from a spring and we are far from thinking that the managers of water production and distribution services must devote sustained efforts to maintaining such a permanence and quality of service. Water is taken from surface resources or from underground resources. Then water is purified in treatment works by physical and chemical processes. The clean water is then pumped into a supply network of pipes. It may be


14

stored in service reservoirs and it is distributed to the consumers through distribution pipe networks. Water is transported through the pipe-networks under pressure derived from the force of gravity and pumps. As users, we do not generally realize how complex the process is until we are victims of trouble such as pressure drops, supply cuts or doubtful quality – smell, taste, and appearance.

It seems useful to briefly recall the structure of the water supply and distribution system. It consists three main parts:

A. Treatment works

It is a process plant with a relatively high level of monitoring and

control and dedicated communications network. Many variables are monitored at frequent intervals including flows, tank levels, water quality parameters etc. The plant contains many local control loops, but from the point of view of the control of an entire water system, the important relationship is between the intake flow from the source (cause) and the outflow (effect). When viewed as an input/output model, the treatment processes impose some operational constraints on the control problem including: minimum and maximum output flow at any time and total volume over 24 hours.

B. Water supply systems

Water supply systems (also called Transmission system) share common features that are important from the operational control point of view:

1. Relatively simple network structure with a limited number of

connections. 2. Pipes of large diameter to transport bulk quantities of water. 3. Large pump stations composed of numbers of high-lift pumps. 4. Interactions with the distribution part of the system can be

modeled as demands and can be predicted with reasonable accuracy.

5. Systems flows are often insensitive with respect to reservoir level variations.

The pipe system has relatively spare measurement and control and,

typically, only key flows and pressures are monitored.

C. Water distribution systems The following features of water distribution systems are important


15

from an operational control point of view:

1. Complicated network structure with hundreds of connections and many pipe-loops.

2. A typical zone contains one service reservoir to sustain supplies and maintain pressures.

3. Reservoir level variations may have significant impact on flows and pressures of the system.

4. Elements such as booster pumps and control valves to control local conditions.

The distribution system has also relatively spare measurements and

control. Typically only a few key flows and pressures are monitored frequently. The distribution part can include many sub-systems.

Complex water systems composed of many sub-systems required an adequate control structure. The lower level decision structure (Level 0- Sensors/Actuators of CIME pyramid) directly interacts with the physical system by a distributed telemetry system (SCADA system). The responsibilities of the operator, in a local control room, can vary from following orders from the upper level to solving some parameterized sub-problems. Schedules for major control elements calculated by the co-ordination level are based on abstract mathematical models and the local manager or operator has to convert them into direct control action taking into account detailed physical layouts of the control elements. Typically a computer model of the water network is the basic tool for the manager and operator so the control decisions before being applied to the physical system are verified by this model.

1.6 Use computer model of water network systems The problem of integrating IT systems is one of which is facing all

hydraulic schema operators. Progress in this field has led to the development of tools and softwares bringing considerable improvement in the performances of their design, execution, operation, maintenance, and marketing and sales services, but most often quite separately. Based on this observation, overall management of these systems has to be optimized by avoiding inconsistencies and redundancies, and by drawing most advantage from the synergies involved. For many years, design and projects have used computer modeling programs (WaterCIME, 1995), a trend that has been amplified by development of computer-assisted drawing and design. It is necessary to use modeling methods for a water network system of a company to correspond to the computer integrated management system of


16

the CIME pyramid. In modern system control of water supply and distribution, there is a need for more systematic handling of system complexities and for prevision of more efficient guidelines for overall operations. A model may be considered as an abstraction and simplified representation of the reality. Its aim is to help to better perceive the reality or to help to better achieve the objectives which have been set, and to predict the results of different solution which may be brought to real problems.

The model should simulate the variations in flow and pressure in the water supply pressurized pipe network. It should represent the dynamic operation of the pumping stations, valves, control valves and reservoirs. Engineers are using water supply modeling in two main areas, substantiating new infrastructure and day-to-day operational planning. A model is constructed to represent the hydraulic behavior of the real system and must be calibrated to ensure that the simulation represents the true operation of the real network.

Once this is achieved the modeler can try different improvements to the system without disturbing real customers or disrupting normal operations. Each scenario can be simulated and the best solution chosen for implementation. The model is also extremely useful in providing support in day-to-day operations for looking at contingency planning, operational maintenance and emergency situations such as firefighting and pollution management.

The construction of a model is a data intensive process and involves manipulating key asset data from a number of different sources. The latest generation modeling software has a number of advanced tools for making the job of building, calibrating and reporting much easier. By linking to Geographical Information Systems (GIS) it is possible to build the network model automatically from asset information held within it to reduce effort in constructing the network in the modeling software. Links to live data sources make the job of calibration much easier and model management enables the modeler to keep track of data sources, different model versions and the updating of live models. When choosing modeling software to undertake water supply network modeling one should consider the following:

- How well does it integrate with GIS systems such as ArcView or

MapInfo? - How fast and robust is the hydraulic simulation? - How quickly will I be able to construct my model and use it? - How will I be able to keep track of my data coming into the

model and then manage it? - How will I be able to keep my models up to date?


17

- What tools will be available to help me validate and verify my model?

- Is it able to be connected with external systems such as SCADA system?

The two major contradictory objectives of modeling and optimizing

the water supply systems are security of water supplying and minimizing the water production and transportation costs (Guhl, 1999). This is the role of the optimization tools. In order to achieve these two objectives optimization tools can be supported by tools that play essential roles in the management and optimization of water supply systems, these tools are (Figure 1.4):

1. Robust model, this depends mainly on the adopted modeling

software. 2. Calibration module. 3. Demand prediction module 4. SCADA system communication is essential in the process of the

optimization. In general, these four mainstays (Figure 1.4) represent the

fundamental elements in the management and optimization problem of water supply systems, and they constitute the core of this thesis and they will be described in details in the chapters coming later.

Figure 1.4 : Mainstays of optimization

To-Be System (Optimized)

As-Is System (Non Optimized) SCADA

Mod

elin

g T

ools

Cal

ibra

tion

Too

ls

Dem

and

Pred

icto

r

2. CHAPTER 2 : Thesis Problematic and Objectives

18

CHAPTER 2

2. Thesis Problematic and Objectives

2.1 Canal de Provence Company and needs for modeling tools As in any regional planning and management operation, it is very

important to implement technical solutions, to mobilize financial plans and to manage the operations of whole system while making profit of all the interventions and while bringing an effective assistant to the most fragile or most difficult zones. As many organizations charged to distribute water, the Canal de Provence Company (French: Société du Canal de Provence, SCP) attaches an increasing importance to the follow-up and the optimization of the operation of its works. This concern relates to the service quality as well as the reduction in the operating costs, maintenance and adaptation of the installations to the evolution of demand (Jean, 2003).

The operation and the hydraulic installations of the Canal de Provence were most important and especially most urgent to realize, it thus should have been made sure that the transport network systems would derive from the Verdon River only volumes necessary to the uses. Consequently, an effective control and regulation are essential to prevent that one does not fall into levels of weak operation and efficiency that waste the resources and generate excessive capital costs.

With the aim of better meeting what we have just presented above, SCP developed and installed, within the framework of its research program, a telemetry network connected to a host computer of supervision at the Control Central, named CGTC (French: Centre Général de Télé-Control), for the operation of the hydraulic works. This one collects and presents the data coming from many sensors of flows, pressures, operation of pumps and valves, disseminated on a wide perimeter. Measurements are filed and stored every fifteen minutes in the database of the supervisor and in the case of the principal hydraulic works ensure a monitoring and a control in real time (Dynamic Regulation).

The great number of information does not allow a permanent follow-up of the state of all the equipments from where SCP had to set up a module of automatic failures control to announce them to the operator. The software of supervision provides to other applications historical measurements that must be coherent the ones with the others. This


19

coherence is generally not respected because of the inaccuracy of the data. The purpose of the module of the measurements reconciliation (Canivet, 2002) is to bring practical solutions to these two problems. For obvious economic reasons, this network of telemetry is much less dense on the feeders and mains supply or distribution pipe networks that represent the majority of linear installations (approximately 5,000 km). However, the operating conditions for the whole are similar:

Continuous follow-up of the networks operation to detect, at the appropriate time, the abnormal operations or the incidents.

Operation optimization primarily from the economic perspective and security of system supplying. This function can be very complex when it applies to multiple works equipping the networks (closed meshes, pumping stations, tanks, turbine, etc.)

Choice of emergency operations to be carried out in case of incident so as to minimize their consequences.

Highlighting the evolution of demand to anticipate the saturation of the networks and to launch in time the reinforcement operations.

The use of numerical simulation models could bring, in theory, an

effective assistant but in practice they are complex when they are used in real-time operation, and are far from having all the necessary functionalities.

Regarding the networks modeling tools, SCP has basically three modeling and simulation softwares that it already used but of which two are today not really installed in an operational way:

o IRMA and RAMI : “House” software developed by SCP (France) o PICCOLO : developed by SAFÉGE (France) o FINESSE : developed by De Montfort University (UK).

The Engineering Division uses usually the “house” tools IRMA and

RAMI. This last allows the optimized dimensioning of the system of branching pipes. IRMA allows modeling all types of networks whose pipe’s diameters are known to check the pressures at the service points or the compensation of the demand by the tanks. IRMA and RAMI are dependent, RAMI is requested by IRMA to dimension the pipes whose diameters are to be defined. The large majority of the networks at SCP are today available under IRMA format files (*.irm).

About PICCOLO software, in spite of the fact that it is available in SCP, it seems that PICCOLO was never used in SCP to realize hydraulic simulation studies on any of its networks. PICCOLO was only used during two projects abroad that carried out on networks that are not operated by


20

SCP. Moreover, this version of PICCOLO is an Off-Line simulator, but the SAFÉGE has developed a new version with a module that allows link between PICCOLO and SCADA system. This version is not available at SCP.

However, feedback from the experience on its own particular case has led SCP to participate as a lead company in the European research and development project so-called WaterCIME (1995). Three years after, during another european project, which related to WaterCIME project, called “WaterMain” Water Management Integration (1998), in co-operation with De Montfort University (DMU – UK), SCP had installed set of software tools on the pilot site at the regional operating room of Trévaresse network at Saint Cannat. They were tried, tested and improved. These set of software tools constitute what was called “WaterMain platform”; and SCP started to test simulation software directly connected to its network of telemetry. The software in question is called FINESSE, acronym for “Fully Integrated Network Editing, Simulation and Scheduling Environment”. FINESSE was developed by DMU. This software is able to reach the data stored in the database of supervisor of the CGTC of SCP.

The innovation brought by this installation is the “On Line” networks simulation, and thus the possibility of connecting the simulation model with the supervision system making it possible to confront measurements in real-time and to use measurements to improve modeling and conversely to use simulation calculations to complete the information for the operators and to optimize the networks operation. After WaterMain; it was appeared that FINESSE is a tool that had its place rather in the CGTC in Tholonet than in a regional control room. The reasons relate mainly to the cost of installation (licenses, materials and time of installation) and to the qualification level necessary for the users, which remains relatively high. 2.2 Thesis objectives

Apart from the practical aspects related to the installation of these

softwares and to their integration with the telemetry systems at SCP, the use of their models raises a certain number of theoretical problems which are far from being taken into account or solved:

Possibility of calibrating of the hydraulic characteristics by simple but robust and sufficiently precise methods. This calibration must be taken again several times per season because of the possible evolution of the roughness of the pipes.

Observability of the system state (pressures and flows) from only


21

limited number of pressure and flow measurements, and the possibility of reconstituting of intermediate series of measures in space and in time.

Forecast of the water demand using historical demands information and evaluation of the precision and the reliability of these forecasts.

Optimization of the operating costs and ensuring the necessary service and the normal constraints of water supply service. Generally it is a question of minimizing the energy expenses but other criteria can be taken into account such as the limitation of the number of labors.

The available softwares mentioned previously are based on hydraulic

simulations and have modules able to offer with more or less precision some of these functionalities.

FINESSE, software of modeling and “On Line” and “Real Time” simulation is obviously not implemented in a really operational way because it does not arrive yet to its state of final maturation. Indeed, SCP maybe could be much interested in FINESSE as a tool that could be effective for daily use by the manager of the hydraulic works. A pump- turbine plant is considered and it is neither modeled nor optimized yet, thus it is the occasion to put to the test the software. Moreover, a collaboration agreement was signed with DMU for technical assistance during this research work and had allowed to more easily analyze the theoretical bases of FINESSE software and to possibly adapt its functionalities to the needs.

The objective of the thesis is thus to study the theoretical and practical problems related to the use of computer simulation models and softwares to optimize the operation of the pressurized water distribution and irrigation networks. The theoretical bases of these softwares will be analyzed, and the complementary modules necessary to their practical use will be developed to meet the needs listed and expressed by the services of networks operation. A particular SCP’s water supply network, called “Toulon Est”, was selected as our case-study where a development program is proposed upon the decision of SCP to improve safety and reliability of the water-supplying service for the eastern zone of the region of Toulon City. The program includes the construction of a reversible pump-turbine plant which will be installed close to a dam called Trapan, of 2 Mm3 in volume.

Thus, in this thesis we will highlight the problems of the optimization of the management of the “Toulon Est” hydraulic system and also Trapan dam and the future pump-turbine plant. Owning to the fact that this pump-turbine plant is not yet constructed its management and operation are still not completely well defined, and many questions rise concerning the following important points:


22

- The optimal scheduling and operation of the revisable pump, Trapan dams, and the water tanks.

- The volume of water that can be pumped and the volume of water that can be turbined.

- The pumping costs and the turbining returns. - When we have to pump and when we can turbine. - The influence on the water quality in the Trapan dam. - The eventual scenarios and hydraulics constrains.

2.3 Presentation of Canal de Provence Company (SCP) Three interdependent territorial communities created the Canal de

Provence Company (SCP) at the behest of the Ministry of Agriculture in 1957: The departments of “Le Var”, “Bouches-du-Rhône”, and “La Vallée de Marseille”. Sharing their rights of water, these communities commissioned to SCP to assure the hydraulic management and planning of the Provence Region, and particularly to conceive, to realize and to operate the Canal de Provence.

SCP is a mixed – semipublic – water company. Its capital of 3.7 million euros is today distributed between the following: Region of “Provence –Alpes – Côte d’Azur (PACA)”, Department of “Bouches-du-Rhône”, Department of “Le Var”, Department of “Vaucluse”, Department of “Alpes-de Haute-Provence et des Hautes-Alpes”, Marseille City, Farmers’ Associations and the Regional Fund of “ Crédit Agricole ” of the above five departments, the National Fund of “ Crédit Agricole ”, the “Deposit and Consignment Office” (Jean, 2003). At the request of the territorial communities concerned, by means of the state and of the region, SCP realized and continues to realize hydraulic managements for the Provence Region. These large-scale managements required the creation of more than 250 million cubic meters of stored reserves backs 7 dams. They implied the realization of 150 Km of subterranean galleries, 121 km of open canals, 34 large regulating structures, 14 civil engineering structures, 75 dams, 580 km of transporting pipelines, 4,200 km of distributing pipelines, 83 pumping stations and boosters, 212 stations of remote transmission, more than 52,000 points of consumption. The Canal de Provence was able to divert high quality water from Verdon River thanks to the hydroelectric management of Durance River and Verdon River realized by France’s Electricity Company (French: Électricité De France, EDF). It will eventually allow the irrigation of 60,000 hectares, which is more than third of the cultivated zones of the concerned region. It supplies more than 500 industrial enterprises, and supplies to hundred of municipalities in “Bouches-du-Rhône” and “Le Var” either drinking water,


23

or a raw water requiring only elementary treatments. The structures of the Canal de Provence can be classified in two groups:

- Main structures including the main canal and four branches that

drive the water since Verdon River towards La Provence and the coastal zone. Flow of water is driven by gravity and the discharges decrease from 40 to 10 m3 /s.

- Secondary installations (or pressurized distribution networks) that include 580 km of pipes between 500 and 1,300 mm in diameter, and 420 km secondary pipes of diameter lower than 500 mm. In harmony with its philosophy, the strategy of SCP, its project, its

quality assurance approach and its system of environmental management, aim to reconcile satisfaction of the customer, respect for the environment and to assure a strict financial balance. Expertise acquired by SCP has allowed it to promote engineering products adapted to the necessities of the public or private specialists of planning and management. Not less than thirty disciplines are represented at SCP: from hydraulics to landscaped architecture, from electronics to agronomy, from civil engineering to microbiology, from geology to land expertise.

On the occasion of its researches and its achievements, SCP established a wide network of French and foreign partners: research or financial organisms, specialized research departments, and big companies. SCP intervened mainly in several countries: Albania, Algeria, Saudi Arabia, Bolivia, Cameroon, China, Egypt, the United States, Greece, India, Iraq, Morocco, Oman, Tunisia, Jordan, etc.

From its creation, SCP dedicated huge efforts in the development researches, particularly in the methods of calculation and operation of hydraulic works and facilities. It led, in the 60s, in major innovations, today adopted all over the world. It is notably about the “Dynamic Regulation” system of Canal de Provence, and optimization methods of the pressurized irrigation networks. The activities of research and development concern today all the domains of competence and intervention of SCP. In most of cases, researches are realized in association with specialized partners; universities and schools, public researches centers, other regional management companies and societies, big public and private companies, research departments. This thesis comes within the framework of the research programs of SCP.


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Figure 2.1 : General view of Canal de Provence


25

2.4 Presentation of the “Toulon Est” water supply network The present study is concerned with one of the SCP’s water

networks constituting the water supply system “Les Laures - Trapan - La Môle” composed of the main supply pipe of the same name and the sets of the derived storage tanks, the unit being commonly called “Toulon Est” (Figure 2.2).

Figure 2.2 : General view of “Toulon Est” water supply network (CGTC-SCADA interface)

2.5 Description of the existing hydraulic system of “Toulon East”

The zone covered by this study understands the whole hydraulic infrastructures, main pipelines and tanks, located downstream from the divisor of “Les Laures” to the outlet of the Valaury gallery, to the supply point of La Môle (Engineering Division-SCP, 2002).

a) “Les Laures” divisor –(Point A) It is an impact block dissipator linking the network to the extremity

of the “Toulon Est” branch of Canal de Provence (Figure 2.3). The water withdrawal from the Canal is carried out through a pressurized gallery and then it derived by a 1,000-mm pipe provided with a butterfly control valve. Two parallels pipes (one is 400 mm, the other is 1,000 mm) equipped with modern electromagnetic flowmeters are linked to the 1,000-mm pipe. This dissipator consists of a basin equipped with a shut-off floating diaphragm

Point A Z= 295.0 m

Point C Z=98.0 m

Point F Z=30.7 m

Point G Z=17.0 m

Point M Z= 35.0 m

Point T Z=75.0 m

Point H Z=6.8 m

Les Laures

Trapan

La MôlePierrascas Fenouillet

Mont Redon

Golf Hôtel


26

(800 mm). An automatic filter extends the basin and retains the suspended particles greater than 2 mm. This work is connected to the main pipeline by a penstock (1,250 mm). The whole of this dissipator is bypassed by 1,250-mm pipe at the beginning and then 600-mm pipe on which is mounted a pressure regulator. The theoretical maximum flow available at the end of the gallery is 10 m3/s at altitude of 295 m above mean see level (French: Nivellement Général de la France, NGF). However the dissipator actual flow is about 3.5 m3/s (maximum). The highest water level of the basin is 295 m NGF, and the lowest water level is 293 m NGF.

Figure 2.3 : Point A – Les Laures

b) “Les Laures – La Môle” main water supply pipeline The “Toulon Est” system is structured around the main pipeline “Les

Laures – La Môle”. This feeder, approximately 43 km in length, can be divided into two sections (Figure 2.2):

- Section N° 1 “Les Laures – Trapan” is 26 km in length, was installed in 1976. It consists of 1,000-mm pipe 7 km in length, 900-mm pipe 7 km in length, and 700-mm pipe 12 km in length. This section extends from the dissipator until the Trapan dam. It supplies the Trapan dam, various irrigation networks, and five submain pipes.

- Section N° 2 “Trapan – La Môle” is 700-mm pipe in 17 km length,

and was installed in 1978. It is an extension of the preceding section to the supply point of La Môle. It supplies some irrigation networks upstream the dissipator at Gratteloup and ends in the downstream at the level of La Môle. From this point departs a pipe to the supply point of the Water Distributing Association of La Corniche des Maures (French: Syndicat Intercommunal de Distribution d’Eau de la Corniche des Maures, SIDECM), and the suction manifold of the small booster of La Môle, which supplies the network of La Verne.

Dissipator

By-Pass

Divisor


27

c) Submain water supply pipelines

The submain pipelines all have the same architecture: control apparatus at the head to the right of the connection point, connecting pipe to a water tank, tank with shut-off floating diaphragm from where departs a supply pipe for the irrigation networks. Characteristics of the submain pipelines are summarized in Table 2.1:

Table 2.1 : Characteristics of the submain pipelines

Water Tank Submain Extension pipe Elevation

(m NGF) Volume

(m3) Pierrascas 1,790 m - 700 mm 194.2 5,500 Fenouillet 2,080 m - 600 mm 215.3 5,400

Mont Redon 1,014 m - 400 mm 180.9 3,900 Golf Hôtel 1,350 m - 700 mm 171.2 7,500

Figure 2.4 : Point C – Pierrascas tank

Figure 2.5 : Point F – Fenouillet tank


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Figure 2.6 : Point G – Mont Redon tank

Figure 2.7 : Point H – Golf Hôtel tank

Figure 2.8 : Point M – La Môle


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Cumulated distance (km)

Elev

atio

n (

m N

GF)

Les Laures Dissipator (295 m NGF) Figure 2.9 : Hydraulic profile of Toulon Est network


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d) Trapan dam The Trapan dam, located at the south-west of the communes of

Bormes Les Mimosas, was constructed with an aim of supplementing the water supply to the eastern zone of Toulon City. The construction of Trapan dam and its operation were confided to SCP in February 1965. The first commissioning of this dam took place in 1968. This dam allows accumulating, in winter, about 2 Mm3 of water which are available to satisfy the water demand during the peak period. The feeding of Trapan dam is mixed, on the one hand the water delivered from “Toulon Est” network coming from the Verdon River; on the other hand the surface water coming from the surface runoff of the catchment area of the small stream of La Pellegrin upstream of the dam. This dam has two principal functions, after potabilization by Water and Ozone Company (French: Compagnie d’Eau et d’Ozone, CEO) downstream the dam, part of the potabilized water is distributed during the summer period of high consumption to the urban district of the nearby shoreline, and it can be also used for the load shedding of the basins of the Canal de Provence; when necessary.

Figure 2.10 : Point T – Trapan dam Trapan dam, in its current operating mode, is a static dam. The

concern of the water quality control rises from this operating mode. The information feedbacks concerning the water quality come from the CEO. CEO carries out physicochemical controls of the water which delivered to the CEO from the dam for potabilization. The problems punctually encountered during the summer period relate to the water temperature sometimes very high near the surface, and a high concentration of Manganese, Iron and Ammonium near the bottom in summer. The operator switch the supply of the CEO directly from the feeder “Les Laures – La Môle” if a water quality problem is detected at the CEO supply point from the dam.


31

In practice the dam useful volume is less than 2 Mm3 because of the deposits at the bottom of the dam and the water quality problems. However the operator points out that in case of emergency water supply, the low water level to be considered is 45 m (1.8 Mm3 useful volume). The existing management of the dam is very simple; the only operating constraint is to start the peak demand season with a full reserve, to limit the water quality problems related to the temperature as mentioned above. For that the filling of Trapan starts in February and spreads out until May.

The dam feeding setup from the main pipeline consists of a dissipator equipped with a shut-off floating diaphragm. The exit of the dissipator is double and makes it possible to supply either the dam from the bottom, or directly supplying the CEO in case of accidental pollution or insufficient water quality of Trapan. The maximum theoretical flow of this work is of 600 l/s. 2.6 Operation and hydraulic management

The hydraulic management of “Toulon Est” system remained of

passive type, without real dynamic control of storage volumes available in the five tanks. Their filling is controlled from the downstream by means of a shut-off floating diaphragm. Their filling flow is determined by the pressure valve downstream the corresponding pressure reducing valve, which ensures also the reduction of the maximum service pressure. Generally, it appears that the tanks are requested very little in their function of demand compensation and that they are maintained full permanently, even during the peak periods of water demand.

Until recently, the hydraulic system of “Toulon Est” was far from saturation because the emergency water supply contract of the SIDECM had been considerably decreased in January 2000. However, the exceptional climatic condition at the end of the year 2001 and at the beginning of the year 2002 led the SIDECM to subscribe an increase in its urban contract to 410 l/s. The totality of this flow was actually mobilized during the peak season of 2002.

A dynamic simulation during peak period showed that this increase in water supply contract would have brought up the water demand to a level close to saturation what would have resulted in a theoretical pressure insufficient at Le Col Gratteloup point during the peak period. A dynamic control of Golf Hôtel tank was therefore set up. The principle is such that filling the tank during off-peak hours and emptying it during peak hours so that the instantaneous demand at the head of the network stays almost close to its continuous average flow.


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2.7 Water demand of the zone “Toulon Est” Globally, the annual volume introduced into the zone of “Toulon

Est” is relatively stable, close to 16 to 17 Mm3 during last years, of which 98% are provided by the Canal de Provence from the divisor of “Les Laures”, and 2% by the sources of Carnoules. An important part of the introduced volumes is not counted (more than 30%). In order to identify the source of these losses the Maintenance Division replaced the flowmeters in the network. The demand can be characterized by type of use:

a) Industrial demand: is very small, it represents approximately 1% of the total demand. Only one customer of this type exists in the zone of “Toulon Est” that is La Varoise Distillery Company concerning a supply of 10 l/s during normal use.

b) Urban demand: it represents approximately 18% of the mobilized

annual volume. The supply is mainly concerned with raw water, except for the commune of Cures and the Naval-Air Base de Cures Pierrefeu to which drinking water is delivered.

c) Irrigation agricultural and nonagricultural demand and diverse

water use: is very significant since it represents nearly 50% of the total demand. The zone “Toulon Est” supplies around twenty irrigation networks, for a total subscribed surface of 6,525 hectares in 2000. These networks all almost derive water from branches on the main pipeline. A small number of them are supplied directly from the main pipeline “Les Laures – la Môle”. These networks gather various types of water use characterized as follow:

- Agricultural irrigation, it concerns mainly water supply for a greenhouse growers. This type of user requires a flow throughout the year. Thus, even in winter, there is a significant irrigation flow.

- Nonagricultural Irrigation, for watering mainly the green areas. - Diverse uses, for the other uses (domestic water supply, swimming

pool, …).

According to the annual report published by the maintenance staff concerning the efficiency of the networks, it is possible to know the overall distribution of billed volumes between the various uses as well as the demand interannual variations.

The low number of operational flowmeters in the zone of “Toulon Est” constrained us to approach the daily demand of the irrigation and diverse uses networks.


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2.8 Development program of the zone “Toulon Est” The general study of the hydraulic operation and the development

program of the zone of “Toulon Est” has as principal objective of maintaining water supply of the customers located between the divisor of Les Laures and the Trapan dam in the case of unavailability of water from Les Laures or in the case of burst on the main pipeline between Les Laures and Trapan. The development program considers the construction of reversible pump-turbine plant at Trapan and of a new water tank to be built at Le Col Gratteloup.

- Reversible pump-turbine station of Trapan dam

According to the development program of “Toulon Est”, the station

had been proposed following the decision of SCP to improve safety and reliability of the water-supplying service for the eastern zone of the region of Toulon City. The primary objective is to maintain the possibility of supplying the priority customers in the case of unavailability of water from Les Laures or in the case of pipe bursting on the main pipeline between Les Laures and Trapan making out of service the infrastructures of the Canal de Provence upstream of the divisor of Les Laures for a long time. The second objective is to generate electrical energy by the possibility of equipping the station with a reversible pump-turbine unit.

- New water tank at Le Col Gratteloup

It is proposed to build a new tank at Le Col Gratteloup that will

come to supplement the five tanks available on the main pipeline of “Toulon Est”. Its function is to contribute in the increase in the available system flow and in association with the future pumping station. In addition, it will make it possible to maximize the potential net income of the electrical energy production. The size of this tank will depend on the requested objective concerning the safety level and energy income. It will be at least of 5,000 m3 for a minimal safety objective and to optimize the operation of the unit as turbine, and it will be to the maximum of 20,000 m3 to maximize the energy income and to increase the safety level.

The operations of the future reversible pumping station of Trapan and proposals, scenarios, and options will be presented and studied later in Chapter 10.

3. CHAPTER 3 : Water Distribution Network System Hydraulics and Modeling

34

CHAPTER 3

3. Water Distribution Network System Hydraulics and Modeling

3.1 Anatomy of water distribution network system Although the size and complexity of water distribution systems vary

dramatically, they all have the same basic purpose; to deliver water from the source (or treatment facility) to the customer.

3.1.1 Source of water

Untreated water (also called raw water) may come from groundwater

sources or surface waters such as lakes, reservoirs, and rivers. The raw water is usually transported to a water treatment plant, where it is processed to produce treated water (also known as potable or finished water). The degree to which the raw water is processed to achieve potability depends on the characteristics of the raw water, relevant drinking water standards, treatment processes used, and the characteristics of the distribution system. In the case of groundwater, many sources offer up consistently high quality water that could be consumed without disinfection.

3.1.2 Customers of water

Customers of a water supply system are easily identified - they are

the reason that the system exists in the first place. Homeowners, factories, hospitals, restaurants, golf courses, and thousands of other types of customers depend on water systems to provide everything from safe drinking water to irrigation. Customers and the nature in which they use water are the driving mechanism behind how a water distribution system behaves (Babbitt, 1931). Water use can vary over time in the long-term, medium-term, and the short-term, and over space. Good knowledge of how water use is distributed across the system is critical to accurate modeling.


35

3.1.3 Transport facilities Moving water from the source to the customer requires a network of

pipes, pumps, valves, and other appurtenances. Storing water to accommodate fluctuations in demand due to varying rates of usage or fire protection needs requires storage facilities such as tanks and reservoirs. Piping, storage, and the supporting infrastructure are together referred to as the water distribution system (WDS).

This system of piping is often categorized into transmission/trunk mains and distribution mains. Transmission mains consist of components that are designed to convey large amounts of water over great distances, typically between major facilities within the system. For example, a transmission main may be used to transport water from a treatment facility to storage tanks throughout several cities and towns. Individual customers are usually not served from transmission mains.

Distribution mains are an intermediate step toward delivering water to the end customers. Distribution mains are smaller in diameter than transmission mains, and typically follow the general topology and alignment of the city streets. Elbows, tees, wyes, crosses, and numerous other fittings are used to connect and redirect sections of pipe. Fire hydrants, isolation valves, control valves, blow-offs, and other maintenance and operational appurtenances are frequently connected directly to the distribution mains. Services, also called service lines, transmit the water from the distribution mains to the end customers. Homes, businesses, and industries have their own internal plumbing systems to transport water to sinks, washing machines, and so forth. Typically, the internal plumbing of a customer is not included in a WDS model; however, in some cases, such as sprinkler systems, internal plumbing may be modeled.

3.1.4 System configurations

Transmission and distribution systems can be either looped or

branched, as shown in Figure 3.1. As the name suggests, in looped systems there may be several different paths that the water can follow to get from the source to a particular customer. In a branched system, also called a tree or dendritic system, the water has only one possible path from the source to a customer.

Looped systems are generally more desirable than branched systems because, coupled with sufficient valving, they can provide an additional level of reliability. For example, consider a main break occurring near the reservoir in each system depicted in Figure 3.2. In the looped system, that break can be isolated and repaired with little impact on customers outside of that immediate area. In the branched system, however, all the customers


36

downstream from the break will have their water service interrupted until the repairs are finished. Another advantage of a looped configuration is that, because there is more than one path for water to reach the user, the velocities will be lower, and system capacity greater.

Most water supply systems are a complex combination of loops and branches, with a trade-off between loops for reliability (redundancy) and branches for infrastructure cost savings (Walski, 2004).

Figure 3.1 : Looped and branched networks

Figure 3.2 : Looped and branched networks after network failure


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3.1.5 Solving network problems Real water distribution systems do not consist of a single pipe and

cannot be described by a single set of continuity and energy equations. Instead, one continuity equation must be developed for each node in the system, and one energy equation must be developed for each pipe (or loop), depending on the method used. For real systems, these equations can number in the thousands.

The first systematic approach for solving these equations was developed by Hardy Cross (1936). The invention of digital computers, however, allowed more powerful numerical techniques to be developed. These techniques set up and solve the system of equations describing the hydraulics of the network in matrix form. Because the energy equations are nonlinear in terms of flow and head, they cannot be solved directly. Instead, these techniques estimate a solution and then iteratively improve it until the difference between solutions falls within a specified tolerance. At this point, the hydraulic equations are considered solved. Some of the methods used in network analysis are described in (Bhave, 1991), (Lansey, 2000), and (Todini, 1987). Chapter 5 of this thesis is devoted for the methods for solving water pipe networks problem.

3.2 Water distribution network system simulation The term simulation generally refers to the process of imitating the

behavior of one system through the functions of another. Here, the term simulation refers to the process of using a mathematical representation of the real system, called a model. Network simulations, which replicate the dynamics of an existing or proposed system, are commonly performed when it is not practical for the real system to be directly subjected to experimentation, or for evaluating a system before it is actually built (Ulanicki, 2001). In addition, for situations in which water quality is an issue directly testing a system may be costly and a potentially hazardous risk to public health.

Simulations can be used to predict system responses to events under a wide range of conditions without disrupting the actual system. Using simulations, problems can be anticipated in proposed or existing systems, and solutions can be evaluated before time, money, and materials are invested in a real-world project. For example, a water utility might want to verify that a new subdivision can be provided with enough water to fight a fire without compromising the level of service to existing customers. The system could be built and tested directly, but if any problems were to be discovered, the cost of correction would be enormous. Regardless of


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project size, model-based simulation can provide valuable information to assist an engineer in making well-informed decisions (Fishwick, 1995).

Simulations can either be steady-state or extended-period. Steady-state simulations represent a snapshot in time and are used to determine the operating behavior of a system under static conditions. This type of analysis can be useful in determining the short-term effect of fire flows or average demand conditions on the system. Extended- period simulations (EPS) are used to evaluate system performance over time. This type of analysis allows the user to model tanks filling and draining, regulating valves opening and closing, and pressures and flow rates changing throughout the system in response to varying demand conditions and automatic control strategies formulated by the modeler.

Modern simulation software packages use a Graphical User Interface (GUI) that makes it easier to create models and visualize the results of simulations. Older-generation software relied exclusively on tabular input and output.

3.3 Water distribution network system modeling Today, water distribution modeling is a critical part of designing and

operating water distribution systems that are capable of serving communities reliably, efficiently, and safely, both now and in the future (Male, 1990). The availability of increasingly sophisticated and accessible models allows these goals to be realized more fully than ever before.

This part is an introduction to water distribution modeling by giving an overview of the basic distribution system modeling, defining the nature and purposes of distribution system models, and outlining the basic steps in the modeling process.

3.3.1 Application of models

Most Water Distribution Models (WDMs) can be used to analyze a

variety of other pressure piping systems, such as industrial cooling systems, oil pipelines, or any network carrying an incompressible, single-phase, Newtonian fluid in full pipes. Municipal water utilities, however, are by far the most common application of these models (Cesario, 1991). Models are especially important for WDSs due to their complex topology, frequent growth and change. It is not uncommon for a system to supply hundreds of thousands of people (large networks supply millions); thus, the potential impact of a utility decision can be tremendous. In general terms the problem area could be related to operational, planning or legislative requirements and more recently to water quality management. An overview


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of problem types in water supply systems, which could be analyzed by using the hydraulic network models are presented in Table 3.1 (Pilipovic, 2004).

Table 3.1 : Types of problems that could be analyzed by modeling

Domain Possible Problem Developing and understanding of how the system operates Training water system operators Assessing the level of service Assessing the carrying capacity of the existing system Assessing the efficiency of current operational management policy Assessing levels of pressures at critical points within the system Identifying and resolving operational anomalies – closed valves Low pressure or high pressure fluctuation problems Low fire flow at hydrants - if it is different from expected capacity Daily operational use - shutting down a section of the system due to major breaks Power outage – impact on pump stations Sizing control points – subsystem metering, control valves – PRV, PSV, FCV Sizing sprinkler systems – fire service and other Assessing the available range of pressure at customer connections

Operational Management

Real time control of the system Identifying the impact of future population growth on the existing system Identifying the impact of major new industrial or commercial developments on the existing system Identifying key bottlenecks in current and future systems Designing the reinforcement to the existing system to meet future demand Designing the new distribution system Optimizing the capital works programs Assessing the new resource option Assessing the effects of rehabilitation techniques Leak control – Reducing losses by lowering maximum pressure Demand management – Reducing the pressure related demand by lowering service pressure Sizing elements of the system to meet fire service requirements in existing and future systems Assessing the value and design of distribution monitoring systems – Telemetry, Data Loggers

Planning

Contingency planning – Answering “ what if “ questions on major outages Long Term Council Community Plan (LTCCP) and Water Assessments – Assessing levels of service, Regulatory levels of service reporting, and options for future planning based on community consultations Public Health - Maintaining levels of residual Free Available Chlorine (FAC) within predefined values. Assessing the financial contribution required for new developments

Legislative

Fire Service Code of Practice – Water and pressure requirements for fire fighting purposes Disinfectant residual assessments - levels of FAC throughout the system Substance tracking, determination of age of water, water blending from various sources Distribution Systems Flushing - velocity and flow assessments, sedimentation trends

Water Quality

Analyzing water quality contamination events


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3.3.2 Modeling process Development and use of water distribution models comprises of

many activities and processes. As with any such complex task, it can be managed more successfully and efficiently if it is broken down into its components or stages. The process is common for almost any such type of project, regardless of the size of the system and it could be divided into eight characteristic stages, namely:

1. Setting up a new modeling project or Re-establishing the

existing, 2. Data Collection, Model Build (or Model Update), 3. Data Verification and Model testing, 4. Model Calibration and Validation, 5. Model Use, 6. Results Interpretation, 7. Reports and model documentation, 8. Change monitoring and model management.

Some tasks can be done in parallel while others must be done in

series. The first step in undertaking any modeling project is to develop a consensus within the water utility regarding the need for the model and the purposes for which the model will be used in both the short- and long-term. It is important to have utility personnel, from upper management and engineering to operations and maintenance, commit to the model in terms of human resources, time, and funding. Modeling should not be viewed as an isolated endeavor by a single modeler, but rather a utility-wide effort with the modeler as the key worker (Cesario, 1995). After the vision of the model has been accepted by the utility, decisions on such issues as extent of model simplification and accuracy of calibration will naturally follow.

Most of the work in modeling must be done before the model can be used to solve real problems. Therefore, it is important to budget sufficient time to use the model once it has been developed and calibrated. Too many modeling projects fall short of their goals for usage because the model-building process takes up all of the allotted time and resources. There is not enough time left to use the model to understand the full range of alternative solutions to the problems (Walski, 2003).

Modeling involves a series of abstractions. First, the real pipes and pumps in the system are represented in maps and drawings of those facilities. Then, the maps are converted to a model that represents the facilities as links and nodes. Another layer of abstraction is introduced as the behaviors of the links and nodes are described mathematically. The model equations are then solved, and the solutions are typically displayed


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on maps of the system or as tabular output. A model’s value stems from the usefulness of these abstractions in facilitating efficient design of system improvements or better operation of an existing system.

Before building a model, it is necessary to gather information describing the network. Many potential sources are available for obtaining the data required to generate a water distribution model, and the availability of these sources varies dramatically from utility to utility. Some of the most commonly used resources, including system maps, as-built drawings, and electronic data files. There are three types of data essential for assembling a water distribution model as outlined in Table 3.2 , Table 3.3 and Table 3.4. These are network data, water demand data, and operational data.

The most fundamental data requirement is to have an accurate representation of the network topology, which details what the elements are and how they are interconnected. If a model does not faithfully duplicate real-world layout (for example, the model pipe connects two nodes that are not really connected), then the model will never accurately describe real-world performance, regardless of the quality of the remaining data (Pilipovic, 2004).

Because models may contain tens of thousands of elements, naming conventions are an important consideration in making the relationship between real-world components and model elements as obvious as possible. Naming conventions should mirror the way the modeler thinks about the particular network by using a mixture of prefixes, suffixes, numbers, and descriptive text.

The following should be noted in the management of the modeling process (Cesario, 1995):

The key decision which must be made at the very start of the

process is whether or not to use the hydraulic network modeling software as the right tool for providing answers to problems faced in managing water distribution systems.

If a hydraulic network model is the right tool, running the water distribution-modeling project is an ongoing activity, which needs regular model updating and checking if the existing model is still an adequate tool for providing answers to actual requirements.

The process of the management of the modeling process inherently has many loops and feedbacks from previous steps.

One of the key characteristics of the process is that these feedbacks make the modeling work an iterative process; not linear as it was traditionally presented.

The modeling process should be considered as a process closely linked to other corporate systems, not as an isolated activity. The model’s output provides input and support to many strategic


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Water Utilities programs or policies, and the model requires strong linkages with GIS, Telemetry, Water billing and other corporate systems.

The process requires at various stages, agreements with involved parties, on reached decisions about the quality of completed work at certain project stages and recommendations prior to commencement of the next stage. Supervision of the project should be continuously run from the beginning of the process by preferably one party based more on a working relationship than on traditional audit control approach.

Depending on the size of the distribution systems, models can vary from very simple - with only one water source and a small network, up to very complex systems with multiple sources and sophisticated operation regimes. Although the level of complexity in managing a modeling project varies with the size and complexity of a particular system the principles of the modeling process remain the same.

Table 3.2 : Network Data

Data Detail Source Nodes

Number or name Coordinates, Elevation Type – Network junctions or end points, source of water

GIS, As-built plans, Operational staff

Pipelines

Initial node, end node Diameter – nominal or internal Length, Material, Construction year Pipe roughness, Minor loss coefficients Water Quality – Reaction rate coefficients: bulk and wall.

GIS, As-built plans, Operational staff Design standards, recommendations, hydraulic textbook Design standards, recommendations, hydraulic textbook

Valves and control equipment

Initial Node, end node Diameter, Length, Roughness coefficients Type – Throttled, NRV, PRV, PSV, PCV, TCV, FCV.

GIS, Control valve database As-built plans

Pumping stations

Initial node end node Diameter of suction and delivery pipe Number or pump, name, pump type Pump delivery rate, delivery head, power Rotating speed, number of stage, efficiency Pump characteristic “Q – H – P curve”, protections Type – Fixed or variable speed pumps

GIS Pump station database As-built plans

Reservoirs

Number or reservoir name Shape and volume Inflow and outflow pipes arrangements Type – Storages, Water Towers

GIS , Reservoir database As – built plans

Zones Boundary

Zone or sub zones boundary lines GIS, Contour plans


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Table 3.3 : Demand Data

Data Detail Source Existing demand

Yearly average or base consumption Type of consumer Level of water losses

Water Billing System, Sub meter readings Water Balance Sheet Minimum Night Flow

Spatial Allocation

Location of water meters or water users Water Billing System, GIS

Time varying factors

Daily and hourly peaking factors Diurnal curves – Patterns of water use

Telemetry or data loggers Typical patterns

Future demand Projected future demand and its allocation Water Utility or regional planning documents

Table 3.4 : Operational Data

Data Detail Source Source node Hydraulic Grade Line

Initial Water Quality, Baseline concentrations and patterns Operational staff

Pump Station Pump’s operational regimes – setting points: pressure at node, water level at reservoir, time

Operational staff SCADA

Reservoirs Water levels ranges – lower and upper operational limits Operational staff, SCADA

Control Valves Control regimes, control points, trigger values, throttled valves Operational staff SCADA

Zone valves Locations of permanently closed valves Operational staff, GIS

3.3.3 Network model elements

Water distribution models have many types of nodal elements,

including junction nodes where pipes connect, storage tank and reservoir nodes, pump nodes, and control valve nodes. Models use link elements to describe the pipes connecting these nodes. Also, elements such as valves and pumps are sometimes classified as links rather than nodes. Table 3.5 lists each model element, the type of element used to represent it in the model, and the primary modeling purpose.

Table 3.5 : Common network modeling elements

Element Type Primary Modeling Purpose

Reservoir Node Provides water to the system

Tank Node Stores excess water within the system and releases that water at times of high usage

Junction Node Removes (demand) or adds (inflow) water from/to the system

Pipe Link Conveys water from one node to another

Pump Node or link Raises the hydraulic grade to overcome elevation differences and friction losses

Control Valve Node or link Controls flow or pressure in the system based on specified criteria


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3.3.4 Water quality modeling Water quality modeling is a direct extension of hydraulic network

modeling and can be used to perform many useful analyses (Rossman, 1996). Developers of hydraulic network simulation models recognized the potential for water quality analysis and began adding water quality calculation features to their models in the mid 1980s. Transport, mixing, and decay are the fundamental physical and chemical processes typically represented in water quality models. Water quality simulations also use the network hydraulic solution as part of their computations. Flow rates in pipes and the flow paths that define how water travels through the network are used to determine mixing, residence times, and other hydraulic characteristics affecting disinfectant transport and decay. The results of an extended period hydraulic simulation can be used as a starting point in performing a water quality analysis.

The equations describing transport through pipes, mixing at nodes, chemical formation and decay reactions, and storage and mixing in tanks are adapted from Grayman, Rossman, and Geldreich (Grayman, 2000). The water quality modeling will not be approached in this research.

3.3.5 Model simplification (skeletonisation)

Model Simplification (or Skeletonization) is the process of selecting

for inclusion in the model only the parts of the hydraulic network that have a significant impact on the behavior of the system. Attempting to include each individual service connection, gate valve, and every other component of a large system in a model could be a huge undertaking without a significant impact on the model results. Capturing every feature of a system would also result in tremendous amounts of data, enough to make managing, using, and trouble-shooting the model a difficult and error-prone task. Simplification is a more practical approach to modeling that allows the modeler to produce reliable, accurate results without investing unnecessary time and money (Ulanicki, 1996).

Eggener and Polkowski (Eggener, 1976) did the first study of simplification when they systematically removed pipes from a model of Menomonie, Wisconsin, to test the sensitivity of model results. They found that under normal demands, they could remove a large number of pipes and still not affect pressure significantly. Shamir and Hamberg (Shamir 1988a, 1988b) investigated rigorous rules for reducing the size of models.

Simplification should not be confused with the omission of data. The portions of the system that are not modeled during the simplification process are not discarded; rather, their effects are accounted for within parts of the system that are included in the model.


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The network model simplification problem can be expressed as in the following statement: Find a hydraulic model of a network with a reduced number of components, which approximates the mapping between the input and output variables over a wide range of operating conditions, where: Input variables are: source inflows, source heads, demands, pump schedules and initial reservoir levels, and output variables are: flows in pipes and heads at nodes over a time horizon (Ulanicki, 1996).

The reduced model should preserve the non-linearity of the original network and approximate its operation accurately under different conditions. It is expected that the relationships between heads and demands are similar in both the full and reduced models. There are three common approaches to model simplification: element by element, variable elimination, and approximation.

The element by element method includes two activities: skeletonisation of the structure and the use of equivalent pipes in place of numbers of pipes connected in parallel and/or in series. The skeletonisation technique eliminates pipes of a small diameter leaving only major pipes in the model. At the same time demands fed by smaller pipes are aggregated and allocated to the nearest upstream node of a major pipe.

Variable elimination is based on a mathematical formalism. A pipe network mathematical model is a system of simultaneous algebraic equations. Some of variables (flows and heads) can be eliminated from these equations using an algorithm, thus reducing the size of a model. The FINESSE simplifier is based on a Gaussian elimination procedure (Ulanicki, 1996).

Approximation is a method based on an estimation technique where an arbitrary topology of a simplified model is assumed where the simplified model includes all reservoirs and all pressure control nodes. The technique calculates parameters of pipes (resistance) and the distribution of the demand (demand factor) minimizing the difference of the behavior of a simplified model and network measurements.

3.3.6 Model calibration

Even though the required data have been collected and entered into a

hydraulic simulation software package, the modeler cannot assume that the model is an accurate mathematical representation of the system (Ormsbee, 1997). The hydraulic simulation software simply solves the equations of continuity and energy using the supplied data; thus, the quality of the data will dictate the quality of the results. The accuracy of a hydraulic model depends on how well it has been calibrated, so a calibration analysis should always be performed before a model is used for decision-making purposes. The calibration process will be discussed in details in Chapter 7.


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3.3.7 Model maintenance Once a water distribution model is constructed and calibrated, it can

be modified to simulate and predict system behavior under a range of conditions. The model represents a significant investment on the part of the utility, and that investment should be maximized by carefully maintaining the model for use well into the future (Basford, 1995).

The user needs to periodically update the model file so that installed piping is accurately distinguished from proposed facilities, and that facilities that will most likely never be installed are removed from the model. The modeler also needs to be in regular contact with operations personnel to determine when new piping is placed into service. Note that there may be a substantial lag between the time that a pipe or other facility is placed into service, and the time that facility shows up in the system map. The version of the model used for operational studies should not be updated until the facilities are actually placed into service.

3.4 Network water consumption The consumption or use of water, also known as water demand, is

the driving force behind the hydraulic dynamics occurring in water distribution systems. Anywhere that water can leave the system represents a point of consumption, including a customer’s faucet, a leaky main, or an open fire hydrant.

Three questions related to water consumption must be answered when building a hydraulic model: (1) How much water is being used? (2) Where are the points of consumption located? and (3) How does the usage change as a function of time?.

Water distribution models are created not only to solve the problems of today, but also to prevent problems in the future (Cesario, 1991). With almost any endeavor, the future holds a lot of uncertainty, and demand prediction is no exception. Long-range planning may include the analysis of a system for 5, 10, and 20-year time frames. When performing long-term planning analyses, estimating future demands is an important factor influencing the quality of information provided by the model.

The uncertainty of this process puts the modeler in the difficult position of trying to predict the future. The complexity of such analyses, however, can be reduced to some extent with software that supports such analysis. The demand prediction will be discussed in details in Chapter 8.


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3.5 Network system security The security of water systems has long been a concern in the water

industry. The potential for natural, accidental, and purposeful contamination or other events that would hinder the ability of the system to provide a safe water supply has been the subject of many studies (Walski, 2003). Because water systems are spatially diverse (see Figure 3.3), they are inherently vulnerable to a variety of activities that can compromise the system’s ability to reliably deliver sufficient water at an acceptable level of quality. There are several areas of vulnerability as water travels to the customer. These areas include (1) the raw water source (surface or groundwater); (2) raw water canals and pipelines; (3) raw water reservoirs; (4) the treatment facilities; (5) connections to the distribution system pipes; (6) pump stations and valves; and (7) finished water tanks and reservoirs. Each of these system elements presents unique challenges to the water utility in safeguarding the water supply. These challenges include:

• Physical disruption that prevents sufficient water flow at an

acceptable pressure to all customers. • Contamination of the water delivered to the customer by a

chemical or biological agent such that the product is not safe to use or is not of an acceptable quality to the customer.

• Loss of confidence by customers in the ability of the water utility to deliver a safe and secure water supply.

Figure 3.3 : Major points of vulnerability in a water supply system Simulation models can be used in vulnerability studies to help a

water utility understand how their system will respond to an accidental or purposeful physical or chemical event. This understanding can be used to identify the consequences of such events, to test solutions to minimize the


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impacts of the events, or to learn how to respond if such events occur. Models are representations of systems that are especially effective in

examining the consequences of “what if” scenarios. Within the context of water system security, some examples of “what if” scenarios include the following (Walski, 2003):

If an oil tank adjacent to a river ruptures and discharges to a river

used downstream as a source of raw water, when should the utility close its water intake and for how long will they need to keep the intake closed?

If a major main in the water system breaks, what happens to pressure throughout the distribution system and will there be sufficient flow and pressure to provide fire protection?

If runoff contaminates a particular well, what customers would receive contaminated water and how quickly will the contaminant reach them?

In the area of water system security, computer models have been

used to examine three different time frames:

• As a planning tool to look at what may happen in the future in order to assess the vulnerability of a system to different types of events and to plan how to respond if such an event occurs.

• As a real-time tool for use during an actual event to assist in formulating a response to the situation.

• As a tool for investigating a past event so as to understand what happened.

The characteristics of models used and the type of information that is

available in these three time frames can vary significantly. A water distribution system model can be applied to a wide range of “what if” scenarios to determine the general vulnerability of the distribution system. For example, the model can be used to determine the effects of a major pipe break or the impacts of a purposeful or accidental contamination of the system. With this information in hand, a water utility is better equipped to develop an effective plan of action.

A water distribution system model can be used to simulate flows and pressures within a distribution system, and the movement and transformation of a constituent after it is introduced into the distribution system. In order to simulate the movement of a contaminant in a distribution system, a hydraulic extended-period simulation (EPS) model of the system is needed (Rao, 1977).

Water distribution system models have been proposed as part of a


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real-time or near real-time system to assist in many aspects of the operation of a water system including energy management, water quality management, and emergency operation (Male, 1990). The major obstacle in such use of water distribution system models is the requirement that the model must be calibrated for a wide range of conditions and is ready to apply quickly and easily in an extended-period simulation mode. Information on the current state of the system must be readily available to the model through direct ties to a SCADA system. In addition, the model must be set up in an automated mode so that operation is represented by a series of logical controls that reflect the existing operating procedures.

The key to using a model as part of a real-time response lies in having the model ready to run. During an emergency, there is no time to construct a model. There is only time to make some minor adjustments to an existing model.

3.6 Using SCADA system for hydraulic modeling SCADA systems enable an operator to remotely view real-time

measurements, such as the level of water in a tank, and remotely initiate the operation of network elements such as pumps and valves. SCADA systems can be set up to sound alarms at the central host computer when a fault within a water supply system is identified. They can also be used to keep a historical record of the temporal behavior of various variables in the system such as tank and reservoir levels. Chapter 6 provides an in-depth introduction to SCADA systems and their components.

3.7 Network optimization Optimization, as it applies to water distribution system modeling, is

the process of finding the best, or optimal, solution to a water distribution system problem. Examples of possible problems are the design of new piping or determination of the most efficient pumping schedule. The typical optimization problem consists of finding the maximum or minimum value of an objective function, subject to constraints (Brdys, 1994). Chapter 9 and 10 will be donated to discuss this topic and the optimization of the “Toulon Est” network.

4. CHAPTER 4 : Pressurized Water Network Modeling and Simulation Softwares

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CHAPTER 4

4. Pressurized Water Network Modeling and Simulation Softwares

4.1 Introduction In the previous chapter we introduced the process of the water

distribution systems modeling, simulation, calibration, and optimization of these systems. One perceived obviously that the realization of these fundamental tasks, which aim to improve the efficiency of the system and the service quality, is almost impossible - specially when it is about a rather complex system - to analyze the system and to carry out the calculations and to find the resolutions of the hydraulic equations in a traditional way, and we can not understand the behavior of the system and the weak points and find solutions and then choose the best one, this is before or after the design of the system, from where results the need of tools which are characterized by the efficiency, preciseness, speed and robustness and which facilitate the task for the designer, the engineer, the manager, or the operator of the system. Doubtless, the computer software packages supply such tools.

Before the advent of computers, the analysis of even very simple distribution systems relied on an engineer’s experience and very crude theoretical models (Ulanicki, 2001). These models relied on gross assumptions plus laborious and time-consuming calculations (WSS, 2002). Since the 1970’s there has been a trend towards the use of digital computers for network analysis. The availability of cheap processing power, the general trend towards more automation in the industry and integrated information technologies, means computer simulation can provide an efficient way of predicting a system behavior.

But today, because of the multitude of the market software packages for modeling of water distribution systems, the question which arises here is that “Which software should I opt to resolve my problem?”.

However, I find that it is convenient to summarize in this research work the main results of three interesting market studies that apprehend software packages concern the modeling. The first and second studies are a comparison between several software packages of the market, and the other


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study is a comparison between FINESSE software and other software packages.

Knowledge: It is indeed necessary that I declare here that the first study is SCP property realized in November 2003 by Frank BESSEAT from Engineering Division-SCP, the second one is prepared by CH2M HILL-USA in 1999, and the third one is a property of De Montfort University, UK -Water Software Systems (WSS) – realized in August 2000. 4.2 Market study for water distribution modeling softwares

4.2.1 Market study aims For the DMU, this market study came about due to the forthcoming

release of FINESSE Water Network Modeling Suite. The fundamental aim of this market study was to help WSS in providing input for the development a business and marketing plan for FINESSE. This research hopefully helps determine factors such as:

• FINESSE’s strengths • FINESSE’s limitations • Marketing strategy • Pricing strategy • Distribution methods • Support and training

Most importantly this research provide suggestions on how WSS

should approach the modeling tool market and identify where FINESSE fits in with the other water network modeling packages (WSS, 2000).

From the SCP’s point of view, firstly, the general purpose of study is to create an exhaustive list of simulation and modeling softwares regarding administrative data, global references, new technology implementation and scope of technical functionalities developed by software companies (Besseat, 2003).

Secondly, SCP, as an engineering and consulting company in water industry, will have a full softwares market comparison. This comparison is based on softwares evaluations and the result can be used to advise potential overseas clients according to their specific constraints. The market study focuses on comparison criteria. The aim is not to obtain a classification of all the softwares but to gather useful information that will be analyzed and compared to be used to choose a simulation and modeling softwares for a new project or to operate an existing water network.


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Finally, this report hopefully provides suggestions on how a Consultant or a Final Client should approach the Network Analysis Software (NAS) and identify which essential criteria must be focused on accordingly to their specific requirements.

4.2.2 Market studies tasks

Before moving into the main body of market study the first task was

to learn the basic concepts of water network modeling and simulation and also the fundamentals of the FINESSE package. This was necessary to get an understanding of the relevant information needed for the comparison of the other modeling tools. The studies consisted of one main task along with three associated subtasks.

Main Task: Identify and analyze competitor products The main task of the study was to identify products on the market.

The main parameters used to select the products were:

Availability of selected functionalities Medium or long term experienced products, Significant references around the world, Global representation.

Subtasks

a- Analyze competitor companies: Tying in with the above task,

there was a need to gather corporate information on the developers of the competing softwares, such as turnover, profit, parent company, number of staff, etc. Information about the network modeling softwares market such as identifying whom the market leaders, market share, and other softwares sold.

b- Analyze modeling/simulation features: This technical task

focuses on the engine features, the main functionalities developed and the optional modules proposed.

c- Links with SCADA, GIS and Customer Management System:

Modern water production and distribution utilities require more systematic handling of system complexities and provision of more efficient guidelines for overall operations. The aim of this task is to analyze the efforts provided to develop integrated solutions with other main system of the network manager.


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4.3 Identifying and analyzing competitor products The first stage of the market studies was to identify the other

packages on the market. Using initial information from SCP - mainly from a market study supplied in 1997 to analyze the Water Colombo Network in Sri Lanka and secondly from the research supplied in the field of WaterCIME RDT project (WATERCIME, 1997), from De Monfort University (DMU, 2000) and from CH2M HILL “Water Distribution Hydraulic Model Selection” research, and also internet advanced research; a preliminary list of water network distribution modeling packages was drawn up. This initial list included:

AQUIS EPAnet FINESSE GAnet H2Onet InfoWorks IRMA KYPIPE

LIQSS NETBASE PICCOLO StruMap SynerGEE Water WaterCAD

4.3.1 Final product list

After some initial research it appeared that some of the names in the

initial list were not as prevalent in the current modeling tool market as first expected. So then using primarily the Internet, more up-to-date modeling packages were identified. A final list was then trimmed down to six products for the purposes of the comparison.

This final list of products included a wide mixture of modeling tool types and origins. From high-end American products such as WaterCAD, H2Onet and SynerGEE, to new European products such as AQUIS and InfoWorks and more established names such as PICCOLO.

PORTEAU is water network simulation software developed by CEMAGREF (Bordeaux-France, 2002), that was not included in the mentioned market studies and I will introduce it in this chapter.

4.3.2 Sources of Information

The following sources have provided the main basis for gathering

information:

- Knowledge within Water Software System: The basis of the initial information came from the different members of WSS, in


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particular all the information concerning FINESSE. - Internet: Along with the internal WSS knowledge, Internet based

information has proved to be one the most extensive and useful sources of information for the research. Most of the competitor developers provided fairly comprehensive details of their products on their respective websites.

- Company Literature: The second most useful source of data was literature sent by the developers. However some of brochure packs were sales orientated rather than technically orientated and but generally did not offer more detail than available on the web sites.

4.3.3 Product information

The following summaries provide a brief overview of each product

considered in the comparison.

AQUIS A new modular based hydraulic simulation package with a very

strong focus on its ability to work in real-time and on-line. AQUIS has been developed by the Danish Company Seven Technologies and is based around the technology of two established platforms — LICwater and WATNET.

>> (http://www.7t.dk/aquis).

H2Onet An AutoCAD based package consisting of a very comprehensive

suite of tools. It has a strong emphasis on speed, ease of use, and also a firm focus on network design and rehabilitation offering modules such as Network designer and Advisor.

>> (http://www.mpact.com/page/p_product/net/net_overview.htm)

InfoWorks InfoWorks is Wallingford Software’s Windows based successor to

Wesnet. But, notably InfoWorks hydraulic and quality simulation is still heavily based around the WesNet simulation engine.

>> (http://www.wallingfordsoftware.com/products/infoworks/)

PICCOLO An established name in the water network market, offering one the

largest choice of optional modules of any of the products in the comparison, including water quality, costing, pipe sizing, transient analysis and more. SAFÉGE make strong emphasis about PICCOLO’s Real-time


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operation, its powerful user interface and its strong performance claiming “PICCOLO uses the most efficient method available for resolving problems in meshed networks”.

>>(http://www.safege.fr/wwwsafegefr/english/dom/logiciel/reseaux/piccolo/atouts.htm)

SynerGEE Water

SynerGEE Water is Stoner’s successor to their original Stoner Workstation Services. SynerGEE Water is based around the base SynerGEE product developed for gas and electric and of course water. Stoner makes the bold claim that “SynerGEE is the most advanced family of network modeling and management application modules commercially available”. Offered in modular format, SynerGEE has modules to allow linking to Customer Information Systems, SCADA linking, main isolation and model simplification.

>> (http://www.advantica.biz) WaterCAD

Another high-end American developed software package that can be used in conjunction with AutoCAD or bought as a standalone windows program. Strong focus on ability to link to virtually any type of external sources e.g. any database, spreadsheet, GIS, SCADA, etc. Also stresses on ease of use and extensive data manipulation features.

>> (http://www.haestad.com/software/watercad/)

PORTEAU To improve the distribution of drinking water the CEMAGREF

(Agricultural and Environmental Engineering Research Institute– Bordeaux– France) developed a software called PORTEAU, which allows to estimate the reliability of the drinking water distribution system and the respect of the water quality standards. PORTEAU software also allows to estimate the water pressure, its stagnation duration in the network, the origins of this water or the disinfectants evolution in the network, such as chlorine.

PORTEAU thus constitutes modeling tools for the steady state behavior of pressurized meshed water supply and distribution networks. It represents a decision-making aid for the management of water supply or distribution networks (CEMAGREF, 2002).

Several modules of calculation are available; each one allows the simulation of a particular use of the network. At present, the modules of calculation associated with this graphical environment are:

• The module “Zomayet”: It allows to study, by an extended-period


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simulation (24 hours to 15 days), the hydraulic operation of a water distribution system and visualize the results on its schema.

• The module “Opointe”: It allows simulating the operation of a drinking water distribution system during peak-demand period and visualizing the results on its schema.

• The module “Quality”: it allows simulating the spatial and temporal evolutions of solution’s concentration through the network. This module takes into account the legitimate requirements of the subscribers who require today of the manager, in the absence of hydraulic problems, that the quality of water should be irreproachable.

>> (http://porteau.CEMAGREF.fr/)

4.3.4 Omitted products Several important names were also not in the comparison. Here is the

explanation for few key-missing products. FINESSE and GAnet were omitted from the comparison list, as they are university research based products. Only commercial products were compared in the SCP and CH2M HILL market study reports. But GANet and FINESSE are mentioned in this report and summarized in this chapter as a showcase of the current research way. KYPIPE, LIQSS and NETBASE are standalone product used mainly by Consulting and Services companies for designing, simulating or modeling small networks quickly and efficiently. Other missing product that is well used by utilities is StruMap. It’s omitted from the final comparison list because of a not clear commercial and support policy from MVM Consultants Company.

GANet - Exeter University/Optimal Solutions

Another key missing product from the list was GAnet; the simulation product based on the use of Genetic Algorithms developed by Exeter University and commercially supported by Ewan Associates (the joint venture is known as Optimal Solutions).

The Optimal Solutions set-up is of great interest to WSS simply because it’s the only other organization that operates in a reasonably similar fashion to WSS; i.e. research based with a commercial partnership. Optimal Solutions appears to be the result of the joining of skills from Exeter Universities and Ewan Associates – a water industry consultancy firm. Optimal Solutions is an operating division of Ewan Associates, who appear to be responsible for all the commercial aspects of GAnet.

GAcal

Optimal Solutions has produced a package called GAcal, which links


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to STL’s StruMap GIS with its embedded HARP hydraulic solver. GAcal’s, sibling GAnet, has already proved to be a highly effective tool for planning the optimal strengthening, rehabilitation and operation of water networks. GAcal, which may be applied by modelers who do not have detailed GA background knowledge, is now available.

“As well as removing most of the routine and tedious aspects of the job, GAcal will generally achieve better fits to the data and will adopt a consistent approach that is more likely to highlight real inconsistencies and problems”.

FINESSE

FINESSE is a well known product from SCP. FINESSE was developed by Water Software Systems WSS – UK.

>> (http://www.eng.dmu.ac.uk/wssys/Software.htm) StruMap Modeling

StruMap Modeling is Geodesys’s hydraulic modeling version of its StruMap GIS package, using an EPANET based simulation engine integrated with the GIS. StruMap Modeling offers a surprisingly comprehensive range of modeling features including water quality, leakage assessment, etc.

Geodesys firstly developed StruMap. Now the product is sold by MVM Consultants plc. But, according to the web site, it seems that the product is maintained but will probably not be developed more. Hence StruMap was omitted from the comparison.

>> (www.geodesys.co.uk)

EPANET One of the key names - EPANET was omitted from the comparison,

as it is a freeware product. EPANET is US Environmental Protection Agency software well known by their hydraulic community. As a freeware, there is no formal support or services offered for EPANET. It’s important to notice that most of the products selected in this report are based on the EPANET Engine.

>> (http://www.epa.gov/ORD/NRMRL/wswrd/epanet.html)

NETBASE Crowder and Co Ltd is an established firm of consulting engineers

and software developers, founded in 1985 – UK. The company offers flexible and competitive services to developers, contractors, architects, water utilities, local authorities and property services companies. Crowder and Co developed NETBASE as an integrated management system for water distribution and wastewater drainage networks. It provides the tools


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to monitor performance in many different ways, to meet regulatory requirements, to plan, develop and operate networks to suit the particular strategies of the end user.

NETBASE has been developed and applied by Crowder and Co analysts and engineers, and by major water utilities for more than 10 years. It fulfils a simple but powerful concept of a single, integrated database and software suite for the management of distribution and drainage systems. Its interfaces with corporate data and with proprietary applications make it both dynamic and flexible.

A team of programmers and analysts whose skills encompass server-database technology, Geographical Information Systems (GIS), client server systems and networks carries out its development and support.

>>(http://www.crowderconsult.co.uk/lang/en/netbase/content_pages/database.htm)

KYPIPE

KYPIPE is a USA product sold by LLC Software Center in Lexington, KY. KYPIPE offers a lot functionalities found in product compared in this reports. There is also a SCADA interface providing some very advanced capabilities for reviewing and modifying settings, which affect the operation of the system, and launching an analysis using these settings. The current version of KYPIPE is the 2000 version. LLC software develops also Gas2000, Surge2000, Steam2000 and Goflow2000.

KYPIPE LCC and MWH software have a string partnership. Here is a quote from LLC websites describing this partnership: “Whereas Surge2000 and H2O SURGE provide identical analysis capabilities (they actually utilize the same binaries) these programs are targeted at different users. The programs are offered at a different price point, have different support arrangements, and have different operational requirements. Partnering with MWH Soft allows KYPIPE LLC to bring our software to a market segment that we would not ordinarily reach”.

>> (http://www.kypipe.com)

LIQSS A mention has to be made about LIQSS software which is one of the

four non-graphical steady-state and transient network analysis simulators developed by Dr. Michael A. Stoner who launched Stoner Associates in seventies. A lot of LIQSS licences still exist all around the world. But, now the SynerGEE water product from Advantica will be the only one commercialize. IRMA-RAMI

“House” software developed by SCP-France. This program includes


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some number of additional features developed for the proper necessities of the SCP. This program is in FORTRAN and uses the SCP graphic library (Bonnadier, 2000).

4.3.5 Developer information

The developers of the products in the comparison varied quite

noticeably in their structure, business intention’s and focuses. The following passage shows that some the companies involved are research and consultancy firms who have software divisions, or firms who specifically provide software and solutions to the utilities markets. There are also several exceptions to this rule in particular Ewan Associates, Geodesys and Haestad Methods.

Advantica – USA – SynerGEE Water

Stoner Associates provide a very wide range of services and software solutions to the natural gas, electric, water, and petroleum industries. They have three locations in the US, one in the UK - Loughborough - and one in Australia – Sydney. Haestad Methods – USA – WaterCAD

Haestad Methods is quite unique in that its key area of work is in developing software, literature and courses related specifically to water management. Their software products include WaterCAD, SewerCAD, StormCAD, WaterGEMS, Darwin Calibrator and Designer, LoadBuilder, Skelebrator, WaterSAfe, Hammer, HEC-Pack, PondPack, CulvertMaster and FlowMaster. The other key area of Haestad is the holding of seminars and courses related to general water management issues and more specifically on the use of their software products (like a training in Dubai in February 2004 including a free modeling social part).

Montgomery Watson Software (MWSoft) – USA – H2ONet

MWSoft are a division of Montgomery Watson, who appear to be a very large Worldwide services/consultancy/research group, in a similar mould to that of WRc in the UK. However Montgomery Watson USA cover a much broader area of work including environmental engineering, applied research, construction and construction management, financing, government relations and IT, where MWSoft is just one part. MWSoft also has an IT solutions division and a specialist CAD group. MWSoft appears to be specifically set-up for the development of water network modeling products such as H2Onet. MWSoft has offices all around the world but only US offices are detailed on the website.


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SAFÉGE – France – PICCOLO SAFÉGE is another large environment consulting and engineering

practice specializing in the following areas: Water Supply Environment Public Utilities Management Regional Development They also develop a wide range of applications including network

modeling, network draught and GIS tools. Notably, SAFÉGE also has office locations on all five continents.

Seven Technologies – Denmark – AQUIS

Seven Technologies headquarter is located in Denmark. Recently, Energy Solutions was representing the UK arm of Seven Technologies, promoting and supporting AQUIS in the UK as they no longer develop their own water network modeling tool (LICWater). But actually, Seven Technologies has its own office in UK – Northallerton. The Third representation of Seven Technologies is in Malaysia. Wallingford Software – UK – InfoWorks

The Wallingford group appears to be a relatively large organization that provides a range of services and products specifically for the water industry. Wallingford group claims to be specialists in consultancy, research and software for the water environment. It is split into two segments, HR Wallingford which is the research and consultancy arm and Wallingford Software which produce InfoWorks and is responsible for developing and supporting other softwares for the water and sewage industry. There are five Wallingford Software representations in the world, but none in Africa or Middle East.

CEMAGREF – Bordeaux – France – Porteau

CEMAGREF is a public research institute whose work focuses on sustainable development in non-urban areas. It contributes to the conservation and acceptable management of land and water systems, the prevention of associated risks and the development of sustainable economic activity. CEMAGREF has been developed common scientific methods on geographical information, modeling, and computing sciences. For many years, CEMAGREF has been working in partnership with domestic water supply operators to improve their water supply system management. A suite of computer programs under the name PORTEAU has been written to model piped water supply system operation and performance. The research


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was done jointly with the post-graduate school of mathematics and information technology at the University of Bordeaux and the post-graduate school of engineering science at the Louis Pasteur University in Strasbourg.

4.3.6 Criteria

A list of criteria was developed to compare the competitors. These

criteria have a strong marketing focus as well as focusing on the general technical aspects of the software. The method for developing the criteria was based around drawing up a large list of all the different features and functionality of all the different packages, and then analyzing where overlaps occurred, and trying to identify commonly occurring features and functions.

The development of the criteria was an ongoing process with numerous changes being made, even up until the completion of all the tables. After much analysis, seven major criteria were identified, each with their own set of sub-criteria. These seven criteria are as follows:

A- General software information B- Hydraulic simulation C- Water quality simulation D- Additional analysis features E- Data exchange tools F- External system linking G- User interface features

This following section explains the seven criteria and their respective

sub-criteria in more detail.

A. General software information Criteria Summary: The first set of criteria looked at all the

significant non-technical information about the products. It is perhaps the most important table for identifying a business strategy as this table gives an idea on how each of the competitors is marketed, distributed, and supported.

Note: Some questions have a simple Yes/No answer, whilst others required a descriptive input. This applies throughout the entire criteria. A.1 Product summary: A brief description about what the product is and how it is aimed at the market. A.2. Platform: The operating system(s) which product is designed to run


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on e.g. Windows, UNIX, etc. A.3. Modular configuration: Indicates if the product is sold in modules; i.e. if the product is sold as a standard unit with optional modules available at extra cost. A.4. Basic simulation functions: Indicates which of the most common simulation functions are available; i.e. if the product is sold as a standard unit (hydraulic simulation) with optional basic functions available (water quality simulation and surge simulation). A.5 Optional modules: The additional modules/functionality that can be added to the standard configuration at extra cost. A.6 Additional 3rd party software: Additional softwares required to operate the product. A.7. Recommended specifications: The developer’s recommended hardware specification(s) for running their software. A.8 Pricing scheme: The method by which the company prices their software, typically by number of links, or number of licences (or combination). Also note that optional modules affect the pricing structure. A.9 Distribution media: The format the product is delivered in e.g. CD, Diskettes or Internet Download. A.10 Customer support: Type of user support offered by company and the format for support such as phone, fax or email. A.11 Support costs: The cost passed on to the customer for user support (support licences). A.12 Training courses: Training courses available to end users of the product.

B. Hydraulic simulation

Criteria summary: The technical details of the two main simulation processes provided by the product – the technical details of hydraulic simulation, and water quality simulation. B.1 Simulation engine: The background simulation process being used to simulate hydraulic models (for example: EPANET). B.2 Steady state simulation: Indicates if product can perform steady state (instantaneous) simulation. B.3 Extended period simulation (EPS): Indicates if the product can perform extended period simulation. B.4 Offline analysis: Indicates if product can perform offline analysis. B.5 Online analysis: Indicates the ability to perform hydraulic analysis using on-line data from SCADA systems. B.6 Real-time analysis: Indicates the ability to perform hydraulic analysis in real-time using data from SCADA systems. B.7 Max network size: An indication of the maximum network size that


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hydraulic simulation can be executed. B.8 Calculation speed: The Speed taken to calculate a typical network (if available). B.9 EPS control: Describes the type of control offered to the user during EPS simulation, for example pausing, stopping, resuming, etc.

C. Water quality simulation

Criteria summary: This criterion looks at the technical details of water quality simulation offered by the products.

C.1 Offered: Indicates if product offers water quality simulation in the first place, and whether it is an optional module or standard. C.2 Simulation engine: The background simulation process being used to simulate water quality models for example EPANET (Typically the same engine as for hydraulic simulation). C.3 Steady state simulation: Indicates if the product can perform steady state (instantaneous) water quality simulation. C.4 Extended period simulation: Indicates if the product can perform dynamic water quality simulation C.5 Conservative substance propagation: States if the water quality simulation can analyze the movement of conservative substances such as Nitrates, Phosphates or Fluoride through the network. C.6 Reactive substance propagation: States if the water quality simulation can analyze the movement of reactive substances such as Chlorine, through the network. C.7 Water age calculation: Indicates if the water quality simulation can calculate the age of water C.8 Source tracing: Indicates the ability to identify origins of water in the system. C.9 Sediment analysis: States if the water quality simulation can analyze the movement of sediment material through network. C.10 Bacterial analysis: Indicates the ability to analyze and track of the growth of bacteria in the system. C.11 Substance conversion analysis: Indicates if the water quality simulation allows for the conversion of substances from one state to another.

D. Additional analysis features Criteria summary: This criterion is the one of the largest of the set.

It highlights the additional analysis features and applications offered by the software on top of the standard hydraulic (and quality) simulation. This


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includes functions such as Calibration, Scheduling, Fire Flow analysis, etc. It also indicates if these extra features are provided as standard or as optional module. D.1 Model calibration: Indicates if the product offers a model calibration feature and whether it is an optional module or offered as standard.

Details: Any further information on calibration such as the algorithms and methods used.

Automatic calibration: Indicates if the calibration is performed automatically rather than manually.

Offline/online: If calibration can be performed online or offline or both.

D.2 Scheduling (Optimization): Indicates if product offers a pump-scheduling optimization feature. D.3 Demand prediction: Indicates if the product offers a demand prediction (future load forecasting) feature. D.4 Cost analysis: (Yes/No) indicates if the product offers ability to calculate operating costs.

Details: Further information on the costs that can be analyzed and the tariffs that can be incorporated.

D.5 Pipe isolation analysis (shut off analysis): Indicates if the product can analyze the effects of shutting off main pipes/nodes; i.e. identify which valves to close and parts of the network will be affected. D.6 Model simplification / skeletonization: Indicates if the product offers a proper model simplification or model skeletonization feature.

Details: Highlights if the method used in model simplification such as skeletonization, is a mathematical procedure, and any further information provided by the developer about the feature.

D.7 Model extracting and merge: Indicates if product can perform sub model management; i.e. the ability to extract model elements and merge them. This feature is very closely related to simplification/skeletonization. D.8 Fire/emergency analysis: Indicates if the product offers analysis of fire/emergency scenarios; i.e. calculates necessary available pressure at different parts of the network. D.9 Leakage analysis: States if the product has a leakage analysis function. D.10 Transient/surge analysis: States if the product can analyze surges events /transient phenomena within the distribution network D.11 Network design optimization: Indicates if the product offers a facility to determine design alternatives for the network distribution system based on user criteria. D.12 Pipe Sizing Analysis: Indicates if the product can calculate optimal pipe diameter for given design and demand criteria. D.13 Network reliability/failure analysis: Indicates if the product has a


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feature that can analyze the effects of pipe or component failure on a network; i.e. identify which parts of the network affected and possibly identifies customers affected D.14 Flushing analysis: This shows if the product can calculate flushing schedules, to show which hydrants to open, and in what order so that polluting material can be removed from the network. D.15 Steady state pressure analysis: Indicates if the product can perform steady state pressure analysis within a network.

Note: Simplification and Skeletonization:

A special note must be made about model simplification and

Skeletonization and the importance of being able to make a distinction between the two. This was the hardest part of the criteria simply because it was not easy to tell what each developer is claiming.

The following rule was used: if the product claims to be able to reduce a hydraulic model and then re-allocate demand to other nodes in the model, it was classed as simplification. Whereas skeletonization is understood to be where the product simply trims or removes unwanted nodes such dead end and small pipes – and then presumably a loss of accuracy in the model.

E. Data exchange tools

Criteria summary: The table focuses on the product’s ability to exchange information with databases, spreadsheets and windows programs, etc. It also highlights the file formats for importing and exporting; network model data input and the import of CAD drawings. E.1 External database linking: Indicates if product can link to external databases, and if it the feature is standard or optional. E.2 Bi-directional link: Indicates if the product has a bi-directional link with the external database(s); i.e. if the external database is updated automatically if the simulation model is changed. E.3 Method/details: method used to connect to databases. E.4 Database’s supported: A list of the database(s) the product claims to be able to link to.

Method: The method used to link to the external databases e.g. ODBC, translator programs, command language, etc.

E.5 GIS linking: Indicates if product can link to external GIS and if it is a GIS based product. E.6 GIS systems/formats supported: A list of GIS format the product claims to be able to link to. E.7 Spreadsheet linking: Indicates if product can link to external


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spreadsheet packages, and if it the feature is standard or optional. E.8 Spreadsheets supported: A list of the spreadsheet package(s) the product claims to be able to link to. E.9 Data exchange with Windows programs: Highlights if the product can exchange data with a variety of other windows based programs.

Programs supported: A list of the windows program(s) the product claims to be able to exchange data with, such as EPANET, Stoner, WATNET, etc.

E.10 Data import file format(s): File format(s) that the modeling tool is capable of importing directly, for example ASCII, CSV. E.11 Data export file format: The export file format(s) the product can generate. E.12 CAD drawing conversion: Indicates if the product can directly import CAD files and convert them into network models/data.

Supported CAD formats: The CAD formats supported for the above process.

F. SCADA system linking

Criterion summary: This table looks at the ability to link with

external systems in particular telemetry systems (SCADA).

F.1 SCADA linking: Indicates if product can link to SCADA system(s) and if the feature is standard or optional. F.2 SCADA systems supported: Brief description of the SCADA systems/formats claimed to be supported by the product.

Method: The file format/method used to by the product to collect SCADA data.

F.3 On-line SCADA link: Indicates if the product can capture online data from SCADA (see notes below). F.4 Real-time SCADA link: Indicates if the product can capture data from SCADA in real time (See notes below). F.5 Automatic SCADA data transfer: (Yes/No) indicates if the product claims to automatically transfer SCADA data into the simulation model database. F.6 Logging equipment support: Indicates the ability to link to logging equipment.

SCADA online and real-time linking Although seven out of the eight tools in the comparison claim to link

to SCADA systems a clear distinction needs to be made between a products ability to link with SCADA systems in either on-line and real-time modes.


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• On-line linking On-line linking refers to the product’s ability to capture historical

recorded data from SCADA that has been collected over a certain period of time e.g. 24 hours or a week. The presumption can be made that any tool that has SCADA linking can perform on-line collection of data as standard as this is the basic function necessary of a SCADA connection.

• Real-time linking

Real-time linking is different as this refers to the collection of the

most recently measured values from SCADA with a delay of few minutes (typically between 5-15 minutes). The term real-time is perhaps a little misleading in water network modeling terms, as it is not instantaneous as it first implies. The rule used for the assessment is that any product is capable of obtaining recently measured values is capable of real-time SCADA linking.

G. User interface tools

Criteria summary: The final set of criteria highlights the key

features offered in the user interface.

G.1 Scenario management: Indicates if the product offers scenario management tools that helps the user to manipulate, reuse and save scenarios. G.2 EPS animation: Indicates if the product offers an animation feature that helps the user to visualize dynamic simulation. G.3 User definable units: Indicates if the product allows the user to create their own new units or modify existing predefined units. G.4 Color coding: Indicates if user interface offers color coding of model attributes

Attributes: The attributes the user can choose for color-coding. G.5 Contour maps: Highlights if the product can display contour maps that graphically display findings

Attributes: The attributes the user can choose for displaying contours.

G.6 Display background maps: Indicates if the product can display background image maps below the network schematic such as those from CAD, GIS or image files.

File formats: The file formats supported for displaying background maps

G.7 Zooming: Indicates if the product offers the basic feature of zooming. G.8 Panning: indicates if the product offers the basic feature of panning


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(scrolling). G.9 Multiple windows: Indicates if the product offers the feature of multiple window displays. 4.4 General conclusions

Choice of competitors A question may be raised about the choice of competitors as several

of them are aimed at the top end of the market. Although the choice of products may not be ideal, now that the criteria list has been created it would be quite straightforward to add other products to the list.

Application or actual function? Because of wording used by the developers, it made it difficult to

decipher if a feature is a specifically designed application or something that can be done by the user by combining various options. For example does a calibration feature mean an estimation procedure, or an option to facilitate “trial and error” calibration?.

Marketing focus Some of the information sources provided by the companies was

quite marketing orientated, focusing on the benefits rather than actual details of operation. For example product X “can help to reduce this”, or “can help to improve that”, etc. It appears that marketing aimed at higher level, not engineers who use software. The only true exception was SAFÉGE who made the effort to provide more technically orientated information such maximum network size and speed of calculation exception.

Web based information The most valuable source of information for the project has been the

use of the internet. Two developers clearly stated that they no longer produce traditional marketing literature as the web allows the put-out as much information and keep it updated more regularly. Presumably this is also cheaper than producing glossy literature on a regular basis.

US products The two main American based softwares – H2Onet and WaterCAD

appear to offer very comprehensive functionality.

In Table 4.1 some of the softwares mentioned here above and their main features are summarized:


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Table 4.1 : General software information and features

Software

AQ

UIS

H2O

net

Info

wor

ks

Picc

olo

Syne

rGE

E

Wat

erC

AD

FIN

ESS

E

EPA

net

Port

eau

Platform Windows Y Y Y Y Y Y Y Y Y Platform Unix N N N N N N N Y N Water Quality Y Y Y Y Y Y N Y Y 3rd Party Software N Y N N N Y Y N N Steady State Simulation Y Y Y Y Y Y Y Y Y Extended Period Simulation (EPS) Y Y Y Y Y Y Y Y Y Offline Analysis Y Y Y Y Y Y Y Y Y Online Analysis Y ? Y Y Y ? Y N N Large Size Network Y Y Y Y Y Y Y Y Y Model Calibration Y Y Y Y N Y N N N Scheduling (Optimization Y Y N Y N N Y N N Demand Prediction Y N N N N N Y N N Model Simplification Y Y N Y Y Y Y N N Leakage Analysis Y N N N N N N N N Transient/Surge Analysis Y N N Y N N N N N Pipe Sizing Analysis Y N N Y N N N N N SCADA linking Y Y Y Y Y Y Y N N Network design optimisation N Y N N N N N N N

Finally, the interested reader can refer to the original market studies

for further information and details.

4.5 Water distribution networks simulation and modeling softwares at the SCP

As it was previously mentioned in Chapter 2, SCP has three

modeling and simulation softwares for pipe networks that it already used but of which two are today not really installed in an operational way:

PICCOLO We had said that this software was never used in SCP to realize

hydraulic simulation studies on any of its networks. For more details about this software and its tools and functionalities please refer to the market Studies presented in this chapter.

FINESSE Developed by De Montfort University-UK. This software is the

modeling tools that will be used in this research work and it will be describe in details in the next section.


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IRMA- RAMI “House” softwares developed by SCP-France. A brief description of

this software is presented in the paragraphs hereafter. This program, property of the SCP, was the object of numerous

evolutions in the course of years to answer the new necessities of the different users as well designers as administrators of networks. This software simulates the behavior of pressurized supply networks. It calculates head at nodes and flows in pipes based on a description of the network geometry, pipes, equipment and water demands.

This software is well adapted to study irrigation and distribution networks, or more or less complex networks grouping several uses of water (irrigation, industrial, drinking water, etc.). It can be used for design (sizing of pipe diameters, tanks and other equipment) or for operation management and diagnosis of existing networks (minimum pressures, infrastructure capacities, saturation level, possible additional flows at specific points). This program is written in FORTRAN and uses the SCP graphic library. In the general case, the flows circulating in sections are calculated by Clément’s law.

Besides, the program includes some number of additional features developed for the proper necessities of the SCP. There are different “bridges” between IRMA and the tools that constitute its immediate environment in the SCP. An automatism of call of RAMI program of optimal sizing of new branched connected with a general infrastructure. This function allows calculating directly the diameters of new branches. It is enough to describe the new branch(s) in the database file without clarifying the diameters. The calculations of optimization will be launched automatically and the database file updated with the diameters resulting from calculations of RAMI.

In the other direction, an interface between RAMI program (calculation of branched networks) and the IRMA program which allows using the data of RAMI’s files for the modeling of SCP networks containing loops. Also, a “bridges” were established between IRMA and the SCP network database to create and to update models of IRMA from valid data stored in the database. An interface is also available to create data files for FINESSE software (Bonnadier, 2000).

4.6 FINESSE (WSS, 2002)

FINESSE « Fully Integrated Network Editing, Simulation, and Scheduling Environment », the advanced modeling software from Water Software Systems, is an on-line operational modeling environment, which seamlessly integrates water-related software components with a database


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and graphical user interface. FINESSE is presented here in details because it will be used in this thesis. This software is intended for water engineering and operators. An engineer may need to use the full range of facilities but infrequently; while an operator may only be required to follow a predefined scenario to schedule pump and valve controls (WSS, 2002).

Complementary modeling functions are integrated to solve operational and design problems. FINESSE has four main modeling functions: hydraulic simulation, demand prediction, operational scheduling, and model simplification. These functions share data through a common database. They share a Microsoft Windows user interface. They also share data processing and communications functions to interface and exchange data with other systems, including Supervisory Control, Automation and Data Acquisition systems for on-line applications. The overall software architecture and main functions are shown in Figure 4.1.

The architecture was first published in 1998. Since then more modeling functions have been added, the software has been converted to Microsoft Windows operating systems and experience has been gained from further case studies. Some of the functions are based on software products, which have been used by industry for some time and others are the result of recent research. The modeling functions are described in the following subsections.

Figure 4.1 : FINESSE architecture

a) Network simulation This provides steady state hydraulic simulation, and extended-period

simulation (e.g. over a 24 hours horizon). It calculates time-profiles of flows, velocities, headloss, pressures and heads, reservoir levels, reservoir inflows and outflows and operating costs. The input data include network topology and component parameters, water demands and control variables.

SCADA

Model Data Files

SCADA Interface

GINAS CONOPT

Model Simplifier

ModelBuilder

Network Simulator

DemandPredictor

Network Scheduler

Microsoft Windows Interface

Modeling Database

GIDAP


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The calculation engine is a third party software called GINAS “Graphical and Interactive program for Network Analysis and Simulation” for water distribution system, which since the 1980s, has been applied by many water companies to many networks. It is also possible to integrate other simulation engines if needed.

b) On-line network simulation

This is a special configuration of the network simulation function for on-line application. It performs steady state hydraulic simulation using the most recently measured state of the network as the initial condition. The Network Simulator is configured to automatically acquire data including reservoir levels, flows and pressures from a SCADA system. It then performs a simulation over a predefined time horizon.

c) Network scheduling

Pumps, valves and water works outputs are scheduled to minimize the total water production and distribution costs, typically over a time horizon of one or more days. The schedules conform to practical operating requirements defined by constraints on variables such as pressures, reservoir levels, flows, etc.

Non-linear hydraulic models are used to calculate least cost schedules, even for large networks. Such models are accurate over wide ranges of operating conditions, which is particularly important in the analysis of operating constraints. The scheduler can use network simulation models directly. The FINESSE Pump Scheduler will later be presented in detail in Chapter 9 of this thesis.

d) Demand prediction

Water demand patterns and volumes are predicted from historical flow time series. Typically, 6 weeks of historical data are required to setup the prediction model, which is based on categorization of demand patterns and a triple exponential smoothing algorithm. Thereafter, the software predicts future patterns of demand (e.g. for 1 to 7 days at 15 minute intervals) from recently acquired time series. FINESSE can be configured to acquire data on-line for a number of zones and then predict demands patterns for each of them. Alternatively, it can be used to analyze historical flow time series off-line. The prediction software was first used in the 1980s, and has been applied successfully to a number of networks. WSS has also applied a number of other methods to water demand and leakage prediction, including Box Jenkins methods and artificial neural networks. FINESSE Demand Prediction will later be presented in detail in Chapter 8 of this thesis.


73

e) Model simplification The model simplifier automatically calculates simplified models

directly from detailed ones. The simplified models contain all key components and critical pressure nodes chosen by the user. The results are typically accurate to within 2% of the original models for comparable quantities. Simplified models can be used directly in either simulation or optimization and they can be recalculated from the detailed models at any time and for any given reason, such as if there are any changes to the network. The simplifier is based on a Gaussian elimination procedure.

f) Pressure control

This is a tool to calculate optimal pressure profiles directly from simulation models of a network. The profiles are calculated to minimize leakage whilst maintaining specified head constraints at each node of the network. The pressure control module can be applied to large pressure management areas of any configuration.

FINESSE - general features

- Model data: model data are stored in a single database and are

shared seamlessly between the modeling functions. Models can be built and edited interactively using FINESSE model building features. The network schematic is created by “drag and drop” from a palette of standard model components.

- User interface: FINESSE has a comprehensive windows user

interface based on a schematic of the network. - Software integration: FINESSE is developed in the Boorland C++

Builder environment, which supports direct access to all major database management systems through ODBC, COM, etc, and the internet through TCP/IP. Data can be exchanged with other information systems to meet specific water company requirements. Tried and tested modeling packages are integrated within FINESSE including GINAS and GAMS / CONOPT. Other computational modules can be added if required. WSS has the expertise to write interface to various computational engines.

- SCADA gateway: provides an interface to SCADA systems for on-

line applications. The user specifies the data servers and the mnemonics for the on-line variables in a simple look-up table. The table also maps the variables to model parameters. FINESSE can also be interfaced to other SCADA and telemetry systems either through CIMVIEW or directly.


74

- Model import: imports data files of other modeling packages and automatically builds the FINESSE database. So far import options for GINAS, EPANET and WATNET have been implemented. These files have also been used as an intermediate interface with GIS systems that export these formats. Other import formats will be added if required.

- Model dimensions and calculation performance: FINESSE

currently has a maximum model size of 10,000 nodes but the dimensions may be increased if required. Calculation times depend on the type of application, model dimensions, model timestep and a number of other model features.

- Hardware requirements: Most standard PCs running Windows 95+

or NT will be adequate. A minimum of 128MB RAM is recommended. Primary FINESSE drawbacks

It was felt that the biggest differences between FINESSE and the

other softwares lied in these following areas:

• Water quality : FINESSE’s biggest omission appears to be its lack of water quality simulation that is offered by all competitor products in this comparison.

• GIS linking : This was another feature that was found on all products. No GIS linking means FINESSE is unable to extract and import network data from GIS systems or display GIS background maps.

• Data exchange tools : Compared with some of the other products FINESSE has quite limited exchange of data with other standard databases such as Access and Oracle. It also lacks the ability to import and convert CAD drawings. Overall FINESSE lacks the degree of “openness” shown by some of the packages here, in particular WaterCAD.

• Model data import : Another aspect of FINESSE’s lack of openness is its inability to directly import models/data from other modeling package. This could be a major issue for users of existing packages wishing to migrate onto FINESSE.

• True real-time hydraulic simulation : Another important feature missing from FINESSE is the ability to perform real-time hydraulic simulation. Several of the competitors offered the ability to perform true real-time analysis using live SCADA data rather than use captured historical on-line data as found in FINESSE.


75

• Limited node capacity : FINESSE may also suffer from its limited maximum network size capability. This was highlighted by PICCOLO that claimed to be able to model up 65,000 node models.

• Main isolation : FINESSE does not offer the user with the specific facility to analyze the effects the closure of a main pipe/node. This was an unexpectedly common feature offered by three other products – all as optional modules.

Secondary FINESSE drawbacks

Other less significant (but still useful) features lacking in FINESSE

but are relatively common in the other packages included:

• Linking to customer, billing and postcode information • Scenario Management • User Command Language • Contour Maps • Background maps • Animation

FINESSE STRONG POINTS

• Demand prediction : FINESSE was one of only two products in

the comparison that offered a demand prediction feature. The other – AQUIS, gave very little information about its “load forecasting” feature, and very little known about how it works or its accuracy.

• True model simplification : FINESSE offers true model simplification with a known level of high model reduction accuracy. This is a strong point because the others do not state the accuracy lost when reducing hydraulic models. More importantly it is not a skeletonization process that simply trims excessive unwanted pipes.

• Scheduling : Although offered by several other packages, FINESSE offers a known high level of accuracy with its scheduling feature.

• Module integration : FINESSE offers a high level of integration between all its “modules”.

• Network design (drag and drop) : Offered as standard. • Complex tariffs : The assessment on FINESSE carried out by

South Staffordshire Water Company-UK found that FINESSE


76

has ability to deal with complex tariffs. • Use of complete hydraulic model for scheduling : Again as

stated by Jay Mistry at South Staffordshire Water Company, FINESSE has the ability to incorporate the complete hydraulic model, important for accurate scheduling.

• Seven-day extended period simulation : FINESSE offers a seven day simulation period which appears to be longer than most.

• Pressure control feature in future : FINESSE has the potential feature in future of steady-state pressure control analysis, which would appears to be unique, however as we have seen PICCOLO and AQUIS already provide transient analysis of networks.

• Ease of use.

Figure 4.2 : FINESSE interface

4.7 EPANET Software I will also briefly introduce EPANET software because it will be

used later to perform some calibration work. EPANET is a freeware computer program that performs extended period simulation of hydraulic and water quality behavior within pressurized pipe networks. EPANET tracks the flow of water in each pipe, the pressure at each node, the height

Toulon Est network model


77

of water in each tank, and the concentration of a chemical species throughout the network during a simulation period comprised of multiple timesteps. In addition to chemical species, water age and source tracing can also be simulated. Running under Windows, EPANET provides an integrated environment for editing network input data, running hydraulic and water quality simulations, and viewing the results in a variety of formats. These include color-coded network maps, data tables, time series graphs, and contour plots. EPANET contains a state-of-the-art hydraulic analysis engine that includes the following capabilities (Rossman, 2000):

Placing no limit on the size of the network that can be analyzed. Computing friction headloss using the Hazen-Williams, Darcy-

Weisbach, or Chezy-Manning formulas. Including minor headloss for bends, fittings, etc. Modeling constant or variable speed pumps. Computing pumping energy and cost. Modeling various types of valves including shutoff, check,

pressure regulating, and flow control valves. Allowing storage tanks to have any shape (i.e. diameter can vary

with height). Considering multiple demand categories at nodes, each with its

own pattern of time variation. Modeling pressure-dependent flow issuing from emitters

(sprinkler heads) Can base system operation on both simple tank level or timer

controls and on complex rule-based controls. In addition to hydraulic modeling, EPANET provides other water

quality modeling capabilities (Rossman, 2000). The method used in EPANET to solve the flow continuity and

headloss equations that characterize the hydraulic state of the pipe network at a given point in time can be termed a hybrid node-loop approach which will be introduced in the next chapter.

5. CHAPTER 5 : Methods for Solving Water Pipe Networks Problem

78

CHAPTER 5

5. Methods for Solving Water Pipe Networks Problem

5.1 Introduction An important element in the examination of many physical systems

is the ability to formulate and solve a variety of mathematical models. Water networks are large scale and non-linear systems (Chenoweth, 1974). The operational control of such system has posed difficulties in the past to the human operator that had to take the right decisions, such as pumping more water or closing a valve, within a short period of time and quite frequently in the absence of reliable measurement information such as pressure and flow values. Computer simulations of such systems have alleviated these difficulties. They allowed “what-if” scenarios to be run by the manager or operator, giving him the possibility to know in advance the operational problems that can arise in the real-life networks due to malfunctions of valves or burst in pipes.

Industry and academia have made a significant investment in the research and development of computer algorithms for the design, modeling and control of water distribution (AWWA, 1987). The industrial use of many of these algorithms is commonplace but there are no standards for their evaluation. Numerical algorithms are complex software procedures used to solve systems of equations. Owing to their complexity, it is difficult to compare different algorithms directly, or to verify that they provide correct results.

Today, fast computers and efficient computational algorithms make both large and small system modeling feasible. Water distribution software using sparse matrix algorithms can solve these large systems with reasonable runtimes compared to a few years ago, when such analyses were impractical. One element to be considered when selecting a hydraulic model is that computer programs differ in their mathematical formulations (Haestad Methods, 1997).


79

5.2 Conceptual model of a water network A conceptual model of a water network can be presented as an input-

output system in Figure 5.1 (Rance, 2002). Control Schedules are pump, valve and source schedules. Demands are node outflows representing water consumption. Initial Conditions are the initial reservoir levels. Output comprises heads at nodes, flows in elements, and operating costs. Water network mathematical model is the set of mathematical equations modeling the behavior of the physical system. Connections between components are described by topology, which for example can be represented by a node-branch incidence matrix. It is useful to distinguish between “basic two terminal components” with regular characteristics and “complex components” with local control loops that potentially have irregular (non-monotonic, non-smooth) characteristics. The two terminal components are described by an equation relating component flow and the headloss. For the complex components the origin and destination heads may appear explicitly as separate variables. Basic components are reservoirs, pipes, valves, and pumps. Complex components with local control loops are control elements such as pressure reducing valves, pressure sustaining valves, pressure control pumps.

Figure 5.1 : Conceptual model Water networks often have control loops in order to achieve the

desired behavior of the network. The control loops can be local, e.g. around pressure reducing valves (PRVs) or global, e.g. a pump controlled by a reservoir level. In the first case the local control loop can be masked and the component together with the control loop can be represented as a complex component. These control loops can not be included within a component characteristic and have to be considered as a separate part of the model. It is important to understand the behavior of the basic network (basic components) before considering control loops. In a computer implementation, a water network model is represented by a set of network data (values of parameters) and a set of equations (physical operation of the model).

Water Network Mathematical

Model

Control Schedules

Demand

Initial Conditions

Output Pressures

Flows Costs


80

5.3 Fundamental mathematical model The fundamental model is formulated using the laws of physics.

Subsequently, different models can be derived by mathematical manipulation. For water network models three physical laws are employed: flow continuity, headloss continuity, and component equations (head/flow law), as follows (DMU, 1999):

( ) ( )tqhSdt

dhrr

r 1−−= Reservoir equation (Eq. 5.1)

nqRh =Δ Component equation (Eq. 5.2)

dq −=Λ Mass balance equation (Eq. 5.3)

⎥⎦

⎤⎢⎣

⎡Δ=ΓΔ

0fh

h Energy balance equation (Eq. 5.4)

Where:

rh = vector of reservoir heads (m) ( )rhS = area of the reservoir at hr level (m2)

rq = vector of net reservoir outflow (m3/s) hΔ = component headloss vector (m)

q = branch (component) flow vector (m3/s) d = demand flow vector (m3/s) R = component resistance matrix (sn/m3n-1):

⎥⎦

⎤⎢⎣

⎡

Λ

Λ=Λ

c

f = n x b node-branch incidence matrix

)5.5.(

0...0...0...0...

......00...0

2

1

Eq

r

rr

R

b⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=


81

This incidence matrix has a row for every node and a column for every branch (component) of the network. Two nonzero entries for each column +1 and -1 indicate the beginning and end of the branch respectively.

cΛ = nc x b connection node incidence matrix as above

fΛ = nf x b fixed grade node incidence matrix as above

⎥⎦

⎤⎢⎣

⎡

Γ

Γ=Γ

l

f = (f+l) x b loop-branch incidence matrix that has a row

for every fixed grade pseudo-loop and for every primary loop and a column for every branch (component) of the network. Two non-zero entries (+1) and (-1) in each row indicate orientation of the branch to go with or against the loop orientation.

fΓ = f x b fixed grade pseudo-loop incidence matrix

lΓ = l x b Primary loop-branch incidence matrix

fhΔ = headloss vector on fixed grade pseudo-loop where a fixed grade pseudo-loop is a chain of branches between the pseudo-datum node and any other fixed grade node. The vectors of reservoir heads and the vector of junction node heads can be combined into one vector of nodal heads:

[ ] )6.5.( Eqhhh

TTc

Tr=

There are Hazen-Williams Formula, Darcy-Weisbach Formula, and

Chezy-Manning Formula in water distribution network to calculate headloss hΔ (Rossman, 2000), the general formula is:

Where:

R = pipe’s resistance, depends on pipe diameter and length, and how rough the pipe inner surface:

-For Hazen-Williams Formula : )8.5.(7.1087.4852.1 aEq

DCLR =

5.7) (Eq.nRqh =Δ


82

-For Darcy-Weisbach Formula : )8.5.(852 bEq

DgfLR

π=

-For Chezy-Manning Formula : )8.5.(33.1033.5

2

cEqD

LmR =

Where: q = flow rate (m3/s) D = pipe diameter (m) L = pipe length (m) C = Hazen-Williams C-Factor (dimensionless) f = Darcy-Weisbach friction factor (dependent on pipe

roughness, diameter, and flow rate, and its dimensionless) m = Manning roughness coefficient n = 1.852 for Hazen-William and 2.0 for Darcy-Weisbach and

2.0 for Chezy-Manning In reality, the pipe C-Factor “C” used in Hazen-Williams formula’s

is not constant. It vary depends on pipe diameter and flow rate variation. Thus if use Hazen-William formula and assume “C” as constant, the result will not be accurate. But in actual application the error of assuming “C” value, as constant and use Hazen-Williams formula will not affect design result significantly, moreover since the formula is simpler, convenience to calculate, thus general engineering application still use Hazen-Williams formula at large (Ming-Chang Tsai, 2002).

The Darcy-Weisbach equation is valid for fully developed, steady state and incompressible flow. The friction factor (f) depends on the flow, if it is laminar, transient or turbulent, and the roughness of the pipe. The friction factor can be calculated by using the Moody Diagram or by the Colebrook equation (Finnemore, 2001).

The work of Lewis F. Moody, Professor, Hydraulic Engineering, Princeton University, and the Moody Diagram, has become the basis for many of the calculations on friction loss in pipes, ductwork and flues (Moody, 1944). The Moody Diagram can be used as a graphical solution of the Colebrook equation.

The friction factor of commercial pipes is described by a semi-empirical equation developed by Colebrook. This equation that expresses the friction factor as a function of relative roughness and Reynolds number (Re) is an implicit one requiring a trial-and-error procedure for its determination (Jerry, 2002). There are tools available today that allow solution of the Colebrook equation, in both its implicit forms and explicit forms, without using the graphical approach (Lester, 2003).


83

Implicit Forms of Colebrook: Friction factor is calculated, generally, by any one of the implicit

equation of Colebrook (Colebrook, 1937). There are at least three forms of the Colebrook equation that can be found in current literature on hydraulics (Lester, 2003). These are:

Where: f = friction factor (dimensionless) ε = absolute pipe roughness (mm) D = inner diameter (mm)

* Note:- (ε /D) is the relative roughness and is dimensionless. Re = Reynolds Number (dimensionless):

ν = water kinematic viscosity (1.0x 10-6 m2/s at 20 °C) These equations can be solved for ( f ), given the relative roughness

(ε/D) and the Reynolds Number (Re), by iteration. Explicit Forms of Colebrook:

To make the solution of Colebrook equation easier, some great

engineers developed explicit expressions for the friction factor and there were many explicit expressions. Out of those, the following are the famous equations (Chen, 1976), (Churchill, 1976), (Jain, 1976), (Chen, 1976) , (Swamee, 1976), (Wood, 1977), (Zigrang, 1982), and (Serghides, 1984).

)9.5.(Re

51.27.3

21 aEqfD

Logf ⎟

⎟⎠

⎞⎜⎜⎝

⎛+−=

ε

)9.5.(Re

7.182274.11 bEqfD

Logf ⎟

⎟⎠

⎞⎜⎜⎝

⎛+−=

ε

)9.5.(Re

3.91log2214.11 cEqfD

DLogf

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛

+−⎟⎠⎞

⎜⎝⎛+=

εε

)10.5.(4Re EqD

qνπ

=


84

1. Serghides equation (for Re > 2,100 and any ε/D)

2. Moody equation (4,000 < Re < 107 and ε/D < 0.01) 3. Wood equation (Re > 4,000 and any ε/D) 4. Jain Equation (for 5,000 < Re < 107 and 0.0000 4 < ε/D < 0.05) 5. Swamee and Jain Equation (for Re > 4,000 and ε/D < 0.02)

( )( )

( )aEq

BD

LogC

AD

LogB

DLogA

ABCABAf

11.5.

Re51.2

7.32

Re51.2

7.32

Re12

7.32

2

22

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

⎬

⎫

⎟⎠⎞

⎜⎝⎛ +−=

⎟⎠⎞

⎜⎝⎛ +−=

⎟⎠⎞

⎜⎝⎛ +−=

⎥⎦

⎤⎢⎣

⎡+−

−−=

−

ε

ε

ε

( )bEqD

f 11.5.Re101021105.5

31643

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+×+×= − ε

)11.5.(

62.1

Re8853.0094.0

134.0

44.0225.0

cEq

Da

DDDf a

⎪⎪

⎭

⎪⎪

⎬

⎫

⎟⎠⎞

⎜⎝⎛−=

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

ε

εεε

)11.5.(Re

25.210.214.119.0 dEq

DLog

f⎟⎠⎞

⎜⎝⎛ +−=

ε

)11.5.(

Re74.5

7.3

25.02

9.0

eEq

DLog

f

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +

=ε


85

6. Churchill Equation (for all values of Re and ε/D) 7. Chen Equation (for all values of Re and ε/D) 8. Zigrang and Sylvester Equation (for 4,000 < Re < 108 and

0.00004 < ε/D < 0.05) The Chezy-Manning formula is more commonly used for open

channel flow that is out of the scope of this study. The fundamental mathematical model of water networks can be seen

as a non-linear differential algebraic equation (DAE) system, where equation (5.1) is the differential part describing the dynamics of the model, equations (5.2), (5.3), and (5.4) are representing the static model, where equations (5.2) and (5.4) are non-linear algebraic equations, and equation (5.3) is linear equation. In order to solve this dynamic model it is necessary to calculate the right-hand side of the differential equation (5.1). This in

( )

)11.5.(

Re37530

27.0Re7457.2

1Re88

16

169.0

121

5.1

5.0

fEq

B

DLnA

BAf

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

⎬

⎫

⎟⎠⎞

⎜⎝⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛

++⎟

⎠⎞

⎜⎝⎛=

ε

)11.5.(

Re8506.5

8257.2

Re0452.5

7065.30.21

8981.0

10987.1gEq

DLogA

AD

Logf

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

⎬

⎫

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛+

⎟⎠⎞

⎜⎝⎛

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛−=

ε

ε

)11.5.(13

7.3Re02.5

7.3

Re02.5

7.30.21

hEq

DDLog

DLogA

AD

Logf

⎪⎪

⎭

⎪⎪

⎬

⎫

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ +−=

⎟⎠⎞

⎜⎝⎛ −−=

εε

ε


86

turn requires solution of a system of algebraic equations (5.2), (5.3), and (5.4) - the static model.

Irrespective of the numerical procedure used, the simulation of water networks has led to the development of many methods of network flow analysis using various types of decompositions. Each decomposition expresses the resulting system of equations in terms of a specific type of independent variables. In the literature there are several types of models derived from the fundamental model, depending on which variables and which equations have been used (Ulanicka, 1998). The flow models have branch flows or loop flows for unknown variables. The nodal model has nodal heads for unknown variables and finally the mixed (or hybrid) model has both branch flows and nodal heads as the unknown variables. The numerical algorithms for solving the non-linear equations are based on iterative techniques, e.g. Newton-Raphson (Brenan, 1989) where during each iteration; a system of linear equations is solved. These methods are commonly used to solve one of the four formulations of the continuity and energy equations that are necessary in implementing hydraulic modeling software. The four systems of equations and models are as follows:

A- Branch Flow Model (BFM)

Where equations describing mass continuity (flow in = flow out) at

each junction are coupled with headloss equations around each loop in the network. This method produces two separate sets of equations to be solved: linear junction equations and nonlinear loop equations. The total number of equations, which must be solved simultaneously, equals the number of branches (or pipes). Therefore, programs using the BFM often take a long time to complete the system calculations:

(Eq. 5.12) The branch flows q are the unknown variables.

B- Nodal Model (NM) Where the Hydraulic Gradient Line (HGL) elevations at nodes are

solved simultaneously. Unfortunately, all nodal model equations developed are nonlinear, but there are fewer equations to solve than with the branch flow model, because no loop equations must be solved: (Eq. 5.13)

⎪⎭

⎪⎬

⎫

⎥⎦

⎤⎢⎣

⎡Δ=Γ

−=Λ

0fn

c

hqR

dq

dhG nTc −=ΛΛ −)(


87

Where G=1/R is the component conductance matrix. The node heads h are the unknown variables.

C- Loop Flow Model (LFM)

Where the program assumes an initial value for flows through a loop

and iteratively solves for the unknown corrective flow rate around each loop. Obviously, there are fewer loops than with either pipes or junctions, so the matrix created by the LFM formulation is smaller than with either of the other methods:

⎥⎦

⎤⎢⎣

⎡Δ=Γ

0),( f

fln h

qqqR (Eq. 5.14)

The unknown variables are flows in fundamental loops ql and pseudo-loops qf. The algorithm requires a complex procedure for finding the loops.

D- Mixed Model (MM)

Known also as Hybrid Model (Hamam, 1971), which uses a

combination of features associated with the nodal model and the loop flow model:

⎩⎨⎧

Λ=

−=Λ

hqR

dqTn

c (Eq. 5.15)

The branch flows q, and nodal heads h, are the unknown variables. These four models are present in the formulation of other application

tasks such as network design, optimization, simplification or state estimation. In order to asses the relative merits of the different formulations for solving large pipe network problems, the comparison can be made in terms of simplicity of input, initial solution, size of the system of linear equations and efficiency of solution of the system of equations. The balance of these merits made the combination of the nodal heads and the Newton-Raphson algorithm to be the most frequently used procedure for solving water networks. Extended time simulations which are used to evaluate system performance over time and allows the human operator to model tanks filing and draining, valves opening and closing, have been implemented based on nodal heads equations. Finally, the combination of the Newton-Raphson method and the loop corrective flows is called the loop system of equations. Over the last decade the numerical simulations based on loop equations have received an increased attention. It has been


88

shown that using the loop equations is a suitable framework for the inclusion of pressure-controlling elements without specifying the operational state of the network (Arsene, 2004).

5.4 Theoretical properties of the mathematical model The differential part of the fundamental model is described by

equation (5.1), and equations (5.2), (5.3), and (5.4) represent the algebraic part. The theoretical properties that have direct practical significance are (Ulanicka, 1998):

Existence of the solution (i.e. do one or more solutions exist?) Index of the model (i.e. is the Jacobian matrix nonsingular?) Stability (i.e. can a hydraulic model become unstable?)

Models of water networks are non-linear systems analogous to

electrical networks. Some results can be almost directly transferred from the theory of electrical networks. The equivalent result for a water network can be formulated as follows:

Theorem 1 (Existence theorem): “The static model (Eq. 5.2, 5.3, and

5.4) of a network comprising reservoirs, pipes, valves, and pumps, has one and only one solution for branch flows and nodal heads”. o Proof: The proof is accomplished by identifying the

corresponding elements in water networks and electrical networks and by checking that pipes, valves and pumps have strictly monotonically increasing head/flow characteristics.

Theorem 2 (Index theorem): The DAE model of a water network consisting of reservoirs, pipes, valves, and pumps, has an index equal to 1. o Proof: The proof is accomplished by investigating the Jacobian

of the algebraic part of the model, and by checking that the Jacobian of (Eq. 5.2, 5.3, and 5.4) is a nonsingular matrix.

Theorem 3 (Stability theorem): The model of a water network consisting of reservoirs, pipes, valves, and pumps is a stable system. o Proof: The model is equivalent to an electrical network made of

non-linear monotonic resistors, independent sources and capacitors and the latter model is stable.

Some water networks include pressure-controlling valves (PRVs and PSVs). These valves have local control loops and cannot be represented by two terminal models with monotonic characteristics. There are strong indications that Theorems 1, 2, 3 are also valid for networks with pressure


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controlling valves. The reasoning can be based on the fact that stabilization of the downstream head is accomplished by modification of the conductance (minor losses) of the valve. The changes in the state of the valve from closed to active and then open are obtained by a continuous change in conductance starting from zero to some maximum value that corresponds to the valve being fully open.

5.5 Numerical methods Simulation of real water distribution systems, that do not consist of a

single pipe and cannot be described by a single equation, consists of solving a system of equations. The invention of digital computers allowed powerful numerical technique to be developed that set up and solve the system of equations describing the hydraulics of the network in matrix form (Rossman, 1996). These numerical methods can be classified as Hardy-Cross method, Newton-Raphson method, Linear Theory method, Linear Graph theory, Finite Element Method (Corneliu, 2004). These classes include methods used for the solution of systems of non-linear equations. Generally to simplify calculation of water network analysis, we assume pipe network’s water flow is steady flow, thus omit time factor in influencing flow volume.

5.5.1 Hardy-Cross method

The oldest method for systematically solving the problem of steady

flow in pipe-networks is Hardy-Cross method. Hardy-Cross invented this method in 1936. Fair Howland and Fair Hurst later improved it (Corneliu, 2004). Hardy-Cross Method is a simplified version of the iterative linear analysis to solve problems related to flow in pipe networks (Ming-Chang, 2002). It is a trial and error method. The Hardy-Cross method is also known as the single path adjustment method and is a relaxation method. The flow rate in each pipe is adjusted iteratively until all equations are satisfied. The method is based on two primary physical laws:

A- The sum of pipe flows into and out of a node equals the flow

entering or leaving the system through the node. B- Hydraulic head (i.e. elevation head + pressure head) is single-

valued. This means that the hydraulic head at a node is the same whether it is computed from upstream or downstream directions.

Pipe flows are adjusted iteratively using the following equation:


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Where:

∆q = loop flow adjustment (m3/s) N = number of pipes in the loop q = pipe flow rate (m3/s) hfi = headloss in pipe I (m) n = 1.852 for Hazen-William and 2.0 for Darcy-Weisbach The pipe flow is adjusted until the change in flow in each pipe is less

than the convergence criteria.

5.5.2 Newton-Raphson method Later, Newton-Raphson method has been utilized to solve large

networks. Computer storage requirements are not greatly larger than those needed by the Hardy-Cross method. Newton-Raphson is an iterative method for solving nonlinear problems. It begins with an initial guess at the solution, and then generates a sequence of points that step increasingly close to the real solution. When the initial guess is far from the solution, the Newton-Raphson method may diverge (Brenan, 1989).

5.5.3 Linear Theory method

An additional method called Linear Theory method has also been

proposed. The Linear Theory Method was first introduced by McIlroy in 1949 (McIlroy, 1949). He based his algorithm on Q-equations (linearized equations based on the difference between estimated and corrected flows in a pipe). The basic idea of the linear theory is to transform non-linear headloss equations into linear equations and then solve the system of equations together with linear continuity equations. Later computer programs were written based on Q-equations (linearized equations of flows in pipes) and h-equations (linearized equation of nodal heads) (Scholz, 2005).

5.5.4 Finite Element Methods

Recently, with the gaining of popularity of Finite Element Methods

(FEM), pipe network is analyzed with relative advantage. The FEM is quite

5.16) (Eq.

1

1

⎥⎦

⎤⎢⎣

⎡±=Δ

∑

∑

=

=N

i i

fi

N

ifi

qh

n

hq


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different from Kirchhoff’s analogy. FEM was introduced originally as a method for solving structural mechanical problems, which was later recognized as a general procedure for numerical approximation to all physical problems that can be modeled by a differential equation description. To solve any problem using the FEM, the boundary conditions for the problem must be known. The FEM based on matrix structuring requires an important volume of iterations and calculations that could constitute a major constraint in the case of a large network. Large volume of literature is available for the first three methods, however, only few literature is available to exploit the advantages of Finite Element Method (Collins, 1975).

5.5.5 Linear Graph theory

The linear graph theory is used in analyzing and optimizing water

distribution networks. The method has many distinct advantages over the existing methods such as Hardy-Cross method, Newton-Raphson method, Linear theory method which are basically relaxation techniques. In these methods, the two independent set of continuity equations do not appear explicitly in the formulation of the problem but are primarily used for verification purpose. Therefore suitability of these methods entirely depends upon the proper initial guess of the variable values and the iteration scheme used in the analysis. Many times the solution does not converge and, even if it converges, it may take unusually large computer time. In the first step, the component model of hydraulic network such as reservoir or tank, pipe, check valve, pressure reducing valve and booster pump based on graph theory approach is formed. Then the analysis based on linear graph theory approach has been carried out which frees the analysis from the problem of convergence and initialization. In this case, the model formulation is based on the direct utilization of both sets of continuity equations and no initial guess or convergence problem occur. The analysis is based on two types of formulation, namely, twig formulation and link formulation. Moreover, the linear graph theory approach, explicitly takes into account the various topographical feature of the system. The addition of pumps, reservoirs etc can also be easily incorporated in the analysis (Rajiv, 2000).

5.6 Extended-period simulation Extended time hydraulic simulation is a process of solving the

mathematical model equations (5.1) to (5.4) over the time horizon with given initial conditions, control schedules and demands in order to


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calculate the output. The network model is an instance of a DAE system but with a very specific structure. The dynamic part is very small and simple and the static part is very complicated. The static and dynamic parts interact by two vectors hf (reservoir head) and qf (reservoir flow). For given reservoir levels the static part can be solved (static simulation). The reservoir levels in turn are affected only by reservoir flows. This structure ensures that instantaneous properties of the model are decided by the static part and a simple Euler integration scheme is sufficient to solve the dynamic model; extended-period simulation (Ulanicka, 1998).

Euler integration is the simplest and most obvious way to numerically integrate a set of differential equations (William, 2001). Euler integration consists of the following steps:

1. Set Time to its initial value. 2. Initialize the levels. 3. Compute the rates of change of the Levels at the current value of

Time. 4. Use the rates of change to compute the Levels at Time +

Timestep. 5. Add Timestep to Time. 6. Repeat steps 3-5 until Time is equal to Final Time.

Euler integration assumes that the rates computed at a given time are

constant through the time interval (timestep). This method is easy to understand, and easy to implement; however it is not accurate enough for integrating over any reasonably long time intervals. It is accurate enough to use in short time integrations though. The error made in using Euler integration is proportional to the square of timestep on an integration step and proportional to timestep over the whole simulation. To make the integration more accurate, one can decrease timestep.

5.7 FINESSE simulator (GINAS) As it was mentioned in Chapter 4, FINESSE simulator provides

steady-state simulation, and extended-period simulation (e.g. over a 24 hours horizon). The calculation engine is a third party software called GINAS (Coulbeck, 1985) and (DMU, 1991).

GINAS is a “Graphical and Interactive program for Network Analysis and Simulation” for water distribution system and is applicable to most of water supply network. Information about a network and about the way in which it is simulated is to be simulated is fed to GINAS via an input data file. The results are presented graphically in response to the user


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request. The types of network components provided for by GINAS are introduced:

- Nodes: Normal junction nodes, Variable load node, Fixed head

reservoir, Variable head reservoir, and Curve head reservoir.

- Elements: Normal pipeline, Completely closed line, Altitude control valve, Borehole head drawdown, Proportional pressure reducing valve, Flow reducing valve, Pressure modulating valve, Non-return valve, Pressure reducing valve, variable control valve, Head controlled valve, Fixed head element, Curve head element, Fixed flow element, Curve flow element, Fixed speed pump, Variable speed pump, Variable throttle pump, Fixed speed turbine.

- Switches: Time switch, Head switch, High head switch with time

delay, Low head switch with time delay, Time switch with high head switch, Time switch with low head switch.

6. CHAPTER 6 : Role of SCADA System for Real Time Hydraulic Simulation

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CHAPTER 6

6. Role of SCADA System for Real Time Hydraulic Simulation

6.1 Objectives of SCADA systems for water distribution network A Supervisory Control and Data Acquisition (SCADA) system is a

widely distributed computerized system primarily used to remotely control and monitor the condition of field-based assets from a central location. SCADA systems enable the manager (or operator) to remotely view real-time measurements, such as the level of water in a tank, and remotely initiate the operation of network elements such as pumps and valves. SCADA systems can be set up to sound alarms at the central host computer when a fault within a water supply system is identified. They can also be used to keep a historical record of the temporal behavior of various variables in the system such as tank and reservoir levels. The value of the SCADA system can be enhanced if it incorporates advanced capabilities, such as modeling and simulation (Cameron, 1998).

When working with SCADA data, the modeler often has access to more data than can be easily processed. For example, the modeler may have several weeks of data from which to calibrate an extended-period simulation (EPS) model and must pick a representative day or days to use as the basis for calibration. Selecting the best modeling analysis period from these thousands of numbers, which may be in several sources, is extremely difficult. Usually, there is no day when all of the instrumentation is functioning properly, so selecting that day is often based on finding the day with the fewest problems (Walski, 2003).

Another challenge of working with SCADA data is that incorrect readings, time-scale errors, or missing values may not be readily apparent in the mass of raw data. Fortunately, the modeler can use any of several procedures to compile and organize SCADA information into a more usable format, usually in the form of a spreadsheet. The tables and graphs developed using these procedures can be then used directly for a range of applications, including EPS model calibration, forecasting of system operations, and estimating water loss during main breaks (Walski, 2003).

For a water distribution network, the common objectives of a


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SCADA system are to do the following:

1. Monitor the system. 2. Obtain control over the system and ensure that required

performance is always achieved. 3. Reduce operational staffing levels through automation or by

operating a system from a single central location. 4. Store data on the behavior of a system and therefore achieve full

compliance with mandatory reporting requirements for any regulatory agency.

5. Provide information on the performance of the system and establish effective asset management procedures for the system.

6. Establish efficient operation of the system by minimizing the need for routine visits to remote sites and potentially reduce power consumption during pumping operations through operational optimization.

7. Provide a control system that will enable operating objectives to be set and achieved.

8. Provide an alarm system that will allow faults to be diagnosed from a central point, thus allowing field repair trips to be made by suitably qualified staff to correct the given fault condition and to avoid incidents that may be damaging to the environment.

However, a hydraulic model can also be used to assist SCADA

operators with setting up controls for an existing SCADA system or for entirely new SCADA installations. Rather than experimenting with the real system, the operator can test out different control strategies in the model and determine if the new controls are an improvement or if there are adverse impacts.

Before a SCADA system comes on line, it is usually tested by simulating events such as tank levels and valve statuses using EPS model runs. Results from these tests can be used to determine control set points, levels, and variable-frequency-drive settings. With model output linked to the man-machine interface of the SCADA system, it becomes possible to simulate much more realistic sequences of events to better test the SCADA system (Cameron, 1998).

In the water industry the water security and reliably providing water is one of it basic core competencies. SCADA data allows operations staff to develop a high level of understanding the effects their actions have on the supply of water, by providing feedback. Most water utilities would have had some form of such feedback even without SCADA (e.g. being able to interrogate tank levels). Another core competency of a water utility is ensuring the water quality is maintained. This means ensuring an


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appropriate chlorine residual is maintained throughout the system. The basic information to do this is the chlorine residual, the rate of turnover of water in the system, the temperature of the water, and the raw water quality. Much of this information is expensive to collect and rarely provided in a comprehensive manner with or without SCADA. If this information is routinely provided it can be seen that the competency of the utility in this area would improve dramatically by increasing the understanding of operations staff of the impact of their operating decisions on water quality (Ian, 2005). Also, secure water systems have properties that reduce the likelihood of successful attacks (Barry C. Ezell, 1998) and the system would provide constant monitoring of all vulnerable areas. It would immediately report any security breaches or abnormal operation conditions. It would eliminate any necessity for regular patrols and significantly reduce the frequency of visits to remote sites. The system would continue operating if the power was cut off or communication line severed. It would be accessible to operations people even if the control room were disables or evacuated. It would provide security from hacking. The system also would be able to react to conditions and perform control actions, which could safely shut down processes or isolate sections of the water distribution system (Bristol Babcock Inc., 2001).

On January 1998 a survey was posted at “http://virginia.edu”. The purpose of the survey was to gather information about the cyber threat, understand the state of SCADA in water supply systems, document any intrusions in the past year, and analyze trends among the administrators of these systems.

6.2 Components of a SCADA system SCADA encompasses the transfer of data between a SCADA central

host computer and a number of remote sites (Remote Terminal Units RTUs), and the central host and the operator terminals. A generic SCADA system employs some form of data multiplexing (MUXs) between the central host and the RTUs (Figure 6.1). These multiplexers serve to route data to and from a number of RTUs on a local network, while using one or very few physical links on a Wide Area Network (WAN) backbone to pass data back to the central host computer.

An important aspect of every SCADA system is the computer software used within the system. The most obvious software component is the operator interface or MMI/HMI (Man Machine Interface/Human Machine Interface) package; however, softwares of some form present throughout all levels of a SCADA system. Depending on the size and nature of the SCADA application, software can be a significant cost item


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when developing, maintaining, and expanding a SCADA system. When software is well-defined, designed, written, checked, and tested, a successful SCADA system will likely be produced. Poor performances in any of these project phases will very easily cause a SCADA project to fail.

Many SCADA systems employ commercial proprietary software upon which the SCADA system is developed. The proprietary software often is configured for a specific hardware platform and may not interface with the software or hardware produced by competing vendors.

Figure 6.1 : Generic SCADA system network

6.3 Data acquisition mechanisms

Data acquisition within SCADA systems is accomplished first by the

RTUs scanning the field data interface devices connected to the RTU. The time to perform this task is called the scanning interval and can be faster than two seconds. The central host computer scans the RTUs (usually at a much slower rate) to access the data in a process referred to as polling the RTUs. Some systems allow the RTU to transmit field values and alarms to the central host without being polled by the central host. This mechanism is known as unsolicited messaging. Systems that allow this mechanism usually use it in combination with the process of polling the RTU to solicit information as to the health of the RTU. Unsolicited messages are usually only transmitted when the field data has deviated by a prespecified percentage, so as to minimize the use of the communications channels, or when a suitably urgent alarm indicating some site abnormality exists.

Control actions that are performed by using the central host are generally treated as data that are sent to the RTU. As such, any control actions by an operator logged into the central host will initiate a


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communication link with the RTU to allow the control command to be sent to the field data interface device under control. SCADA systems usually employ several layers of checking mechanisms to ensure that the transmitted command is received by the intended target.

6.4 Types of SCADA data and SCADA data format Data received from SCADA systems fall into one of the following

categories:

a) Analog data (real numbers): Analog data are usually represented by integers or IEEE floating-point numbers (these are numbers that have no fixed number of digits before and after the decimal point and that follow the popular Institute of Electrical and Electronics Engineers standard IEEE). It may be trended (placed in charts that show variation over time) or used to generate alarms indicate an abnormal condition.

b) Digital data (on/off or open/closed): Digital data may be used to sound alarms, depending on the state (on/off or open/closed) reflected by the data.

c) Pulse data: Pulse data, such as the number of revolutions of a meter, are accumulated at either the site collection point or at the SCADA central host computer. They are typically converted to the same number format as analog data; however, they are physically derived in a different manner from pure, real number analog data obtained from field instrumentation.

d) Status bits (or flags): Status bits are usually auxiliary to analog data. For example, a data flag can accompany an analog input if the SCADA system determines that a value is possibly invalid. SCADA systems generally allow some form of data transfer to

external applications. For example, data may be exported as ASCII text, as a spreadsheet file, or to a proprietary “data historian” software package. Once the data are in tabular format within a spreadsheet, it is possible to manipulate the data to investigate the behavior of the instrument or the associated plant being monitored.

6.5 Handling of data during SCADA failures and processing of data from the field

Different SCADA systems cope differently with a failure event.


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Some systems rely primarily on the inherent redundancy of the SCADA system, and others may use some form of storage mechanism to archive data that may be recovered once the SCADA system has returned to normal operating capacity. These options are:

Storage of data in the RTUs System redundancy

Most SCADA systems employ a combination of the preceding

mechanisms to ensure data continuity during failure events. The primary interface to the operator from the operator terminal is a

Graphical User Interface (GUI) display that shows a representation of the plant or equipment in graphical form. Live data are shown as graphical shapes (foreground) over a static background. As the data changes in the field, the foreground is updated. For example, a valve may be shown as open or closed, depending on the latest digital value from the field. The most recent analog values are displayed on the screens as numerical values or as some physical representation, such as the amount of filled color in a tank to represent water level. Alarms may be represented on a screen as a red flashing icon above the relevant field device. The system may have many such displays, and the operator can select from the relevant ones at any time.

6.6 Responding to data problems and verifying data validity When incorrect SCADA readings are found, the modeler typically

examines another time period and set of data where the problems do not occur. However, if a unique distribution system event is to be analyzed or if collecting the SCADA data requires a special effort by SCADA operators, the modeler may not have the option of selecting another problem-free period. Discussions with SCADA operators can provide insight into the causes of inconsistencies in the data and permit the modeler to make appropriate allowances. Completing the data series with information from chart recorders, data loggers, or other monitoring devices, and shifting time scales where justified also can address SCADA data issues sufficiently to support modeling applications (Walski, 2003).

EPS modeling analyses require SCADA information to be divided into model timesteps. The duration of the model timestep depends on the type of analysis being performed and is usually based on separating the total analysis time period into a reasonable and manageable number of steps. However, it may be difficult to download SCADA data at time increments that directly correspond to model timesteps (Walski, 2003).


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Along with the convenience of remote monitoring via SCADA comes the drawback of data consumers becoming overly reliant on the data received from the SCADA system. A user of data may mistakenly assume the correctness of data received from a SCADA system when in fact the only way to be assured of its integrity is through critical analysis. Software for the central host is available that offers automatic detection of sensor data errors through continuous automatic analysis of data using such techniques as neural network analysis. However, more conventional data techniques are typically used to verify the validity of critical sensors and systems associated with a SCADA system.

6.7 Integrating SCADA systems and hydraulic models SCADA systems monitor the water distribution system performance

at discrete stations scattered throughout the service area. However, there may be locations in the distribution system, such as meter pits, that lack the power or communication connections required for a functional SCADA station. For these situations, the flows and pressures can be estimated from SCADA information at nearby stations. When these calculations are not complicated, they can be performed within the SCADA software (for example, by offsetting pressure readings from other stations based on differences in elevation). However, when the situation is more complex, a hydraulic model interfaced with the SCADA software is required to estimate parameters at non SCADA locations (Ingeduld, 2000). The steps involved in calculating information for non-SCADA sites include: Export data on boundary conditions from SCADA, Configure the hydraulic model to match those specific conditions, Execute the model, and finally view the results or import results from the model back into SCADA. This type of procedure is typically automated and accomplished with some form of dynamic data linkage between the SCADA system and modeling software.

Another example of this integration is estimating water loss during main breaks. Tracking the water discharged from the system during main breaks can help quantify losses. Generally, a significant main break will show up in SCADA records as low pressures readings, an unexplained decline in tank levels, excessive pump flow, or other unexplained data inconsistencies. SCADA information for the time period surrounding the break can be downloaded to a hydraulic model and the model can then be executed to simulate system conditions at the time of the break. By adjusting the demands - or emitter coefficients - at the break location and trying different start and finish times for the break, the modeler should be able to match modeling results to the SCADA records during the break and thus determine the quantity of water lost.


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In Chapter 4 of this thesis the hydraulic modeling and simulation softwares were introduced. Most of the softwares packages offered linking with external systems in particular SCADA. AQUIS, PICCOLO and SynerGEE make linking to SCADA an optional extra whilst the others provide it as standard. With the information provided by the developers from their Websites or brochures, it was quite difficult to determine exactly if the different packages offered real-time links to SCADA, or if in fact the links were merely on-line. The only packages that offer true real-time linking were AQUIS, InfoWorks, H2Onet and PICCOLO. It could not be determined if SynerGEE and WaterCAD perform real-time linking.

AQUIS – Optional real-time module for SCADA linking The system can operate in two modes, on-line and real-time. In on-line mode, the system will use SCADA and logger data collected over a period, say 24 hours or a week, while in real-time mode new SCADA data is used every few minutes.

H2Onet - SCADA Interface provided as standard with Analyzer H2ONet Analyzer provides the capability to extract real-time modeling data directly from SCADA system in ASCII format.

InfoWorks – SCADA interface provided as standard Real-time links with telemetry and logger data systems. Live Data Links enable transfers and fixed heads to be updated automatically at a frequency determined by field data download. This allows the simulated network to reflect current hydraulic behavior making the model a true operational tool.

PICCOLO – Optional real-time module for SCADA linking PICCOLO Real-time is an application which allows a hot link between a SCADA system and a PICCOLO model, and provides alarms on unexpected events such as abnormal data, or discrepancy between real time data and model results. PICCOLO Real-time analyzes a network’s real time operation conditions and validates pumping strategies in terms of water quality and pressure.

SynerGEE Water – Optional on-line module for SCADA linking On-line Module capabilities provide automatic transfer of operational and reference data from SCADA system into SynerGEE and hydraulic simulation using that data. This is all done without operator intervention.

WaterCAD – SCADA interface provided as standard No information provided by Haestad on whether WaterCAD could perform real-time linking with SCADA.


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FINESSE – SCADA Interface provided as standard It can perform “On-Line” and “Real time” simulation. FINESSE SCADA interface provides the capability to extract real-time modeling data directly from SCADA system. * Note: All the above information was taken from the same sources as those of Chapter 4. 6.8 Description of SCADA systems at SCP

The problem of the hydraulic management arises when the system’s

manager and operators have to administer hydraulic streams of openflow structures (canals, galleries) and storage tanks. This kind of hydraulic systems needs particular research for control applications because they are big scale systems, open and characterized by big delays and great inertia. The main purpose of the automatic control of open channel hydraulic systems, such as irrigation canals, is to optimize the water supply in order to match the expected or aleatory water demands at the offtakes level. In real situations with the traditional management tools, an open-channel water conveyance and delivery system is very difficult to manage, especially if there is a on-demand operation (Almeida, 2002). The objectives of the systems of hydraulic management are to answer in appropriate time and in sufficiency the necessities and behavior of the users, to respect the constraints of use of hydraulic works, to optimize resources in water, and to optimize the set of the costs of construction, running costs of works and equipments. These objectives are reached by means of a system of remote supervision.

The management and operation of the Canal de Provence are assured by automatic regulation software connected to a real-time supervisor. This supervisor centralizes and archive data coming from numerous sensors spread on a vast perimeter. The following sections describe the main components of this SCADA system at SCP (Canivet, 2002).

6.8.1 The equipments of the supervisor system

Data processing is assured by two workstations of type Alpha Server

300 (HP) used under the operating system VMS based in the Control Central (CGTC). The CGTC supervises 11 Regional Operating Room (French: Centre Régional d’Exploitation, CRE). Each of these centers possesses a PC or a workstation using the same software packages that CGTC uses. These regional operating rooms are connected to host computers but also control their own tele-measurements locally (Figure 6.2). Hence, the system of data acquisition via the remote control network


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is done either:

Directly by remote transmission stations or automatons, By the remote transmission front-ends at the equipment room of

CGTC, Or by “calculator” connected to the supervisors at the regional

operating rooms.

The different media serve as means of remote transmission are:

• Private cables • Rented specialized connections • Public telephone network • GSM network • Radio links

The securing of information is assured by the redundancy of

information and by looping some connections. Generally the GSM network is used as standby network in case of rupture of cabled communication. The real-time database of the CGTC supervisor is composed of:

o 1,300 telemetries (TM) which include the measurements of levels,

position of gates, pressure, quality of the water …), o 13,000 remote-signalization (RS) (states or defects of the equipments), o 41 remote-regulation (by sending signals of flow or gate opening at

the automaton), o 375 remote-controls (direct, on gates securities or pumps).

The acquisition of measurements from automatons is done every

minute. Data archived in the real-time database of the supervisor is done every 15 minutes. The used equipments provide, first of all, information on the state of the canal all the time. This information is mainly obtained by means of measuring sensors.

6.8.2 Description of the measuring chain of SCP This section aims at describing the architecture of the chain of

network measurement of Canal de Provence. It describes in details the various types of measurements made within the framework of the networks and canals supervision, as well as data connected to these measurements and collected in the real-time database.

In the case of the measurements that are made on the Canal de Provence, we shall distinguish two types of measurements:


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Figure 6.2 : Architecture of SCADA communication at SCP

1) Direct measurements, which represent measurements whose error results from the calibration of the measuring chain.

2) Calculated measurements, which are the measurements obtained from direct measurements. They use mathematical laws to transform these measurements into final measurements. This class concerns the measurements of flow in the case of openflow surface.

a) The measurements of levels The measurements of levels are used to follow:

- The variation of water levels in the reservoirs and water tanks (static regime),

Specialized connections Specialized connections Public telephone network

Support of RT

STATION RT

STATION

RT

STATION RT

REGULATOR AUTOMATONS

Actuator

Gate Pump

Sensors

TM

RS

On-Off Switch

RC

Equipments Equipments

Host Computers

RT front-end


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- The evolution of water levels in the canals (dynamic regime). On the majority of hydraulic works, the measurements of levels are

done in measuring wells communicating with the controlled work. This technique allows filtering the fluctuations in levels that disrupt measurements (notably those due to the wind). The types of used devices are very different:

- Sensors measuring hydrostatic differential pressure, - Immersed probes whose height is at least equal to the maximal height of the reservoir.

At present, two new types of devices come to be used. These devices

use a method based on the use of the radiation to deduct the level. Radiation can be:

• Acoustic wave: The sensor is composed of a receiving- emitting

station and is placed either at the top of the reservoir or at the bottom. the acoustic devices utilize an acoustic “shock-wave” sent down a vertical wave-guide. After striking the water surface, the wave is reflected back to a transducer and microcomputer that converts travel time to distance based on the speed of sound in air. This type of device allows more precise measurements but the speed of acoustic waves in the air depends on the temperature.

• Microwaves: Used technology is identical to acoustic wave. The

propagation of waves is close to the light speed so independent on the temperature and the pressure surrounding the receiving- emitting station.

The levels measurements are considered by the operator as the most

reliable measurements among the set of measurements made on the canal. They belong to the class of direct measurements.

b) The flow measurements

The measurements of flow are divided into two classes:

1. The direct flow measurements Numerous types of sensors allow knowing the flow that passes

through a pressurized pipe. At SCP, we find:


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>> The electromagnetic flowmeters The emission of a magnetic induction field perpendicular to the flow

velocity of a fluid in a pipe of diameter D, creates an electromagnetic force whose amplitude is directly related to the flow velocity.

>> Ultrasound flowmeters The speed of the sound depends on the physical media of

propagation and its temperature. If this media is in movement then the time of propagation of the acoustic wave is affected by the velocity of moving media. The measurement of this propagation time allows to measure the velocity of the fluid and hence the measurement of flow. In this case, it is possible to build a mathematical expression, which relates the propagation time of the wave directly to the distance that separates receiving- emitting stations, and to the flow velocity of the fluid, without taking into account the speed of the sound. Generally, ultrasound flowmeters is installed in the pressurized networks just like the electromagnetic flowmeters.

>> Venturi Flowmeters A contraction of the pipe carrying a flow creates between the

upstream and downstream a difference of pressure ΔP related to the flow. The knowledge of the geometry’s constant of the device as well as the density is necessary to establish this relation.

2. The indirect flow measurements

The knowledge of flow rates in the case of openflow surface is done

from laws that are empirical and mathematical laws that allow relating various direct measurements to obtain an estimate of the flow rate. In the case of the Canal de Provence two types of laws are used: laws of gates and laws of weirs.

These laws allow knowing flow according to the used type of gate/weir as well as the opening of the gate/weir and the water level at the upstream and at the downstream of the gate/weir.

c) Volume measurements Volume measurements are indirect measurements, which are

dependent on the water levels measurements and the reservoir geometry. For canals, the volume measurement in a canal depends on the average inflow and on the downstream level of the canal.


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6.8.3 The measurements acquisition in real-time Every minute, the host computer comes to interrogate the local

stations of remote transmission to obtain immediate measurements. These measurements are displayed on representative synoptic of the hydraulic works and facilities of Canal de Provence. Every fifteen minutes, the measurements archiving procedure is launched. Measurements can be:

>> Valid if the station sends back a value which falls within the

defined measuring range corresponding to the interrogated sensor. >> Non-valid for the cases where: - Communication with the remote transmission station is not done

neither by the direct communication nor by the standby network. - Communication between the sensor and the remote transmission

station is impossible (sensor is out of service, or is being repaired …), - Measurement does not fall into the defined measuring range

corresponding to the interrogated sensor, - The system of supervision is stopped before the phase of

acquisition and restarted later. Measurement is then absent in the database. A measurement code is archived in the database and translates the

causes of the absence of measurements:

If value in the database is (- 1), interrogated measurement was invalidated by a posterior treatment (measurements out of range, sensor out of service …)

If value in the database is (- 2), measurement is absent in the database (communication with the station is impossible, task of acquisition from supervision is stopped …),

If value in the database is (- 3), measurement does not exist in the interrogated base (computer address corresponding in the measurement is not recognized by the database).

In case of prolonged absence of measurements in the database, a

special acquisition task is set up. This task interrogates the databases of the computers at the regional operating rooms. If a measurement is faulty in the central database and present in the regional operating room database, then, the values of this measurement are replaced by the data from the regional database. This task is launched every morning (at 06:00 AM) for measurements verification for the day before.

The water levels measurements in the supervisor real-time database


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are instantaneous measurements that are archived every 15 minutes. The archived flows measurements are the average flow of the instantaneous measurements over 15 minutes stored in the remote transmission stations. It is not so strictly speaking instantaneous measurements.

Calculated measurements are dependent on the presence of valid measurements in the database. So if a direct measurement serving for constructing a calculated measurement is absent, then calculated measurement will be in turn non-valid. All the acquisitions tasks which cannot succeed and which are due to non-valid measurements in the database are announced to the operator by alarms.

6.8.4 Measurements conciliation technique

The measurements reconciliation consists in generating information

representing a physical unit, which will be regarded as credible and reliable by the users. The algorithm used for data validation is made up as shown in Figure 6.3.

6.9 Establishing link between FINESSE SCADA Gateway and CGTC supervisor

FINESSE is able to carry out two types of simulation: either “Off-

Line” simulation where the software employs all the data already entered in its database since the model building stage; or “On-Line” and “Real time” simulation where the software must be connected to the supervisor such as it will look up data necessary for the simulation (Rance, 2002).

The CGTC supervisor data that is at the disposal of FINESSE is mainly:

a- Tanks Level (m) b- Tank inflow or outflow (m3/s) c- Pump pressure (bar) d- Pump flow (m3/s) e- Pump rotation speed (rpm) f- Valve opening (%) g- Water-meters measurements h- Pressure sensors measurements (bar)


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Figure 6.3 : Schema of data conciliation algorithm Each one of these data has its own address to which it is saved in the

database of the supervisor. According to the data storage system of the CGTC, this address is made up of five sub-addresses separated by “points”, for example: TM.07.03.03.00, and PM.03.01.01.02, where:

1) Two characters refer to the “data category”, for example: TM refers

to TeleMeasured one, PM refers to PseudoMeasured one. The “Pseudo” prefix indicates that this measurement is estimated, calculated or derived from one measured value or more. For example if the pumping flow is measured, the pressure can be estimated from the pump characteristic curve.

All estimated data is valid

Acquisition of measurements

Global estimation under constraints: - of positivity of measurements,

- of respect of flows balance.

Calculation of the residues of normalized estimation

Not all estimated data is valid

End of estimating procedure

Sequential estimation of measurements and bias

under constraint:

Verified Test

Non-verified Test

Recalculation of residues considering the bias


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2) Two digits refer to the “Front-end Number” of the interrogated station by the CGTC server.

3) Two digits refer to the “Station Number” interrogated by the Front-

end.

4) Two digits refer to the “Address-Word Number” linked to the station sensor.

5) Two digits refer to the “Number of Bits” in the Address-Word.

In order to carry out “On-Line” simulation, it is necessary to define

the following six elements in FINESSE input data:

A. Simulation Period: the numbers of days for which FINESSE will look up data from the supervisor and perform the simulation. It lies between one and seven days.

B. Simulation timestep: the lapse of time, in minutes, to which FINESSE will carry out calculations. In all cases, the maximum ratio of the simulation period to the timestep must be less than or equal to 168. For example, if the simulation period is seven days (10,080 minutes), the timestep must be at least 10,080/168 = 60 minutes.

C. Curve: this curve represent a data storage and the variation of the stored data (pressure, flow, pump rotation speed, …) over the simulation period at each timestep mentioned above. This curve must be defined by its ID number and it will be automatically filled in during the “On-line” simulation if the data are available in the supervisor.

D. Starting Date of the simulation. E. Supervisor name and address where the data is stored and to which

FINESSE will be connected. F. Data address label in the supervisor. This address should be identical

to that explained above. This address is defined in FINESSE by what is called “Mnemonic”. The schema of Figure 6.4 shows the “Telemetric Link” between

FINESSE and CGTC/SCP supervisor. However, this link is tested in at the CGTC and it was working correctly.


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Figure 6.4 : “Telemetric Link” between FINESSE and CGTC/SCP supervisor

Res_X

Water Level Sensor ( Size = 2 bits )

Address Word N°1

Address Word N°2

Address Word N°3

Address Word N°4

Station N°1

Station N°2

Station N°3

Station N°4

Front-end N°1

Front-end N°2

Front-end N°3

Front-end N°4

CGTC

Alpha Server

( Database )

TM.03.01.02.02

TM.02.01.03.02

TM.01.01.01.02

TM.04.01.02.01

CG

TC

Sup

ervi

sor

FIN

ESS

E S

CA

DA

Inte

rfac

e

7. CHAPTER 7 : Calibration of Pipe Network Hydraulic Model

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CHAPTER 7

7. Calibration of Pipe Network Hydraulic Model

7.1 Introduction Scarcity of water in many countries imposes a rational use of

resources. For this reason, hydraulic network management is very important. Modeling hydraulic network can be very useful in managing the system and making decisions about a system rehabilitation or major expansion. The simulation models, with introducing of SCADA system for an efficient management, have also eased the decision-making process by predicting the behavior of a real water distribution system under existing or modified condition. One of the most important problems concerning the use of the mathematical simulators is determining how well they represent the physical system (Walski, 2003).

The primary objective of a simulation is to reproduce the behavior of a real system and its spatial and dynamic characteristics in a useful way. It is unlikely that the pressures and flows computed by the simulation model will absolutely agree with observed pressures and flows (Pérez, 2001). Significant mathematical assumptions are employed by the simulation software to make the simulation computationally tractable, yet allow the simulated results to be meaningful and useful.

Even though the required data have been collected and entered into a hydraulic simulation software package, the modeler can not assume that the model is an accurate mathematical representation of the system. The hydraulic simulation software simply solves the equations of continuity and energy using the supplied data; thus, the quality of the data will dictate the quality of the results. The accuracy of a hydraulic model depends on how well it has been calibrated.

Calibration is the process of comparing the model results to field observations and, if necessary, adjusting the data describing the system until model-predicted performance reasonably agrees with measured system performance over a wide range of operating conditions (Walski, 2003). The process of calibration may include changing system demands, fine-tuning the roughness of pipes, altering pump operating characteristics,


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and adjusting other model attributes that affect simulation results. Some may assume that calibration can be accomplished by adjusting

only internal pipe roughness values or estimates of nodal demands until an agreement between observed and computed pressures and flows is obtained. Generally speaking, the basis for this claim is that unlike pipe lengths, diameters, and tank levels, which are directly measured, pipe roughness values and nodal demands are typically estimated, and thus have room for adjustment. Numerous factors, however, can contribute to disagreement between model and field observations. Any and all input data that have uncertainty associated with them are candidates for adjustment during calibration to obtain reasonable agreement between model-predicted behavior and actual field behavior.

In the case of water quality models, a match between some observed and predicted water quality parameter such as chlorine or fluoride concentrations is usually used for calibration purposes. However in the case of non-conservative species such as chlorine not only are system-wide concentrations dependent upon the network hydraulics, but they are a function of any reactions that take place in the system. Clearly one can see that calibrating for water quality can greatly increase the level of effort required to obtain a suitable match between observed and computer predicted performance (Walski, 2003).

A discrepancy found during the calibration process can also mean that the system itself has problems. A review of the system should be done before any changes are made to rationally developed model data. Possible system problems are large leaks, previously undetected errors in the metered consumption, errors in recorded pipe sizes, unknown throttled or closed valves, worn pump impellers, or old construction debris left in pipes. Also, discrepancies between the model and observed values are not always a sign of model inaccuracies. Even though data may have come from a SCADA system with several digits of precision, it should not be assumed that the data are accurate to that level.

7.2 Calibration approach The most challenging part of calibrating a model is making

judgments regarding the adjustments that must be made to the model to bring it into agreement with field results. This section introduces methods for making these calibration judgments. The following is a seven-step approach that can be used as a guide to model calibration described by Ormsbee and Lingireddy (Pérez, 2003):


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a. Identify the intended use of the model Identifying the intended use of the model (pipe sizing, operational

studies, design studies, water quality studies) is the first and most important step because it helps the designer establish the level of detail needed in the model, the nature of the data collection, and the acceptable level of tolerance for errors between field measurements and simulation results. Water quality and operational studies require an extended-period analysis; whereas some design studies may be performed using a steady-state analysis.

b. Determine estimates of model parameters

In most models some degree of uncertainty is associated with several

parameters. Parameters to be estimated are those that are less likely to be measured and change within time. Special emphasis will be put on pipe roughness and node demand factors but these could be generalized to pump curves or valves coefficients. Initial estimates of pipe roughness values may be obtained using average values from literature but this information’s specific applicability decreases significantly as the pipes age increases. To obtain initial estimates of roughness it is best to divide the water distribution system into composite zones that contain pipes of similar material and age.

c. Collect calibration data

The most common types of data are those for flow rate, tank water

level and pressure. Depending on the level of instrumentation and telemetry, much of the data may already be collected as part of normal operations. Data collection plays an important role in managing water distribution systems. The main aim of the field data collection planning exercise is to determine what, when, under what conditions, and where to observe the behavior of the system and collect data that, when used for calibration, will yield the best results. This is what is known as a sampling design problem.

Depending on the flow conditions being simulated, the model will have different reactions to different types of data changes. For most water distribution systems, the Hydraulic Gradient Line (HGL) throughout the system (also referred to as the piezometric surface) is fairly flat during average-day demand conditions. The reason for these small headloss is that most systems are designed to operate at an acceptable level of service during maximum day demands while accommodating fire flows. As a result, the pipe sizes are usually large enough that average-day headloss are


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small. For this reason, calibration during average conditions does not provide much information on roughness coefficients and water use. Average conditions do, however, provide insights into boundary conditions and node elevations. During periods when flows through the system are high, such as peak hour flows, pipe roughness and demand values play a much larger role in determining system-wide pressures. Therefore, pipe roughness values, and to a lesser extent demands, should be adjusted during periods of high flow to achieve model calibration.

d. Evaluate model results based on initial estimates of model

parameters Using collected data the model can be evaluated, different simulators

are available (see Chapter 4). The evaluated pressures, flows and tank water levels are then compared with the observed values in attempt to assess model accuracy, and large discrepancies can be addressed simply by looking at the nature and location of differences between the model results and the field data.

e. Perform a rough-tuning or macrocalibration analysis

During macrocalibration the major errors and mistakes are removed.

A human normally performs this task. If measured values are different from the modeled values by an amount significantly excessive, the cause for the difference probably extends beyond errors in the estimates for either pipe roughness or demands. The typical causes are inaccurate plant models such as pumps and reservoirs, incorrect network topology, and incorrect boundary conditions. The only way to adequately address such errors is to systematically review the data associated with the model and compare them with the field data. This stage of calibration is normally done manually using some common sense rules (WSS, 1998). But it can be time-consuming and require skill and judgment. An automatic system could carry out the macrocalibration that concerns the topological and crude errors in the model, or at least could support the task of the experts. In order to perform macrocalibration automatically, the knowledge has to be organized. An expert system allows the diagnosis of errors and finding their causes. Another approach would be the classification of the errors for correction. This automatic system is presented in (Pérez, 2003).

f. Perform a sensitivity analysis

Next, a sensitivity analysis can be conducted to judge how

performance of the calibration changes with respect to parameter


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adjustments. For example, if pipe roughness values are globally adjusted by 10 percent, the modeler may notice that pressures do not change much in the system, thus indicating that the system is insensitive to roughness for that demand pattern. Alternatively, nodal demands may be changed by 15 percent for the same system, causing pressures and flows to change significantly. In this case, time may be more wisely spent focusing on establishing good estimates of system demands. If neither roughness coefficients nor demands have a significant impact on system heads, then the velocity in the system may be too low for the data to be useful for this purpose.

g. Perform a fine-tuning or microcalibration analysis

The parameters to be adjusted in this final phase of calibration are

pipe roughness and nodal demands. Historically, most attempts at model calibration have employed an empirical or trial-and-error approach which can be time-consuming, particularly if there are a large number of pipes or nodes that are candidates for adjustment. Several researchers have proposed different algorithms for use in automatically calibrating hydraulic network models. Most of these techniques have been restricted to steady-state calibration. These techniques have been based on the use of analytical equations, simulation models and optimization methods.

In addition to these standards, the AWWA Engineering Computer Applications Committee (AWWA, 1999) posted some calibration guidelines on its web page. However, each modeling application is unique and requires its own unique set of calibration requirements.

7.3 Calibration methods Several procedures were developed for hydraulic network

calibration, based on analytical and simulation model methods. More recently, different techniques that solve the problem using an optimization procedure were proposed. Model calibration has been a manual task by adjusting the uncertain model parameters on a trial-and-error basis. Because many potential combinations of calibration parameters exist, finding the best set of parameters presents a challenge to the modeler. Therefore, by using a computer-based techniques the modeler can calibrate the system much more efficiently and consistently to achieve as close a match as possible to the field data. Generally, calibration methods can be grouped into the following categories:


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Direct method: This method is the simplest one and is used when the pipe’s roughness is the only unknown parameter and the demands and pressures are measured for all the nodes in the network (as it is the case for “Toulon Est” network) and, hence, the pipe’s headloss and flow are known for all the pipes. For each pipe, the pipe roughness is computed directly from the headloss equation (Darcy-Weisbach formula, Hazen-Williams formula, or Chezy-Manning formula) where the unknown parameter is the pipe’s roughness.

Trial-and-error method (Iterative method): This method is based on some specifically developed, iterative, trial-and-error procedures. Networks that have a small numbers of calibration parameters can be effectively handled. To reduce number of calibration parameters for large network the simplification of the network is typically necessary (Ormsbee, 1986). The convergence rate of the iterative methods is rather slow. However, these iterative procedures are the fundamental principles and guidelines regarding water distribution calibration were used to develop more sophisticated calibration techniques as a result.

Explicit methods (hydraulic simulation methods): is based on solving an extended set of steady-state, mass-balance, and energy equations. The extended set consists of the initial set of equations; those normally used in network simulation models, augmented by a set of equations derived from available head and flow measurements (one additional equation per measurement), and it is solved numerically. The number of unknown calibration parameters is limited by the number of available measurements, so when the number of unknown calibration parameters is larger than the number of available measurements (underdetermined problem), the number of calibration parameters must be reduced by grouping. Explicit calibration methods have several disadvantages and limitations. The calibration problem must be even-determined; that is, the number of calibration parameters must be equal to the number of measurements. Measurement errors are not taken into account and it is difficult to quantify the uncertainty of the estimated calibration parameters (Ormsbee, 1986).

Implicit methods (optimization methods): consists of optimization-based methods. In this case, the calibration problem is represented as an optimization problem by introducing an objective function. The problem is solved implicitly, usually by minimizing the objective function, errors. Errors are calculated as differences between measured and output variables computed by the hydraulic model. Hydraulic models linked to optimization methods are steady-state


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models (single- or multiple-demand condition), extended-period simulation models, or unsteady (transient) models. Transient equations in such cases are much more complicated, especially for huge networks from which their use is not generally extended in simulation, optimization and, generally, in water management procedures (Ormsbee, 1989).

Since the calibration problem could be treated as an optimization one

(Meredith, 1983) and (Pérez, 2003), in the recent years, much research has been directed to developing global optimization methods for automatic calibration of the conceptual models as well as hydrodynamic models. The solution of optimization problem was extensively discussed by many authors in the past. However, the proposed numerical algorithms can be classified into the following categories: Gauss-Newton, Gradient search, and Direct search methods. The direct search method is not very used because the rate of the convergence is generally slow. In the Gauss-Newton method and its variations it is necessary to compute the sensitivity matrix (Jacobian) of the state variables with respect to the unknown parameters at each iteration of the non-linear least square minimization. Gradient search method needs to compute the gradient vector of the objective function with respect to the unknown parameters, instead of the sensitivity matrix, that takes less computer time. Although they can require more iterations for convergence they are usually more efficient. In this respect, population- based algorithms such as Genetic Algorithms (GA), Evolutionary Strategy (ES), and Shuffled Complex Evolution (SCE) have shown to be effective and efficient in locating global optimum of a model with respect to single objective calibration.

One of the approaches to solve a global optimization problem that has become popular during the recent years is the use of the so-called Genetic Algorithms (GA). GA is a robust search paradigm based on the principles of natural evolution and biological reproduction. For optimizing calibration of a water distribution model, a genetic algorithm program first generates a population of trial solutions of the model parameters. A hydraulic solver then simulates each trial solution. The resulting hydraulic simulation predicts the junction pressures and pipe flows at a predetermined number of nodes (or data points) in the network. This information is then passed back to the associated calibration module. The calibration module evaluates how closely the model simulation is to the observed data, the calibration evaluation computes a “goodness-of-fit” value, which is the discrepancy between the observed data and the model predicted pipe flows and junction pressures, for each solution. This goodness-of-fit value is then assigned as the “fitness” for that solution in the GA.


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One generation produced by the GA is then complete. The fitness measure is taken into account when performing the next generation of the GA operations. To find the optimal calibration solutions, fitter solutions will be selected by mimicking Darwin’s natural selection principal of “survival of the fittest”. The selected solutions are used to reproduce a next generation of calibration solutions by performing genetic operations. Over many generations, the solutions evolve, and the optimal or near optimal solutions ultimately emerge.

The integration of GIS and hydraulic modeling software, offers many additional capabilities of analysis and data management. The benefits of the integration are quite evident. The modeler can save a lot of time in constructing a network model making use of all the potential that the GIS offers when it comes to data management, manipulation and analysis. GISRed is an extension to ESRI’s ArcView GIS software that integrates the widely used hydraulic modeling software EPANET 2.0 and a calibration module based on a GA, along with all the original GIS functions. This “built-in” application was originally conceived to make water distribution network models, and be used besides, to perform complex tasks such as importing a whole or partial network from an external source, creating a hydraulic network model and automatically calibrating it.

The modeling of the water network using optimization techniques for the parameter estimation may have convergence problems unless macrocalibration is performed first to remove crude errors.

Models can be calibrated using one steady-state simulation, but the more steady-state simulations for which calibration is achieved, the more closely the model will represent the behavior of the real system. At a minimum, a steady-state calibration should be performed for a range of demand conditions. To improve results further, the model should be calibrated for time-varying conditions using an extended-period simulation. In Chapter 4, the software packages that provided calibration tools are listed in Table 4.1. No further information on these calibration tools such as the algorithms and methods used is available. These were simply the result of the developers not offering any (or insufficient) information (WSS, 2000).

7.4 State estimation of water network The physical water network behavior is monitored through a

telemetry system. However only a limited number of flows and heads are measured directly and they do not constitute a complete picture of the System State. It is therefore necessary to estimate unknown variables based


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on available measurements and mathematical models of the network (Pérez, 2003).

The concept of State Estimation has a long history and occupies a central position in modern control theory. The state can be expressed as the values of given variables. In traditional system description, the number of variables must be equal to the number of equations, and the state is determined as the values of the variables exactly fulfill the equations. In practices however, the number of variables often is not equal to the number of equations. Microcalibration process belongs to a class of State Estimation problems (Pérez, 2003).

The network model is assumed to be represented by flow continuity equations and by pipe flow-headloss characteristics. Some parameters appear in the equations, such as roughness and demand factors. The state estimation problem assumes that these parameters are known so that a model of the network is available. If all of these parameters are not known they will have to be estimated as well and the problem becomes a generalized one, a state and parameter estimation. The calibration process of a network includes the measurement of physical parameters but some parameters have to be estimated. These are generally roughness of pipes and demand distribution factors; this is the state and parameter estimation problem. The main difference between variables and parameters is that the latter are constant in time, assuming a determined time horizon.

7.5 Observability and identifiability of water network Observability is a property of the coupling between the state and the

output. A linear system is observable at t if x(t) can be determined from the output function y(t0,t) (or output sequence) for t0≤t, where t is some finite time. If this is true for all t and x(t) it is called completely observable (Pérez, 2003). Full observability means that the values of all variables are known.

A problem common to all calibration approaches deals with identifiability. The problem of identifiability occurs when an underdetermined calibration problem is being solved. An undetermined calibration problem is when the number of calibration parameters is larger than the total number of independent observations. Similar difficulties may occur even for even-determined or over-determined problems, that is, when there are at least as many observations as calibration parameters. Difficulties occur because the set of available observations simply fails to provide sufficient information for determination of one or more calibration parameters, for example, pressure monitoring points may not be properly located to enable identification of all or some of the parameters (Pérez,


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2003). The identification problem tries to determine parameters such as

roughness and demand coefficients, which are constant (they change in a large period of time). Also it tries to determine the necessary meters that have to be installed in order to have a good calibration but not to increase the cost unnecessarily. When parameters are estimated, identifiability substitutes observability concept. Problems associated with identifiability can be overcome by grouping unknown parameters, for example, pipe roughness coefficients for all pipes that share the same material, diameter, age, and location, or by increasing the quantity of observed information through additional field measurements. Grouping is based on the assumption that pipes laid in roughly the same time period with the same material will have the same roughness properties. Grouping greatly reduces the identifiability problem, but it may introduce errors if the pipes and nodes in a given group should not have the same adjustments applied.

As more measurements are available, namely outputs, the calibration will be possible or easier and more robust. The variables not measured; flows, heads, boundary flows, demands, demand factors and roughness have to be treated as parameters to be determined and a large number of such unmeasured parameters reduce the identifiability of the system.

As the parameters of the network (roughness and demand factors) are constant in time they relate measurements taken in different timesteps. That means that if the same measurements are taken more than once the number of unknown variables increases but not as the number of equations does. So a system that is not identifiable with just one timestep can become identifiable if some timesteps are included. The interest of using more than one timestep in the measurement makes necessary the generalization of the identifiability conditions. The identifiability study should determine; which are the variables that have to be measured, how many timesteps must be taken into account, and which are the conditions in each timestep that make all these measurements useful for the calibration.

Water network’s models are in general non-linear, only in special cases where all heads or flows are measured it will become linear. The approximation by Taylor series drives to the use of Jacobian to study the identifiability of the network (Pérez, 2003).

7.6 Problem formulation for network calibration From a mathematical point of view, the calibration or parameters

identification is an inverse problem, because measurements of state variables are used to determine the unknown parameters by fitting the model output with measurement. However, the optimization methods for


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calibration search for a solution describing the unknown calibration parameters that minimizes an objective function, while simultaneously satisfying constraints that describe the feasible solution region. The objective function usually minimizes the sum of the squares of differences between observed and model-predicted heads and flows.

The total equation number is n = np+nn, where np is the number of pipes, and nn is the number of nodes. In the forewarned problem nodal demands are known and the problem unknowns are nodal heads and pipe flows. They are n, as the equations. We saw in Chapter 5 that these equations represent an algebraic non-linear system of equations, and can be written as:

7.1) (Eq. n ..., 2, 1,i 0 ) x,, x,(xf n21i ==… The unknowns x1, x2,…, xn are nodal heads and pipe flows. System

(Eq. 7.1) can be solved using Newton-Raphson technique. The Jacobian matrix of this system is:

In a calibration problem the network geometry is known, but nodal demands and pipes roughness are unknowns and named calibration parameters. Since function fi of system (Eq. 7.1) depends from the calibration parameters, the system can be written as:

In which p= (p1, …, pnc) is the vector of the calibration parameters.

For solving a calibration problem, it is necessary to have some measurements, likes pipe flows or nodal heads. As said, calibration objective is to choose system parameters so that the differences between observed and computed values are as small as possible. If the vector of those unknown parameters is given as p (roughness, demand), the objective function may be given as:

7.3) (Eq. n ..., 2, 1,i 0 x)(p,f i ==

( )[ ] 7.4) (Eq.)(2

1

*∑=

−=N

iiii pxxwpfMin

7.2) (Eq.

xf......

xf

............

............xf......

xf

A

n

n

1

n

n

1

1

1

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

∂∂

∂∂

∂∂

∂∂

=


123

Where: f(p) = objective function to be minimized p = vector of unknowns N = number of observations wi = weighting factors xi

* = observation (head, flow) xi (p) = model predicted system variable (head, flow) The set of constraints associated with this problem are implicit

hydraulic constraints (continuity and energy loss relationships), known initial conditions (device statuses and tank levels), and boundary conditions (reservoir levels). Rather than explicitly incorporating the equations of conservation of mass and energy into the optimization routine, later approaches have simply called out to a standard hydraulic simulation program to evaluate the hydraulics of the solution. Then the solution is passed back to the optimization routine, where the algorithm computes the objective function, evaluates the constraints, and, if necessary, updates the decision variables. New values of the decision variables are then passed to the simulation routine, and the process is repeated until an acceptable calibration is obtained.

7.7 FINESSE for automatic network calibration The Water Software Systems (WSS) group in Leicester proposed a

microcalibration procedure where the calibration problem is implemented in GAMS programming language to solve the optimization problem. The non-linear programming solver called CONOPT is called by GAMS to solve the calibration problem.

However, the FINESSE calibration module was developed for the purpose of WaterMain project in 1998 to calibrate the Trévaresse network at SCP. This module is not yet robust nor generic and need to be improved; thus it has been removed from the current version of FINESSE. As users of FINESSE, we can not modify its codes nor add new module to its interface.

For these reasons, we looked for another calibration tool. EPANET software was selected because its computational engine can be customized. In addition it is easy to be used and free. EPANET Programmer’s Toolkit is a dynamic link library (DLL) of functions that allow developers to customize EPANET’s computational engine for their own specific needs. The functions can be incorporated into 32-bit Windows applications written in C/C++, Delphi Pascal, Visual Basic, or any other language that can call functions within a Windows DLL. There are over 50 functions that can be used to open a network description file, read and modify various network


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design and operating parameters, run multiple extended period simulations accessing results as they are generated or saving them to file, and write selected results to file in a user-specified format (EPA website).

7.8 Calibrating “Toulon Est” network This section aims to present an automatic trial-and-error calibration

approach of the pipe roughness using EPANET software and to apply it to “Toulon Est” network. For this intention, a visual basic macro was written in MS Excel to perform the calibration process using extended-period measurements of the flows and pressures available from the SCADA system at SCP’s control center. This macro is linked to a simulation model for “Toulon Est” network that was built in EPANET simulation software. The macro will be called here “EPAXL Calibrator” and it will be presented in the following section. This calibration work is divided into two parts:

Part#1: Single-period calibration Part#2: Extended-period calibration

7.8.1 “EPAXL Calibrator” approach

Now, I will present the automatic trial-and-error calibration approach

used in this work to calibrate the pipes roughness for “Toulon Est” network using EPAXL Calibrator. The calibrator is a visual basic macro created in MS Excel. This macro is linked to EPANET software and its function is to prepare the extended-period calibration data (flows and pressures) and export those to the simulation model created in EPANET for the case in hand and it triggers the simulation process and then sends the simulated pressures back to excel and compares them to the measured pressures.

The hydraulic head lost by water flowing in a pipe due to friction with the pipe walls can be computed using one of three different formulas (Rossman, 2000):

Darcy-Weisbach formula Hazen-Williams formula Chezy-Manning formula

The Darcy-Weisbach formula is the most theoretically correct

(Rossman, 2000). It applies over all flow regimes and to all liquids, and it is usually used at SCP to calculate the headloss and hence for these raisons it will be used in this work. Darcy-Weisbach formula uses the following


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equation to compute headloss between the start and end node of the pipe:

Where:

hf = pipe headloss (m) Q = pipe flow (m3/s) D = pipe diameter (m) L = pipe length (m) f = Darcy-Weisbach friction factor

In Chapter 5 (see section 5.3) we introduced Colebrook equation that

expresses the friction factor as a function of relative roughness and Reynolds number (Re) and we saw that there are many implicit and explicit forms for this equation. EPANET uses different methods to compute the friction factor ( f ) depending on the flow’s Reynolds Number (Re):

1. The Hagen–Poiseuille formula is used for laminar flow (Re < 2,000).

2. Or by a cubic interpolation from the Moody Diagram is used for transitional flow (2,000 < Re < 4,000).

3. The Swamee and Jain approximation to the Colebrook-White equation

is used for fully turbulent flow (Re > 4,000).

( ν ) is the water kinematic viscosity and it equals to 1.0x 10-6 m2/s

at 20 °C. ( ε ) is the pipe roughness in mm and this is the calibration parameter.

EPAXL Calibrator has two options for the pipe roughness calibration; Option #1 assumes that all the pipes have the same roughness (ε), and Option #2 assumes that the pipes have different roughness values.

)6.7.(Re64 Eqf =

)7.7.(

Re74.5

7.3

25.02

9.0

Eq

DLog

f

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +

=ε

)8.7.(4Re EqDQ

νπ=

)5.7.(8 252 EqQ

DgfLhf ×=

π


126

A) Option #1: All the pipes have the same roughness We simplify the problem by assuming that the roughness is the same

for all the pipes. The calibration problem is treated as optimization problem where the objective function is that the residuals between measured and simulated pressures are as small as possible. If the pressure is measured at (N) nodes in the system over an extended period (T), the objective function can be given as:

( ) ( )9.7.1 1

),(),( EqPmPsRMinimizeN

i

T

ttiti∑ ∑

= =

−=ε

Where:

period. extended theoflength Tmeasured. are pressures heat which t nodes ofnumber N

pressure. simulated Pspressure. measured Pm

).(Roughness riableunknown va .(Residual) minimize tofunction objective )R(

======

εε

The set of constraints associated with this problem are continuity and

headloss equations. The calibration module attempts to find the roughness at which R(ε) is minimal, and we will call this value as ε optimal. The problem is solved by iteration on ε such that for each value of ε the calibrator will send this value to EPANET and the nodes pressures are evaluated. Then the solution is passed back to the calibration module, where the objective function R(ε) is evaluated. To initiate the calibration process we have to define the minimum and maximum value of ε, and also the increment by which the roughness will grow throughout the calibration process (εminimum, εmaximum, and εincrement). When the objective function is evaluated for all values of ε, the R(ε)minimal and thus ε optimal are determined and then the average of the absolute differences between the simulated and measured pressures ( PΔ ), standard error (σ), and confidence interval (C.I.) are evaluated at ε optimal. The calibration approach is shown in the schema of Figure 7.1. Furthermore, this approach and module described here to calibrate “Toulon Est” network can be used to calibrate pipe roughness for any network.

B) Option #2: Pipes have different roughness values In this option we calibrate the pipes such that each pipe has its own

roughness ε and of course this is closer to the reality than assigning a


127

unique value for all the pipes. For this purpose, the same approach described in the previous paragraph and in Figure 7.3 is applied. But in this case the procedure is executed for each pipe instead of executing it only once for all the pipes as in the first option. However, EPAXL Calibrator is able to do this task automatically. In Option#1 the initial roughness is set to ε i = ε minimum at the beginning of the iteration process, but in this option the calibrator randomly generates and assigns roughness for each pipe within the predefined constrains: ε minimum ≤ ε ≤ ε maximum, this could reduce the time required to find a solution. Then the procedure in Figure 7.1 is repeated for each pipe and at the end of the iteration new ε-values are obtained. For each iteration, the new ε-values are compared to the ε-values obtained from the previous iteration and if the ε-values do not change any more then the process is terminated and an optimal solution is found.

EPAXL Calibrator approach will be applied to “Toulon Est” network to calibrate its mainline roughness and for this purpose a simulation model for the “Toulon Est” mainline was built in EPANET simulation software and it will be introduced in the next section. On the 1st February 2006 the SCP’s Maintenance Division has performed two field measurements test on this network in order to estimate the evolution of the mainline roughness of “Toulon Est”. The results of these field measurements tests will be presented, and then the same field measurements will be provided to EPAXL Calibrator to validate the approach presented here above and the results of this calibration also will be presented, commented on and compared with the SCP results.

7.8.2 Schematic diagram of the mainline of “Toulon Est” network

The mainline of “Toulon Est”, dated from 1970s, is composed of

steel pipe approximately 43 km in length and 1,250 mm to 700 mm in diameter. The water flows under gravity through these pipes. The network has been presented in Chapter 2 of this thesis. All the hydraulic measurements of “Toulon Est” necessary for the calibration and their locations on the mainline are described and indicated in Table 7.1 and Figure 7.2.


128

Figure 7.1 : Calibration approach for pipe roughness

Input

EPANET Network Model

Extended period demand flows

(Q)

Extended period measured pressures

(Hm)

ε bounds: ε minimum ε maximum ε increment

R(ε)minimal = R(ε i) ε optimal = ε i

Calibration Module

Set: i = 1 , R(ε)minimal = ∞ , ε i = ε minimum

Run EPANET and get extended period simulated pressures

Evaluate the objective function R(ε i)

Start

Check

R(ε i)<= Rminimum ?

ε i+1 = ε i + ε increment

i = i + 1

Check ε i > ε maximum ?

Stop

Yes

No

Yes

No

(ε optimal , TN

)R(P optimal

×=Δ

ε , C.I. ) Output

Set Roughness = ε i for all pipes

Export the extended period demands to EPANET


129

7.8.3 Part#1: Single-period calibration In this part we will use a single-period (or a steady-state) field

measurements to estimate the pipes roughness.

Table 7.1 : Description of hydraulic measurements of “Toulon Est”

Symbol Description Comment Q1 Total flow entering the system (m3 /s) Measured Q2 CEO company water demand (m3/s) Measured Q3 Pierrascas tank inflow (m3 /s) Measured Q4 La Bastidette water demand (m3 /s) Measured Q5 Fenouillet tank inflow (m3 /s) Measured Q6 Mont Redon tank inflow (m3 /s) Measured Q7 Golf Hôtel tank inflow (m3 /s) Measured Q8 La Pascalette water demand (m3 /s) Measured Q9 Trapan dam inflow (m3 /s) Measured Q10 La Môle water demand at Point M Measured

P Pressure measurements on the mainline ( bar) Measured q1 , q2 Water demand taken directly from the mainline Non- Measured

Figure 7.2 : Schematic diagram of the mainline of “Toulon Est” network

Legend:

Node q Non-Measured P Pressure Q Water

A

Q1

B C E F G H K T M

Les Laures

Q2

Q3

Q4

Q5Q6 Q7

Q8

Q9

Q10

P

P

P P P

P

q1 q2

Pierrascas Fenouillet Golf_Hôtel

Mont Redon Trapan

CEO La Bastidette La Pascalette

La Môle P

P P


130

7.8.4 SCP’s Maintenance Division calibration tests

The Maintenance Division has performed two field measurements tests on “Toulon Est” network. For the purpose of the tests, water was delivered only to the following consumption points: Point H (Golf Hôtel), Point T (Trapan), and Point M (La Môle). The pressure measurements were made at the following points: A, C, E, F, G, H, K, and T.

The SCP’s Maintenance Division computes pipe roughness by using a pre-prepared commercial excel sheet, named “CLA-VAL SIZING SOFTWARE” and developed by CLA-VAL Company-UK (SCP’s Maintenance Division). It uses Darcy-Weisbach formula (Eq. 7.5) to compute pipe headloss and the friction factor ( f ) is calculated from an implicit commercial formula:

The water kinematic viscosity ( ν ) used to calculate Reynolds

Number from (Eq. 7.8) and the acceleration of gravity (g) are set by default to 1.3 x 10-6 m2/s (at 10 °C) and 10.0 m/s2 respectively. For the purpose of this calibration, we changed these values to be the same as those used in EPANET software (ν =1.0x 10-6 m2/s at 20 °C, g = 9.82 m/s2 where these values are more realistic). The solution finding procedure is not automatic. For each pipe, the user has to manually change the cell assigned for pipe roughness, and the friction factor and, hence, headlosses are computed. Then the user compares the computed headloss with the headloss obtained by field measurement. This process is repeated until the computed headloss is equal to the headloss obtained by field measurement. The results obtained by this procedure for each test are summarized here after.

Test#1_SCP

Table 7.2 : Flow measurements during Test#1_SCP Date and Time Average Flow (l/s)

Q_Point H = 504 l/s

Q_Point T = 570 l/s

Q_Point M = 0 l/s

1st February 2006 10:10 AM - 11:30 AM

Q_Total = 1,074 l/s

( )

)10.7.(

00001.0Re51.2

7.3

25.02

5.0

Eq

fDLog

f

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+

+

=ε


131

Table 7.3 : Calibration results for Test#1_SCP

Pipe Q (l/s)

L (m)

DN (mm)

Pup (m)

Pdown (m)

Hf (m)

ε_SCP#1 (mm)

A-C 1,074 3,063 1,250 20.98 195.48 2.52 3.79 C-E 1,074 2,714 1,050 195.48 237.64 5.93 4.61

E-F 1,074 4,000 1,050 237.64 248.67 7.81 3.11

F-G 1,074 2,264 900 248.67 255.01 9.30 2.42

G-H 1,074 3,774 900 255.01 250.10 14.10 1.69 H-K 570 4,786 700 250.10 231.23 20.70 2.34

K-T 570 7,414 700 231.23 142.52 29.45 1.72

Test#2_SCP

Table 7.4 : Flow measurements during Test#2_SCP

Date and Time Average Flow (l/s) Q_Point H = 0 l/s

Q_Point T = 360 l/s

Q_Point M = 400 l/s

11:30 AM - 12:55 PM 1st feburary 2006

Q_Total = 760 l/s

Table 7.5 : Calibration results for Test#2_SCP

Pipe Q (l/s)

L (m)

DN (mm)

Pup (m)

Pdown (m)

Hf (m)

ε_SCP #2 (mm)

A-C 760 3,063 1,250 21.11 196.99 1.14 2.57

C-E 760 2,714 1,050 196.99 241.81 3.27 6.33

E-F 760 4,000 1,050 241.81 256.90 3.75 2.64

F-G 760 2,264 900 256.90 267.67 4.87 2.83

G-H 760 3,774 900 267.67 269.95 6.91 1.54

H-K 760 4,786 700 269.95 234.55 37.23 2.45

K-T 760 7,414 700 234.55 122.31 52.98 1.80


132

7.8.5 EPAXL Calibrator results

An EPANET simulation model was built for the “Toulon Est” mainline shown in Figure 7.2, then EPAXL Calibrator was executed to calibrate the pipes roughness. The EPAXL Calibrator performed: a steady- state calibration (single-period hydraulic analysis) using the field measurements for Test#1, a steady- state calibration using the field measurements for Test#2, and a calibration using the field measurements for both Test#1 and Test#2. For these calibrations, we set the roughness bounds such that:

(εminimum =0.05 mm) ≤ εoptimal ≤ (εmaximum =10.0 mm)

εincrement =0.05 mm.

For each calibration, in order to estimate the confidence interval for

the pipe roughness we carried out a stochastic analysis. From the pressures measurements we randomly generate new pressures values (Pr) such that:

Pm - σ ≤ Pr ≤ Pm + σ

Where:

Pm = measured pressure (m) Pr = randomly generated pressure (m) σ = standard error of the pressure device (m) The accuracy of the pressure device is about ± 1.0 m, this equals to

3σ, thus σ = 0.3 m. Each time new pressure values generated, EPAXL uses these values to find new roughness values. This procedure is repeated 20 times, and hence 20 values for the roughness are obtained for each pipe and the confidence interval is estimated from these values. The optimal solution (ε-values) and the results of this analysis are summarized in the following tables:


133

Test#1_EPAXL

Table 7.6 : Calibration results for Test#1_EPAXL

Pipe ε_EPAXL#1 (mm) C.I.

A-C 3.50 0.13

C-E 6.00 0.18

E-F 2.70 0.12

F-G 2.30 0.14

G-H 1.60 0.10

H-K 2.35 0.14

K-T 1.70 0.10

Test#2_EPAXL

Table 7.7 : Calibration results for Test#2_EPAXL

Pipe ε_EPAXL#2 (mm) C.I.

A-C 2.55 0.11

C-E 6.35 0.13

E-F 2.85 0.08

F-G 2.60 0.11

G-H 1.50 0.10

H-K 2.55 0.11

K-T 1.70 0.12


134

Test#1 and Test#2_EPAXL Table 7.8 : Calibration results for Test#1 and Test#2_EPAXL

Pipe ε_EPAXL (mm) C.I.

A-C 4.35 0.20

C-E 6.25 0.23

E-F 2.15 0.25

F-G 2.45 0.26

G-H 1.45 0.19

H-K 2.50 0.17

K-T 1.75 0.21

Figure 7.3 : ε_values computed by EPAXL

7.8.6 Calibration results discussion

We will discuss and comment on the calibration results in the following manner:

0

1

2

3

4

5

6

7

Pipe A-C Pipe C-E Pipe E-F Pipe F-G Pipe G-H Pipe H-K Pipe K-T

Rou

ghne

ss (

mm

)

ε_EPAXL# 1ε_EPAXL# 2ε_EPAXL


135

A) First we will compare the ε-values of Test#1_SCP to the ε-values of Test#2_SCP.

B) Then we will compare the ε-values of the Test#1_EPAXL to the ε-values of Test#2_EPAXL. Some remarks on A and B will be made.

C) Then we will compare the ε-values of Test#1_SCP to the ε-values of Test#1_EPAXL.

D) Then we will compare the ε-values of Test#2_SCP to the ε-values of Test#2_EPAXL. Some remarks on C and D will be made.

E) And then we will discuss and comment on the calibration results and the errors and discrepancies between Test#1 and Test#2 and between SCP and EPAXL results; if there is any.

A) Differences between ε_SCP#1 and ε_SCP#2

The ε-values of Test#1_SCP (ε_SCP#1 in Table 7.3) were different from the ε-values of Test#2_SCP (ε_SCP#2 in Table 7.5) and the differences (ε_SCP#2 - ε_SCP#1) are calculated for each pipe section as a percentage of ε_SCP#1, and also the average roughness of the two tests are calculated (έ_SCP):

Table 7.9 : Differences between ε_SCP#1 and ε_SCP#2

Pipe ε_SCP #1(mm)

ε_SCP #2(mm)

Difference(%)

έ_SCP (mm)

A-C 3.79 2.57 -32.2 3.18 C-E 4.61 6.33 37.3 5.47 E-F 3.11 2.64 -15.1 2.88 F-G 2.42 2.83 16.9 2.63 G-H 1.69 1.54 -8.9 1.62 H-K 2.34 2.45 4.7 2.40 K-T 1.72 1.80 4.7 1.76

B) Differences between ε_EPAXL#1 and ε_EPAXL#2

The same is applied on EPAXL where the ε-values of Test#1_EPAXL (ε_EPAXL#1 in

Table 7.6) were different from the ε-values of Test#2_EPAXL (ε_EPAXL#2 in Table 7.7) and the differences (ε_EPAXL#2 - ε_EPAXL#1) are calculated for each pipe section as a percentage of ε_EPAXL#1, and also the average roughness of the two tests are calculated (έ_ EPAXL):


136

Table 7.10 : Differences between ε_ EPAXL#1 and ε_ EPAXL#2

Pipe ε_EPAXL#1(mm)

ε_EPAXL#2(mm)

Difference(%)

έ_EPAXL (mm)

A-C 3.50 2.55 -27.1 3.03 C-E 6.00 6.35 5.8 6.18 E-F 2.70 2.85 5.6 2.78 F-G 2.30 2.60 13.0 2.45 G-H 1.60 1.50 -6.3 1.55 H-K 2.35 2.55 8.5 2.45 K-T 1.70 1.70 0.0 1.70

• Remarks on (A) and (B)

For both A and B the differences are plotted on Figure 7.4. One can see that the differences between ε-values of Test#1_SCP and those of Test#2_SCP are considerable and they lie between 4.7% and 37.3%. The ε-values for Pipes: A-C, E-F, and G-H decreased, while for Pipes: C-E, F-G, H-K, and K-T the ε-values increased. On the other hand, because the same field measurements were used in EPAXL different ε-values were obtained but the differences between ε-values of Test#1_EPAXL and those of Test#2_EPAXL are less and they lie between 0.0% and 27.1%. The ε-values for Pipes: A-C and G-H decreased, while for Pipes: C-E, E-F, F-G, H-K, and K-T the ε-values increased.

Figure 7.4 : Differences between ε_values of Test#1 and Test#2

-40

-30

-20

-10

0

10

20

30

40

Pipe A-C Pipe C-E Pipe E-F Pipe F-G Pipe G-H Pipe H-K Pipe K-TDiff

eren

ce (

%)

ε_SCP ε_EPAXL


137

C) Comparison between ε_SCP#1 and ε_EPAXL#1

The ε_values of EPAXL will now compared to those of SCP for

Test#1 and then for Test#2. The differences between ε_SCP#1 and ε_EPAXL#1 (ε_SCP#1 - ε_EPAXL#1) are calculated for each pipe section as a percentage of ε_SCP#1:

Table 7.11 : Difference between ε_SCP#1 and ε_EPAXL#1

Pipe ε_SCP#1 (mm)

ε_EPAXL#1 (mm)

Difference (%)

A-C 3.79 3.50 7.7 C-E 4.61 6.00 -30.2 E-F 3.11 2.70 13.2 F-G 2.42 2.30 5.0 G-H 1.69 1.60 5.3 H-K 2.34 2.35 -0.4 K-T 1.72 1.70 1.2

D) Comparison between ε_SCP#2 and ε_EPAXL#2

The same as for Test#1, the differences between ε_SCP#2 and

ε_EPAXL#2 (ε_SCP#2 - ε_EPAXL#2) are calculated for each pipe section as a percentage of ε_SCP#2:

Table 7.12 : Difference between ε_SCP#2 and ε_EPAXL#2

Pipe ε_SCP#2 (mm)

ε_EPAXL#2 (mm)

Difference (%)

A-C 2.57 2.55 0.8 C-E 6.33 6.35 -0.3 E-F 2.64 2.85 -8.0 F-G 2.83 2.60 8.1 G-H 1.54 1.50 2.6 H-K 2.45 2.55 -4.1 K-T 1.80 1.70 5.6

• Remarks on (C) and (D)

For both C and D the differences are plotted on Figure 7.5. One can see that the ε-values of EPAXL and SCP are not the same and the differences lie between 0.4% and 30.2% for Test#1, and between 0.3% and 8.1% for Test#2. Roughly speaking, the ε-values of EPAXL are less than those of SCP.


138

Figure 7.5 : Differences between ε_values of SCP and EPAXL

E) Discussion and errors sources

Before passing judgment on EPAXL, let’s first consider the two field measurements and the results obtained by the SCP’s Maintenance Division. The two field measurements were made under controlled conditions and by the same team and with the same measuring devices (flowmeters and pressure sensors). According to the persons who carried out the tests, the main source of errors during the test is due to the accuracies of the measuring devices. The accuracies of the measuring devices are:

Flowmeters: ±1.0% (Scale 4,000 l/s thus ±40 l/s). Pressure sensor ±0.5% (Scale 10 bar thus ±0.05 bar or ±0.5 m) at

Point A. Pressure sensor ±0.5% (Scale 30 bar thus ±0.15 bar or ±1.5 m) at

Points C, E, F, G, H, K, and T.

The devices can be considered accurate. Even though, each test gave ε_values different from the other test as shown in (A) where the difference was up to 40%.

For both tests, the calculated total headloss in the pipes were considered only due to the pipe friction and then they were used in Darcy-Weisbach formula (Eq. 7.5) to calculate the pipe roughness. But in fact, the total headloss is composed of the friction headloss due to the pipe roughness and of the minor headloss due to the pipe fitting (elbows, tees,

-35

-25

-15

-5

5

15

25

35

Pipe A-C Pipe C-E Pipe E-F Pipe F-G Pipe G-H Pipe H-K Pipe K-TDiff

eren

ce (

%)

Test # 1Test # 2


139

valves, etc). The same for EPAXL where in the simulation model for “Toulon Est” built in EPANET the pipe fittings are not considered and only the mainline pipe was modeled. Moreover, the pipe diameters used in these calculations are the nominal diameters of the steel pipes, but in fact a concrete lining was applied to the inner surface of the mainline pipe of “Toulon Est”. The thickness of this lining is estimated between 8 mm and 12 mm.

The roughness obtained by the SCP’s Maintenance Division are computed by using a pre-prepared excel sheet and the formula of (Eq. 7.10) as we mentioned previously (see section 7.8.4). It is clear that this implicit formula is not the same as the explicit formula in (Eq. 7.7) used in EPANET software to compute the friction factor ( f ). To show how this causes some discrepancies between the calibration results of the SCP’ Maintenance Division and that of EPAXL Calibrator the following simulation are performed:

1. The ε-values of Test#1_SCP are passed to the EPANET model of

“Toulon Est” and EPANET is executed and then the differences between the measured pressures (Pm) and simulated pressures (Ps_ε_SCP) are calculated.

2. The ε-values of Test#1_EPAXL are passed to the EPANET model of “Toulon Est” and EPANET is executed and then the differences between the measured pressures (Pm) and simulated pressures (Ps_ε_EPAXL) are calculated.

3. The ε-values of Test#2_SCP are passed to the EPANET model of “Toulon Est” and EPANET is executed and then the differences between the measured pressures (Pm) and simulated pressures (Ps_ε_SCP) are calculated.

4. The ε-values of Test#2_EPAXL are passed to the EPANET model of “Toulon Est” and EPANET is executed and then the differences between the measured pressures (Pm) and simulated pressures (Ps_ε_EPAXL) are calculated.

The results of simulations (1) and (2) are shown in Table 7.13 and

Figure 7.6, and the results of simulations (3) and (4) are shown in Table 7.14 and Figure 7.7. For each simulation the average of the differences between the measured and simulated pressures (average ∆|P|), standard error (σ), and confidence interval (C.I.) are computed. One can note that for both tests the simulated pressures using the ε-values of EPAXL (Ps_ε_EPAXL) are closer to the measured pressures (Pm) than the simulated pressures using the ε-values of SCP (Ps_ε_SCP) as shown in the figures and the tables. Moreover, we perceive that the Ps_ε_SCP is always less than the Pm and the deviation from Pm increases, almost exponentially,


140

as we move downstream the mainline from Point A to Point K. In fact, this is because of that the ε-values of SCP passed to the simulation model are not computed by using the same formula in EPANET as we mentioned in the previous paragraph, and since these values are a little higher than those of EPAXL Calibrator the headloss are also a little higher in each pipe and this additional headloss accumulate as one moves downstream the mainline from Point A to Point K.

Table 7.13 : Difference between measured and simulated pressures –Test#1

Point Pm (m)

(Pm) - (Ps_ε_SCP) (m)

(Pm) - (Ps_ε_EPAXL) (m)

A 20.98 0.00 0.00 C 195.48 0.07 -0.05 E 237.64 0.10 0.46 F 248.67 0.15 0.18 G 255.01 0.21 0.08 H 250.10 0.26 -0.08 K 231.23 0.32 0.01 T 142.52 0.44 0.04 Average ∆|P| = 0.19 0.13

Stander error σ = 0.14 0.15 Confidence Interval CI= 0.10 0.10

Figure 7.6 : Difference between measured and simulated pressures –Test#1

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

A C E F G H K T

Pres

sure

Diff

eren

ce (m

)

(Pm) - (Ps_ε_SCP)

(Pm) - (Ps_ε_EPAXL)


141

Table 7.14 : Difference between measured and simulated pressures –Test#2

Point Pm (m)

(Pm) - (Ps_ε_SCP) (m)

(Pm) - (Ps_ε_EPAXL) (m)

A 21.11 0.00 0.00 C 196.99 0.03 0.00 E 241.81 0.05 0.01 F 256.90 0.09 0.10 G 267.67 0.12 0.01 H 269.95 0.27 -0.01 K 234.55 0.54 0.51 T 122.31 0.84 -0.16 Average ∆|P| = 0.24 0.11

Stander error σ = 0.30 0.18 Confidence Interval CI= 0.21 0.12

Figure 7.7 : Difference between measured and simulated pressures –Test#2

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

A C E F G H K T

Pres

sure

Diff

eren

ce (m

)

(Pm) - (Ps_ε_SCP)(Pm) - (Ps_ε_EPAXL)


142

7.8.7 Part#2: Extended-period calibration

In this part we will perform an extended-period calibration to

estimate the pipes roughness by using extended-period measurements of the flows and pressures available from the SCADA system at SCP’s control center for “Toulon-Est” network.

7.8.8 Continuity equation

We will apply the continuity equation to the “Toulon Est” network;

in other words, the total flow entering the network at Point A (Les Laures) must be equal to the total demands leaving the network. The continuity equation can be written like this:

7.11) (Eq.

q2) (q1 Q10 Q9 Q8 Q7 Q6 Q5 Q4 Q3 Q2 Qout Q1Qin :Where

Q Q outin

⎪⎪⎭

⎪⎪⎬

⎫

++++++++++==

=

For the non measured demand q1 and q2 we do not have records for

these demands, but however they are very small with respect to the other measured demands and thus they will be neglected in this calibration.

Another parameter that doesn’t appear in the right-hand side of (Eq. 7.11) is the “unaccounted-for water” (the portion of total consumption that is lost due to system leakage, unmetered services, or other causes). According to the SCP’s Maintenance Division this portion is approximately 8% of the total consumption.

The calibration data that used here are the hourly measured flows (Q) and pressures (P) for three selected periods:

- From 1st to 7th of April 2005. - From 1st to 7th of August 2005. - From 1st to 7th of October 2005.

First of all, we will check the validity of the continuity equation (Eq.

7.11). Figure 7.8 shows the hourly Qin and Qout during these selected periods. Then, the differences between Qin and Qout (∆Q) are calculated and plotted in Figure 7.9. The average ∆Q is about -2.4 ± 2.3 l/s.


143

Figure 7.8 : Hourly total water demand – Toulon Est, Year 2005 Figure 7.9 : Differences between system inflows and outflows

7.8.9 Extended-period calibration approach We will perform two extended-period calibrations using the demand

flows and pressures for the previously mentioned periods. The first calibration is a direct approach and the second one is EPAXL Calibrator approach.

A. Direct approach

1st to 7th of April 2005 1st to 7th of August 2005 1st to 7th of October 2005

Hou

rly d

eman

d (m

3 /s)

0.0

0.5

1.0

1.5

2.0

2.5

Qin

Qout

∆Q = (Qout - Qin )

1st to 7th of April 2005 1st to 7th of August 2005 1st to 7th of October 2005

∆Q (

m3 /s

)

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08Average ∆Q=-2.4

∆Q C.I. =2.3 l/s


144

As one can see on the hydraulic schema of “Toulon Est” (Figure 7.2) the pressures are measured at the start and end node of each pipe (except for pipe K-T and pipe T-M where no pressure data is available at the SCP’s control center) and the pipe’s flow can be calculated from the continuity equation at each node. Therefore, the pipes can be calibrated easily. From the pressure measurement at the start and end node for a pipe we compute the total head at each node (node’s elevation + node’s pressure), and the difference between total head at the start and end node is the headloss in that pipe (hf). The roughness can be obtained in two manners:

A.1 Linear regression

Let’s rewrite Darcy-Weisbach formula given by (Eq. 7.5) like this:

Where : 52

8Dg

fLkπ

= and the friction factor ( f ) is computed from

Colebrook-White equation (Eq. 7.7) and it depends on the pipe flow (Q). However, for Reynolds Number Re > 25,000 and relative roughness (ε/D > 3.5 x 10-5) the Colebrook-White equation can be reduced to:

(Eq. 7.7) is plotted against (Eq. 7.13) on Figure 7.10. The differences between friction factors computed by the two equations are less than ±3%.

Figure 7.10 : Colebrook vs. simplified friction factor equations

)12.7.(2 EqeQkhf +=

)13.7.(1006.1

7.3

25.0ˆ2

5

Eq

DLog

f

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ×+

=−ε

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

f

f

9998.0

ˆ 1.00082 =

=

Rff


145

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Q2 (m6/s2)

hf (m

)

R-Squared = 0.93

Thus, the friction factor is not anymore function of the pipe flow and

if we perform linear regression between (hf) and (Q2) for each pipe, the slope k of (Eq. 7.12) can be estimated and, hence, the friction factor f and then the pipe roughness ε also can be estimated. The small e that appears in (Eq.7.12) is the intercept with the vertical abscissas (hf) and it must be zero in the ideal case.

Linear regression results

The linear regression and parameters estimation were carried out

using the statistical analysis software “NCSS” (Hintze, 2005) and the results are summarized in Table 7.15. The headloss (hf) are plotted versus the pipe’s flows squared (Q2) for each pipe as shown on the figures below:

Table 7.15 : Results for linear regression parameters estimation - 2005

Pipe L (m) D (mm) k (s2 /m5) f ε_Reg_05 (mm) e (m)

Pipe A-B 1,050 1,250 0.948 ± 0.023 0.033 8.44 ± 0.66 2.767 ± 0.060

Pipe B-C 665 1,000 1.717 ± 0.053 0.031 4.94 ± 0.53 0.465 ± 0.081

Pipe C-E 2,716 1,050 5.317 ± 0.125 0.030 4.76 ± 0.40 0.718 ± 0.138

Pipe E-F 3,964 1,050 7.239 ± 0.251 0.028 3.60 ± 0.47 1.762 ± 0.217

Pipe F-G 2,264 900 9.038 ± 0.291 0.029 3.24 ± 0.39 -0.777 ± 0.195

Pipe G-H 3,774 900 13.718 ± 0.432 0.026 2.32 ± 0.29 0.306 ± 0.245

Pipe H-K 4,789 700 71.570 ± 2.049 0.030 3.17 ± 0.32 -0.765 ± 0.557

Figure 7.11 : hf vs. Q2 for Pipe A-B


146

-1.0

1.0

3.0

5.0

7.0

9.0

11.0

13.0

15.0

0.0 0.5 1.0 1.5 2.0 2.5

Q2 (m6/s2)

hf (m

)

R-Squared = 0.93

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Q2 (m6/s2)

hf (m

)

R-Squared = 0.88

Figure 7.12 : hf vs. Q2 for Pipe B-C

Figure 7.13 : hf vs. Q2 for Pipe C-E


147

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Q2 (m6/s2)

hf (m

)

R-Squared = 0.86

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Q2 (m6/s2)

hf (m

)

R-Squared = 0.87

Figure 7.14 : hf vs. Q2 for Pipe E-F

Figure 7.15 : hf vs. Q2 for Pipe F-G


148

-1.0

1.0

3.0

5.0

7.0

9.0

11.0

13.0

15.0

17.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Q2 (m6/s2)

hf (m

)

R-Squared = 0.88

-3.0

2.0

7.0

12.0

17.0

22.0

27.0

32.0

37.0

0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5

Q2 (m6/s2)

hf (m

)

R-Squared = 0.90

Figure 7.16 : hf vs. Q2 for Pipe G-H

Figure 7.17 : hf vs. Q2 for Pipe H-K


149

Discussion of linear regression results

In the ideal case where the pressure and flow measurements are

accurate then plotting (hf) versus (Q2) must perfectly fit a straight line whose intercept is equal zero. In practice, nothing is ideal and the measuring devices are not perfectly accurate and, hence, there are always errors in the measured parameters. As shown on the figures from the linear regression performed here, the points (hf, Q2) are not perfectly linear as R-squared between 0.86 and 0.93, and the intercept (e) is not null. This mainly is because of the errors in the measured pressures and flows and also because of the fact that we did assume that the headloss are only due to the friction in the pipe and we ignored the loss due to pipe fittings.

For Pipe A-B, the intercept was significant (2.767 m) and the estimated roughness was high (8.44 ± 0.66 mm) and this is because in the reality there is an electromagnetic flowmeter, a butterfly control valve and filter in proximity to point A (see Figure 2.3) and the headloss in these device is important even it might be higher than the friction headloss. However, for Pipe F-G and Pipe H-K the intercepts were negtive and relativly small (-0.777 ± 0.195 m for Pipe F-G, and -0.765 ± 0.557 m for Pipe H-K) and this might be explained by that the errors are more important than the fitting headloss in these two pipes.

A.2 Equation inversion

From Darcy-Weisbach formula given by (Eq. 7.5) we can obtain: Also, from the reduced Colebrook-White equation (Eq. 7.13) we can

obtain: Substitute (Eq. 7.14) in (Eq. 7.15) :

)14.7.(8 2

52

EqQh

LDgf f×=

π

)15.7.(1006.1107.3 5ˆ5.0

EqD f

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡×−= −

−

ε

)16.7.(1006.1107.3 58

5.0

2

52

EqD Q

hLDg f

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×−= −×

−

π

ε


150

This inverted equation explicitly states pipe roughness (ε) as a

function of pipe headloss (hf), flow (Q), length (L), and diameter (D). For each pipe and for each pair (hf, Q) from the extended-period measurements of the flows and pressures available from the SCADA system at SCP’s control center for the previously mentioned periods, a roughness value can be computed. Then, the average roughness and its confidence interval can be estimated for each pipe. The results are summarized in Table 7.16:

Table 7.16 : Calibration results for equation inversion

Pipe ε_EqIn_05 (mm)

Pipe A-B 310.08 ± 28.16 Pipe B-C 24.53 ± 4.93 Pipe C-E 16.95 ± 3.83 Pipe E-F 17.22 ± 1.94 Pipe F-G 3.84 ± 1.22 Pipe G-H 7.10 ± 2.07 Pipe H-K 5.80 ± 1.90

The roughness values obtained by equation inversion are very large

for Pipe A-B, B-C, C-E, and E-F; even they are not physically possible. This is not due to the equation inversion but it is due to the errors in the measured pressures and flows and also because we did assume that the headloss are only due to the friction in the pipe and we ignored the loss due to pipe fittings. The inverted equation (Eq. 7.16) is a mathematical solution for pipe roughness and considers the headloss and flow as being accurate. If we assume that the error in the measured pressures plus minor headloss for Pipe A-B are roughly 2.0 m and we subtract this from the calculated headloss and recalculate the roughness, the recalculated roughness will be 70% less; i.e. ε = 93.74 mm instead of ε = 310.08 mm). Therefore, (Eq. 7.16) can be used only when the measurements are accurate enough.

B. EPAXL Calibrator

EPAXL Calibrator was executed to perform an extended-period

calibration using the demand flows and pressures records for the periods mentioned previously. For this calibration, we set the roughness bounds such that:

(εminimum =0.1 mm) ≤ εoptimal ≤ (εmaximum =15.0 mm)


151

εincrement =0.05 mm. As we did before and in order to estimate the confidence interval for

the pipe roughness we carried out a stochastic analysis as described in section (7.9.2).

B.1 EPAXL Calibrator results In this calibration, the time needed to find a solution is quite long

because the size of the problem is relatively large as there are 7 nodes and 504 pressure measurements at each node, and 7 pipes and 300 possible values for the roughness for each pipe. It took about 8 hours to solve the calibration problem of “Toulon Est”. The pipes roughness values computed by EPAXL and their confidence intervals are listed in Table 7.17:

Table 7.17 : Results for EPAXL Calibrator - 2005

Pipe ε_EPAXL_05 (mm)

Pipe A-B 7.10 ± 0.38

Pipe B-C 11.15 ± 0.47

Pipe C-E 9.15 ± 0.47

Pipe E-F 6.80 ± 0.39

Pipe F-G 4.40 ± 0.21

Pipe G-H 2.60 ± 0.12

Pipe H-K 2.75 ± 0.12

B.2 Comparison between linear regression and EPAXL Calibrator results

The simulated pressures computed by using the roughness obtained

from linear regression (ε_Reg_05) and the simulated pressures computed by using roughness obtained by EPAXL (ε_EPAXL_05) were compared to the measured pressures for each point and they are plotted on the figures below:


152

152

153

154

155

156

157

158

159

160

161

162

P_MeasuredP_EPAXLP_Regression

April 2005 August 2005 October 2005

Pres

sure

(m)

182

184

186

188

190

192

194

196

198

200



Pres

sure

(m)

Figure 7.18 : Measured and simulated pressures at Point B

Figure 7.19 : Measured and simulated pressures at Point C


153

220

225

230

235

240

245

250



Pres

sure

(m)

Figure 7.20 : Measured and simulated pressures at Point E

Figure 7.21 : Measured and simulated pressures at Point F

220

225

230

235

240

245

250

255

260

265

270



Pres

sure

(m)


154

Figure 7.22 : Measured and simulated pressures at Point G

Figure 7.23 : Measured and simulated pressures at Point H

220

230

240

250

260

270

280

290



Pres

sure

(m)

220

230

240

250

260

270

280

290

300



Pres

sure

(m)


155

0

1

2

3

Point B Point C Point E Point F Point G Point H Point K

Δ

Figure 7.24 : Measured and simulated pressures at Point K

It can be seen that the simulated pressures are, generally speaking,

higher than the measured pressures. However, the simulated pressures of EPAXL (Ps-EPAXL) are a bit closer to the measured one than those of linear regression (Ps-Reg) and since this is not seen clearly on the figures hereabove we calculate delta (Δ) as:

If delta is less than 1.0 this means that the Ps-EPAXL is the closest to

the Pm and if delta is greater than 1.0 this means that the Ps-Reg is closest to the Pm. As shown on Figure 7.25, the delta’s values are less than 1.0 in most cases.

Figure 7.25 : Calculated delta’s values (Δ)

200

210

220

230

240

250

260

270

280

290

300



Pres

sure

(m)

)17.7.(P - P

P - P

s_Regm

s_EPAXLm Eq=Δ


156

7.9 General discussion and conclusion

From this calibration work we obtained four values for roughness for

each pipe, which are: - The average roughness obtained by SCP’s Maintenance Division

from the two field tests for year 2006 (έ_SCP in Table 7.9). - The average roughness obtained by EPAXL Calibrator of the two

field tests for year 2006 (έ_EPAXL in Table 7.10) - The roughness obtained from linear regression for year 2005

(ε_Reg_05 in Table 7.15) - The roughness obtained by EPAXL for year 2005 (ε_EPAXL_05

in Table 7.17) These values are summarized in Table 7.18 and Figure 7.26:

Table 7.18 : Summary of ε_values for calibration 2005 and 2006

Pipe ε_Reg_05 ε_EPAXL_05 έ_SCP_06 έ_EPAXL_06

Pipe A-B 8.44 7.10 3.00 3.03 Pipe B-C 4.94 11.15 3.00 3.03 Pipe C-E 4.76 9.15 5.80 6.18 Pipe E-F 3.60 6.80 2.85 2.78 Pipe F-G 3.24 4.40 2.80 2.45 Pipe G-H 2.32 2.60 1.70 1.55 Pipe H-K 3.17 2.75 2.55 2.45 Pipe K-T # # 1.85 1.70

Figure 7.26 : Comparison between the ε_values 0

2

4

6

8

10

12

Pipe A-B Pipe B-C Pipe C-E Pipe E-F Pipe F-G Pipe G-H Pipe H-K Pipe K-T

Rou

ghne

ss (m

m)

ε_Reg._05 ε_EPAXL_05

έ_SCP_06 έ_EPAXL_06


157

One may ask “what are the true pipes roughness?”. In the single-

period calibration (2006) we compute the roughness that satisfy only two field measurements while in the extended-period (2005) we compute the roughness that satisfy a wide-rang operation conditions, but the flows measurements were more accurate in the single-period calibration since the measurements were made under controlled conditions, and in the extended-period calibration the flows measurements are less accurate because of the unaccounted-for water which is around 8%. However, the maximum and minimum of these four values for roughness could give an idea about the range within which the true roughness falls.

One must be careful when using pipe headloss hf to estimate the pipe roughness. The problem of hf is that the hf is computed such that:

hf =(Pup + Zup) – (Pdown + Zdown) (Eq. 7.18)

Where Pup and Zup are the pressure and the elevation of the upstream node, and Pdown and Zdown are the pressure and the elevation of the downstream node. If we assume that the elevations are exact but the error in the pressure measuring device is about ±0.5 m and the headloss are around 1.65 m (pipe of L =1,000 m, D =1.0 m, ε =1.0 mm, Q =1.0 m3). If the errors committed in measuring Pup and Pdown have, luckily, the same magnitude and sign then the hf will be correct. However, if the error in measuring Pup is equal to +0.25 m and the error in measuring Pdown is equal to -0.25 m then the error in hf will be +0.50 m and this is about 30% of the computed parameter hf.

Also, this calibration work shows how difficult is the calibration process of the hydraulic model for water pipe network; even for a simple network like “Toulon Est” network, where there is no loops and the state of the system is well-identified (i.e. nodes demands and pressures and pipes flows are known in space and in time) and there is only seven parameters to be calibrated (roughness). However, when the system contains many pipes and loops and not only the pipes roughness are the calibration parameters but the nodes demand factors are to be calibrated too, and if there is a limited number of pressure and flow measurements in the system, then the calibration process is a real challenge to the modeler. Regarding EPAXL Calibrator, the algorithm presented here needs to be improved to be faster and more robust.

Finally, the calibration process understands some choices and parameters that have an effect on this process, such as:

- Headloss equation: Darcy-Weisbach or Hazen –Williams equation?


158

- Pipe diameter: Nominal pipe diameter or inner pipe diameter? - Water kinematic viscosity: 1.0 x 10-6 m2/s or 1.3 x 10-6 m2/s? - Acceleration of gravity: 9.82 m/s2 or 10.0 m/s2? - Pressure: 1.0 bar is 10.0 m or 10.2 m? - Friction factor: implicit or explicit Colebrook-White formula? - Extended or single period calibration? - Accuracy of the measuring devices? - Node’s elevation: is the datum the bottom, the center line or the

top of the pipe? - Minor and fitting headloss? - Calibration approach to be implemented?

8. CHAPTER 8 : Demand Prediction

159

CHAPTER 8

8. Demand Prediction

8.1 Introduction The term “Prediction” or “Forecasting” is the estimation of the value

of a variable or set of variables at some future point in time. A forecasting exercise is usually carried out in order to provide an aide to decision-making and planning the future. Typically all such exercises work on the premise that “if we can predict what the future will be like we can modify our behavior now to be in a better position, than we otherwise would have been when the future arrives”. However, forecasting techniques are applied in some of life’s domain, for example inventory control and production planning where forecasting the demand for a product enables to control the stock of raw materials and plan the production schedule, investment policy for forecasting financial information such as interest rates, exchange rates and the price of gold, economic policy for forecasting economic information such as the growth in economy, unemployment and the inflation rate, and water demand forecasting for effective water resources planning and management. All these forecasting exercises are vital both to government and business in planning the future (Opitz, 1998), (Baumann, 1998), and (Weigend, 1994).

One way of classifying forecasting problems is to consider the timescale involved in the forecast, in other word, how far forward into the future we are trying to forecast. Short, medium and long-term are usual categories but the actual meaning of each will vary according to the situation that is being studied, for example in forecasting energy demand in order to construct power station 5 to 10 years would be short-term and 50 years would be long-term, while in forecasting costumer water demand in many water distribution systems up to one month would be short-term and over a couple of years long-term (Ani, 2003). The terms “Forecasting” and “Prediction” will be used alternatively throughout this chapter.

8.2 Water demand prediction Prediction of consumer demands is a pre-requisite for water


160

resources demands management and planning, and also for water optimal control of water supply and distribution systems. The main objectives of demand forecasting are management and conservation of natural water resources, and optimization of water supply (Guhl, 1999).

A water utility’s primary purpose is to provide water to its customers, but it must also plan for its customers’ future water needs. A critical aspect of this planning is predicting short-term, medium-term, and long-term water demands and optimizing the water supply system to meet these demands and also managing water demands and supplies in the future. Moreover, understanding the magnitude and location of future water demands, and any potential changes from existing water demands, allows to develop recommendations that will meet or manage demands for water quantity and quality into the future (Ani, 2003). If changes in water demand can be predicted, the inflow can be changed in advance and the operation becomes more effective and efficient. For this reason, anticipation is often used to improve the control response.

Making more efficient use of existing water resources through demand management is an economical and environmentally responsible way to meet growing demand for water. Water conservation is an important component of managing water demands and supplies in the future. Agricultural practices could achieve conservation at an on-farm level e.g., by reduction of applied water, and at a district level e.g., through such methods as canal lining, spill recovery, and automation (AWWA, 2001).

Water demand forecasts are used in many areas of utility planning. These demand forecasts can contribute to identifying appropriate management alternatives in balancing supply and demand. From small utility models to long-term interstate resource management, reliable forecasts are critical components of water planning and policy. To be reliable, water demand forecasts must include social, economic, and environmental factors. The use of such forecasts has become standard, particularly when considering new water resource supplies. Forecasting water demand is inherently challenging, as the factors that most directly affect water demand are difficult to predict. Viewed in its simplest form, future water demands are a function of a region’s population, the growth or decline of its industrial activity, technological changes, code changes, water pricing, and changes in outdoor water use associated with weather and landscaping choices. Unforeseen events significantly impact these factors (Ani, 2003) and (Jowitt, 1992).

Water demand forecasts are essential to many planning activities including expansion, expanding existing distribution systems, preparing contingency plans for droughts, evaluating conservation methods, performing sensitivity analysis using different assumptions about the explanatory variables, and assessing utility revenues (Ani, 2003). In


161

addition to these applications, forecasts also play an important role in cases related to climate change where demand forecasts will be critical to providing information about the future of regional water resource demands and how they should be distributed.

Today, water demand forecasting has become an essential ingredient in effective water resources planning and management. Water forecasts, together with an evaluation of existing supplies, provide valuable triggers in determining when, or if, new sources of water must be developed. However, the cost of securing new water supplies has grown dramatically (Ani, 2003). Forecasts also provide an opportunity to organize important utility information and demand data. With increasing acclaim and accuracy, demand forecasting may guide communities toward a more sustainable future in water resources.

Demand forecasting became necessary as urban populations dependent on public water supplies grew rapidly. New demands for water could not always be met. In some cases, water infrastructure required long lead times to construct, requiring long planning horizons. In other cases, multiple options for water supply existed and the optimal choice depended on understanding likely future requirements. In either case demand forecasting was a means to optimize expansion of the water supply system (Opitz, 1998).

Other water resource issues that would benefit from water demand forecasts include water conflicts. For example, California continues to struggle with limited state resources, a contract battle over the Colorado River and growing urban populations, demand forecasts are useful to decisions about water transfers, contract battles, and new techniques in water conservation in agriculture (Ani, 2003).

Though water demand forecasts are rarely used as the only determining factor in resource planning, forecasts can prevent utilities from making needless investments and policy errors in development (AWWA, 2001).

For the purpose of this thesis, we will focus on the water demand prediction for water distribution systems. In a typical water distribution system, the source of water might be a lake, river, underground well or canal. Water is delivered to the distribution system either by gravity or pumped directly form the source to the distribution system or is pumped to reservoirs at a number location in the system and then is pumped from the reservoirs to the distribution system, or to another reservoir. Pressures and rates of flow throughout the system can be controlled by means of pumps and valves housed in pumping station. The human operator, who controls the operations of the distribution system, uses sometimes heuristics or rule of thumb to optimize the water supply. Documenting the heuristics of the most experienced expert operators in an expert system is one way to reduce


162

operating costs and improve the supply and distribution of water. In order to develop an expert system for monitoring and control of the water distribution system, we conduct knowledge acquisition through interviews with human experts and obtained heuristics for effective water utility operations. Analysis of these heuristics indicates that it is important that short-term forecasts of water demand is accurately estimated in order that the optimization of water supply and effective operation may be derived. The inaccurate demand estimations by the experience of the experts possibly results in insufficient operations of the water distribution system, and the lack of knowledge on water demand prediction translates to a gap in the knowledge base of the expert system and, thus, manual knowledge acquisition by itself is inadequate for handling all situations that may arise in a complex engineering application (An, 1995).

Therefore, resource engineers have developed predictive models that guide our management of water supply and demand. Predictive models have become commonplace in all phases of planning, providing resource managers guidance for the various possible futures (Law, 2000). The goal is to create a predictive model that appropriately captures the uncertainty of the future and guides decision making. Forecast models are primarily dependent on the data available and the model’s intended use. The complexity of a model hinges on the level of detail in the data required by the model. However, a more complex model is not always more appropriate.

Water demand models can have various timesteps: long (annual or decadal), medium (monthly to annual), or short term (hourly, daily, or weekly) (AWWA, 1996). For the purposes of this study, we focus on short-term models, more precisely daily demand prediction.

Water resource engineers commonly use the past as a guide to the future, planning as if events that have not occurred are unlikely to occur. However, the future’s uncertainty has required planners to predict water demand two or three decades into the future. Past, long-term forecasts have allowed resource managers to be generous in their estimates of water demand. Long-term water demand modeling is a difficult task; it requires robust data sets and consideration of uncertain climate, economic, and cultural conditions. Therefore, water resource managers felt the professional responsibility to generate demands that were unlikely to be exceeded. For example, during the post-World War II years, resource managers and planners typically chose the largest feasible project. While population and the economy grew, such decisions were justifiable (DeKay, 1985). Now, however, we find population growth more stable and significant environmental considerations. These changes have caused many water resource managers to rethink long-term demand planning.

Long-term models are helpful for supply planning, reservoir or urban


163

infrastructure changes (i.e., water mains, transfer pipes, etc.), extended conservation programming or plumbing code changes, and regional urban planning and development. Unlike short-term models, long-term water demand models do not contribute to near-term or seasonal operations’ policies regarding drought, instream flows, or climate variability. Instead, long-term models provide extended foresight for resource managers to address overall system capacity and management (Bauman., 1998).

Long-term models usually focus on forecasts for 10 or more years into the future. These models help managers determine long-term infrastructure or supply changes while considering variables such as changes in population, price structure, or climate change. While these forecasts are critical to future management, such forecasts are often highly uncertain. Of course, the greater the forecast time (i.e., 30 years, 40 years), the less accurate the forecast or predictive variables tend to be.

Unlike the long-term vision of the decadal model, the medium-term model typically investigates periods of less than one year. These models may be used to examine the impacts of climate variability and planned seasonal operations or financial changes. Medium-term models are often quite accurate, but may be plagued by unexpected changes in weather or sociologic factors.

Short-term demand projections help water managers make more informed water management decisions to balance the needs of water supply, residential, industrial, and agricultural demands, and instream flows for fish and other habitat. Short-term demands aid utilities in planning and managing water demands for near-term events (Jain, 2002). Short-term forecasting can also help managers make decisions during unexpected climate conditions, emergencies, or unanticipated financial change. Short-term forecasting models are typically based upon recent trends and actual conditions. Short-term method of modeling water demands plays an important role in seasonal water resource management techniques (Bauman, 1998) and (Billings, 1996).

The short-term model demonstrates the importance of several independent variables: temperature, precipitation, and water use. A long-term model often uses additional household characteristics such as income, size (number of people), house age, housing density (number per km2), water price, etc. These variables are more likely to change on an annual or decadal basis, whereas the short-term model accounts for data variation within a shorter time-frame. Most long-term water demand models refer to a handful of standard model variables from the most influential categories: population, economy, technology, climate, water price, conservation, housing characteristics, and land-use (AWWA, 1996).

Moreover, in the water demand forecasting one should consider the methods by which water is distributed to the users. In water distribution


164

systems, there are three water delivery methods which can be distinguished according to the degree of freedom given to the water users in choosing the flow rate, duration, and frequency of water delivery. Clemmens (1987) describes various water delivery schedules, with their intended flow rate, duration, and frequency:

- Proportional water distribution: this method consists in distributing

water in proportion to the size of supplied area or to the water rights. This method is applied in Pakistan and India and known as “Warabandi”.

- Rotational schedule water distribution: in this method, the users get

water according to a pre-prepared rotation schedule. It has very little or no flexibility built into it, and the flow rate, duration, and frequency are therefore fixed. This method is the simplest for the managers, but the most rigid for the users, and it is the most popular one in the world. This method is applied in the Jordan Valley.

- On-demand water distribution: this method allows the users to get

water when they want, and thus the flow, duration, and the frequency are flexibles. Only the value of the maximum flow is fixed. This method is particularly applied to the pressurized networks as in Canal de Provence Company in France.

Generally speaking, the estimation of the future demand will depend

on the method by which water is distributed to the users.

8.3 Prediction methodology and techniques While predicting the future is impossible, there are wide range

techniques for thinking about what might happened, and how we can influence that. More than one hundred and thirty principles are used to summarize knowledge about forecasting. They cover formulating a problem, obtaining information about it, selecting and applying methods, evaluating methods, and using forecasts. Each principle is described along with its purpose, the conditions under which it is relevant, and the strength and sources of evidence (Armstrong, 2001).

Statisticians spend much time on the development of methods for time-series forecasting. According to Fildes and Makridakis (Fildes, 1995), few statisticians even address whether their models can be applied to forecasting (Fildes, 1995). In their survey of the literature, they estimated that about 21% of the time-series papers addressed forecasting issues.


165

When they looked at the time-series forecasting papers published in the Journal of the American Statistical Association from 1971 to 1991, only about 10% looked at out-of-sample forecast accuracy, and only 11% made forecasting comparisons against reasonable alternative approaches (Yurkiewicz, 2004). In general, forecasting methods can be classified into three different categories:

• Qualitative method

Where there is no formal mathematical model, often because the data available is not enough to be representative of the future long-term forecasting. Qualitative methods rely on judgment, intuition, and subjective evaluation (Ernest, 2001). Among the major techniques within this category are market research (surveys), Delphi (panel consensus), historical analogy, and management estimation (guess). Not everyone has estimation talent; however, some studies have shown that a mathematical technique, consistently followed, will lead to better results than the “expert modification” of those forecasts. Nonetheless, many mathematical techniques need significant quantities of historical data that may not be available. When substantial data are lacking, subjective management judgment may be the better alternative.

• Connectionist methods This method is commonly known as “Artificial Neural Networks

ANN” which is a branch of artificial intelligence. ANNs are types of information processing system whose architectures are inspired by the structure of human biological neural systems (Refenes, 1994). They concentrate on machine learning which was based on the concept of self-adjustment of internal control parameters. The ANN environment consists of five primary components; learning domain, neural nets, learning strategies, learning process, and analysis process. The data used in the model to train neural networks are historical recorded data. Combining the learning capabilities of neural networks and time series techniques and using wavelet decomposition technique to explore more details of the time series signals. The wavelet transform has its roots in the Fourier transform. Typical neural network models are closely related to statistical models. However, high noise, high non-stationarity time series prediction is fundamentally difficult for these models. A wide range of interesting applications of ANNs has been investigated; it can be applied in pattern recognition, to diagnosing problems, in decision making and optimization, for design and planning, for management, and can be also applied for prediction or forecasting. The behavior of complex systems has been a broad application domain for neural networks. In particular, applications such as electric load forecasting, economic forecasting, and forecasting


166

natural and physical phenomena have been widely studied (Grino, 1992), (Metaxiotis, 2003), (Dillon, 1991), and (Refenes, 1994).

• Time series methods methods of this type are concerned with a variable that changes with

time and which can be said to depend only upon the current time and previous values that it took ( i.e. independent on any other variables or external factors). Time series methods are especially good for short-time forecasting where the past behavior of a particular variable is a good indicator of its future behavior at least in the short-term (Franmlin, 1986) and (Weigend, 1994). The typical example here is short-term demand forecasting for a water distribution system. The time series method uses different technique to forecast the future variable such as: moving average, exponential smoothing, and AutoRegressive Integrated Moving Average (Box-Jenkins approach).

In this thesis we will consider only the time series method for

forecasting the water demand for the system being studied here.

8.4 Time series methods The term “univariate time series” refers to a time series that consists

of single (scalar) observations recorded sequentially over equal time increments (Brockwell, 1991 and 1996). Time series forecasting methods are widely used in business situations where forecasts of a year or less are required. Classically, researchers approach the problem of modeling a time series by identifying four kinds of components. These four components are known as Seasonality, Trend, Cycling, and Residual (Abu-Mostafa, 1996).

The Seasonal variation in a time series is the repetitive pattern

observed over some time horizon (day, month, year, etc). The Trend is the increase or decrease in the series over a long period

of time. For this reason is also known as the long-term trend. The Cyclical variation is the wavelike up and down fluctuations about

the trend, and it is not tied to the seasonal variation. Lastly, the Residual effect is what remains, having removed the

Trend, Cycling and Seasonal components of a time series. It represents the random error effect of a time series, caused by events as widespread wars, hurricanes, strikes and randomness of human actions.


167

( ) ( )[ ]

( ) ( )∑ ∑

∑

=

=

−−

−−=

×=

T

ttt

T

ttt

yx

yyxx

yyxx

YVarXVarYXCovR

1

22

1, )()(

),( ( Eq. 8.1 )

The foundation of time series analysis is stationarity (Ruey, 2002). A stationary time series has a constant mean, a constant variance and autocovariances (or autocorrelations), which depend only upon the difference in the time index and not on their location in time. A non-stationary time series is a time series in which one or all of these conditions are not satisfied. A stationary time series is generated by a process that remains the same over time. Thus, the mean, variance, and auto-covariances are all independent of time.

8.4.1 Autocorrelation function (ACF) and partial autocorrelation function (PACF)

The correlation coefficient between two random variables X and Y is

defined as: Where x and y are the mean of X and Y, respectively, Cov(X,Y) is

the covariance of X and Y, Var(X) and Var(Y) are variance of X and Y, respectively. It is assumed that the variances exist. This coefficient measures the strength of linear dependence between X and Y, and it can be shown that −1 ≤ Rx,y ≤ 1 and Rx,y = Ry,x . The two random variables are uncorrelated if Rx,y = 0. In addition, if both X and Y are normal random variables, then Rx,y = 0 if and only if X and Y are independent.

• Autocorrelation function (ACF) Time series data often exhibits something called autocorrelation.

This means that observations are not independent one from another. Consider a stationary series rt, when the linear dependence between rt and its past values rt−i is of interest, the concept of correlation is generalized to autocorrelation. The correlation coefficient between rt and rt−l is called the lag-l autocorrelation of rt and is commonly denoted by ρl, which under the weak stationarity assumption is a function of lag-l only. Specifically, we define:

( Eq. 8.2 )0)(

),()()(

),(γγρ l

t

ltt

ltt

lttl rVar

rrCovrVarrVar

rrCov=== −

−

−


168

Where the property Var(rt) = Var(rt−l) for a stationary series is used. From the definition, we have ρ0 = 1, ρl = ρ−l, and −1 ≤ ρl ≤ 1. In addition, a stationary series rt is not serially correlated if and only if ρl = 0 for all l > 0. Stationary series applications often require to test that several autocorrelations of rt are zero.

Autocorrelation plots are a commonly-used tool for checking randomness in a data set. In addition, autocorrelation plots are used for model identification in ARIMA Box-Jenkins model.

• Partial autocorrelation function (PACF) The partial autocorrelation at lag l is the measure of the strength of

correlation between rt and rt-l that is not accounted for by lags 1 through (l -1). Partial autocorrelation plots are a commonly-used tool for model identification in ARIMA Box-Jenkins model, specifically in identifying the order of an autoregressive model.

• White noise A time series rt is called a white noise if rt is a sequence of

independent and identically distributed random variables with finite mean and variance. In particular, if rt is normally distributed with mean zero and variance σ2, the series is called a Gaussian white noise. For a white noise series, all the ACFs are zero. In practice, if all sample ACFs are close to zero, then the series is a white noise series.

8.4.2 Simple autoregressive models

The fact that rt has a statistically significant lag-1 autocorrelation

indicates that the lagged rt−1 might be useful in predicting rt. A simple model that makes use of such predictive power is:

Where ta is assumed to be a white noise series with mean zero and

variance σa², Φ0 and Φ1 are model parameters. This model is in the same form as the well-known simple linear regression model in which rt is the dependent variable and rt−1 is the explanatory variable. In the time series literature, Model (Eq. 8.3) is referred to as a simple autoregressive (AR) model of order 1 or simply an AR(1) model. A straightforward generalization of the AR(1) model is the AR(p) model:

( Eq. 8.3 ) ttt arr ++= − 110 φφ

( Eq. 8.4 ) tptptt arrr ++++= −− φφφ ...110


169

Where p is a non-negative integer and ta is defined in (Eq. 8.3). The AR(p) model is in the same form as a multiple linear regression model with lagged values serving as the explanatory variables.

8.4.3 Simple moving-average models

We now turn to another class of simple models that are also useful in

modeling stationary time series. These models are called moving-average (MA) models. There are several ways to introduce MA models. One approach is to treat the model as a simple extension of white noise series. Another approach is to treat the model as an infinite-order AR model with some parameter constraints. In adopting the second approach, there is no particular reason, but simplicity, to assume a priori that the order of an AR model is finite. We may entertain, at least in theory, an AR model with infinite order as:

However, such an AR model is not realistic because it has infinite

many parameters. One way to make the model practical is to assume that the coefficients Φis satisfy some constraints so that they are determined by a finite number of parameters. A special case of this idea is:

Where the coefficients depend on a single parameter θ1 via Φi =− i

1θ for i ≥ 1. For the model in (Eq. 8.6) to be stationary, θ1 must be less than one in absolute value; otherwise, i

1θ and the series will explode. Because | θ1 | < 1, we have i

1θ → 0 as i → ∞. Thus, the contribution of rt−i to rt decays exponentially as i increases. This is reasonable as the dependence of a stationary series rt on its lagged value rt−i, if any, should decay over time. The model in (Eq. 8.6) can be rewritten in a rather compact form. To see this, rewrite the model as:

The model for rt−1 is then: Multiplying (Eq. 8.8) by θ1 and subtracting the result from (Eq. 8.7),

we obtain:

( Eq. 8.5 )tttt arrr ++++= −− ...22110 φφφ

( Eq. 8.6 )ttttt arrrr +−−−−= −−− ...33

122

1110 θθθφ

( Eq. 8.7 )tttt arrr +=+++ −− 022

111 ... φθθ

( Eq. 8.8 )1032

1211 ... −−−− +=+++ tttt arrr φθθ


170

( Eq. 8.12 )

Which says that except for the constant term rt is a weighted average

of shocks at and at−1. Therefore, the model is called an MA model of order 1 or MA(1) model for short. The general form of an MA(1) model is:

Where c0 is a constant and at is a white noise series. Similarly, an

MA(q) model is:

8.4.4 Simple Box-Jenkins ARMA model In some applications, the AR or MA models discussed in the

previous sections become cumbersome because one may need a high-order model with many parameters to adequately describe the dynamic structure of the data. To overcome this difficulty, the autoregressive moving-average (ARMA) models are introduced; known as Box-Jenkins ARMA model (Box, 1994) and (Ruey, 2002). A general ARMA(p, q) model is in the form:

Where at is a white noise series and p and q are non-negative

integers. The AR and MA models are special cases of the ARMA(p, q) model.

• Non-stationary time series Many real time series do not satisfy the stationarity conditions stated

earlier for which ARMA models have been derived. Then these times series are called non-stationary and should be re-expressed such that they become stationary with respect to the variance and the mean. One of the methodologies that can be used to make a non-stationary time series stationary is to apply a difference operator to a data series.

However, differencing can sometimes reduce a non-stationary series to stationarity. Differencing once or twice is often enough. The Box-Jenkins model assumes that the time series is stationary. Box and Jenkins recommend differencing non-stationary series one or more times to achieve stationarity. Doing so produces an ARIMA model, with the “I” standing for “Integrated”.

( Eq. 8.9 )1110 )1( −−+−= ttt aar θθφ

( Eq. 8.10 )110 −−+= ttt aacr θ

( Eq. 8.11 ), where q > 0 qtqttt aaacr −− −−−+= θθ ...110

∑∑=

−=

− −++=q

iitt

p

iitit iaarr

110 θφφ


171

8.4.5 ARIMA model ARIMA processes have been studied extensively and are a major

part of time series analysis. They were popularized by George Box and Gwilym Jenkins in the early 1970s (Box, 1994). The acronym ARIMA stands for Auto-Regressive Integrated Moving Average. In fact, the easiest way to think of ARIMA models is as fine-tuned versions of random walk and random-trend models. Lags of the differenced series appearing in the forecasting equation are called auto-regressive terms, lags of the forecast errors are called moving average terms, and a time series which needs to be differenced to be made stationary is said to be an integrated version of a stationary series. Random-walk and random-trend models, autoregressive models, and exponential smoothing models (i.e., exponential weighted moving averages) are all special cases of ARIMA models. A non-seasonal ARIMA model is classified as an ARIMA(p,d,q) model where:

- p is the number of non-seasonal autoregressive terms, - d is the number of non-seasonal differences, and - q is the number of non-seasonal moving average terms.

Seasonality

Some time series exhibits certain cyclical or periodic behavior. Such a time series is called a seasonal time series. If seasonality is present, it must be incorporated into the time series model. Box-Jenkins models can be extended to include seasonal autoregressive and seasonal moving average terms. Although this complicates the notation and mathematics of the model, the underlying concepts for seasonal autoregressive and seasonal moving average terms are similar to the non-seasonal autoregressive and moving average terms. The most general ARIMA Box-Jenkins model includes difference operators, autoregressive terms, moving average terms, seasonal difference operators, seasonal autoregressive terms, and seasonal moving average terms.

A seasonal ARIMA model is classified as an ARIMA(p,d,q)x(P,D,Q)S model, where P = number of seasonal autoregressive terms (SAR), D = number of seasonal differences, Q = number of seasonal moving average terms (SMA), S = number of seasons.

8.4.6 Box-Jenkins Model Identification

1) Identifying the order of differencing (d)

The first and most important step in fitting an ARIMA model is the

determination if the series is stationary and if there is any significant


172

seasonality, and then to determine the order of differencing needed to stationarize the series. Stationarity and seasonality can also be detected from an autocorrelation plot. Specifically, non-stationarity is often indicated by an autocorrelation plot with very slow decay. Normally, the correct amount of differencing is the lowest order of differencing that yields a time series which fluctuates around a well-defined mean value and whose autocorrelation function (ACF) plot decays fairly rapidly to zero, either from above or below. Integrated component (d) is usually 0, 1, or 2. The integrated component is simply 0 if the raw data are stationary to begin with, 1 if there is a linear trend, or 2 if there is a quadratic trend. Higher positive values are possible but very rarely useful.

2) Identifying the numbers of AR (p) and MA (q) terms

Once stationarity and seasonality have been addressed and a time

series has been stationarized by differencing, the next step is to determine whether AR or MA terms are needed to correct any autocorrelation that remains in the differenced series. The primary tools for doing this are the autocorrelation plot and the partial autocorrelation plot.

- AR and MA signatures: If the PACF displays a sharp cutoff while

the ACF decays more slowly (i.e., has significant spikes at higher lags), we say that the stationarized series displays an “AR signature”, meaning that the autocorrelation pattern can be explained more easily by adding AR terms than by adding MA terms.

In principle, any autocorrelation pattern can be removed from a stationarized series by adding enough autoregressive terms (lags of the stationarized series) to the forecasting equation, and the PACF tells you how many such terms are likely be needed. However, this is not always the simplest way to explain a given pattern of autocorrelation: sometimes it is more efficient to add MA terms (lags of the forecast errors) instead. The autocorrelation function (ACF) plays the same role for MA terms that the PACF plays for AR terms, that is, the ACF tells you how many MA terms are likely to be needed to remove the remaining autocorrelation from the differenced series. If the autocorrelation is significant at lag l but not at any higher lags; i.e. if the ACF “cuts off” at lag l this indicates that exactly k MA terms should be used in the forecasting equation. In the latter case, we say that the stationarized series displays an “MA signature” meaning that the autocorrelation pattern can be explained more easily by adding MA terms than by adding AR terms.

In practice, the sample autocorrelation and partial autocorrelation functions are random variables and will not give the same picture as the theoretical functions. This makes the model identification more difficult. In


173

( )n

r ... r r r 1n-t1-tt

1t+

+

+++= ( Eq. 8.13 )

1n-tn1-t2t11t .r w .r w .r w r ++ +…++= ( Eq. 8.14 )

particular, mixed models can be particularly difficult to identify. Although experience is helpful, developing good models using these sample plots can involve much trial and error. For this reason, in recent years information-based criteria such as FPE (Final Prediction Error) and AIC (Aikake Information Criterion) and others have been preferred and used. These techniques can help automate the model identification process. These techniques require computer software to use (Ruey, 2002).

8.4.7 Smoothing methods

A time series is a sequence of observations, which are ordered in

time. Inherent in the collection of data taken over time is some form of random variation. There exist methods for reducing of canceling the effect due to random variation. A widely used technique is “smoothing” (Brown, 1962). This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components. It is used to filter random “white noise” from the data, to make the time series smoother or even to emphasize certain informational components contained in the time series. There are two distinct groups of smoothing methods: Averaging Methods and Exponential Smoothing Methods.

• Moving averages (MA) The best-known forecasting methods is the moving averages or

simply takes a certain number of past periods and add them together; then divide by the number of periods. Simple Moving Averages is effective and efficient approach provided the time series is stationary in both mean and variance (Brockwell, 1991). The following formula is used in finding the moving average of order n, MA(n) for a period t+1:

Where n is the number of observations used in the calculation. The

forecast for time period t + 1 is the forecast for all future time periods. However, this forecast is revised only when new data becomes available.

• Weighted Moving Average (WMA) They are widely used where repeated forecasts required-uses

methods like sum-of-the-digits and trend adjustment methods. A weighted moving average is:


174

tt1t F F εα+=+ ( Eq. 8.16 )

tt1t F ) - (1 r F αα +=+ ( Eq. 8.15 )

Where the weights (w) are any positive numbers such that: w1 + w2 + …+wn = 1 • Exponential Smoothing One of the most successful forecasting methods is the exponential

smoothing (ES) techniques. Moreover, it can be modified efficiently to use effectively for time series with seasonal patterns. An ES is an averaging technique that uses unequal weights; however, the weights applied to past observations decline in an exponential manner (Pollock, 1999).

- Single Exponential Smoothing: It calculates the smoothed series as

a damping coefficient times the actual series plus 1 minus the damping coefficient times the lagged value of the smoothed series. The extrapolated smoothed series is a constant, equal to the last value of the smoothed series during the period when actual data on the underlying series are available. While the simple moving average method is a special case of the ES, the ES is more parsimonious in its data usage. The forecasting formula is the basic equation:

Where: rt = actual value Ft = forecasted value α = smoothing factor, which ranges from 0 to 1 t = current time period.

This can be written as:

Where (εt) is the forecast error (actual - forecast) for period (t). In

other words, the new forecast is the old one plus an adjustment for the error that occurred in the last forecast. A small (α) provides a detectable and visible smoothing. While a large (α) provides a fast response to the recent changes in the time series but provides a smaller amount of smoothing.

An exponential smoothing over an already smoothed time series is called double-exponential smoothing. In some cases, it might be necessary to extend it even to a triple-exponential smoothing, and the resulting set of equations is called the “Holt-Winters (HW)” method after the names of the inventors. While simple exponential smoothing requires


175

stationary condition, the double-exponential smoothing can capture linear trends, and triple-exponential smoothing can handle almost all other time series.

8.5 Evaluating the accuracy of forecasting All forecasting models have either an implicit or explicit error

structure, where error is defined as the difference between the model prediction and the “true” value. Using any method for forecasting one must use a performance measure to assess the quality of the method. The most straightforward way of evaluating the accuracy of forecasts is to plot the observed values and the one-step-ahead forecasts in identifying the residual behavior over time. The widely used statistical measures of error that can help us to identify a method or the optimum value of the parameter within a model are:

a. Mean absolute error (MAE): is the average absolute error value.

Closer this value is to zero the better the forecast is

b. Mean squared error (MSE): is computed as the sum (or average) of the squared error values. This is the most commonly used lack-of-fit indicator in statistical fitting procedures. As compared to the mean absolute error value, this measure is very sensitive to any outlier; that is, unique or rare large error values will impact greatly MSE value.

c. Mean Relative Percentage Error (MRPE): The above measures rely on the error value without considering the magnitude of the observed values. The MRPE is computed as the average of the Relative Absolute Percentage Error (RAPE) values:

t

tt

XFX −

×= 100 RAPE t ( Eq. 8.19 )

( )

Ni∑

==

N

1

2ii F-X

MSE( Eq. 8.18 )

Ni∑

==

N

1ii F-X

MAE( Eq. 8.17 )


176

d. Correlation coefficient and R-Squared: Correlation is one of the most common and most useful statistical techniques which can show whether and how strongly pairs of variables are related. The main result of a correlation is called the correlation coefficient (or “R”). A correlation coefficient is a single number and it ranges from (-1.0) to (+1.0). The closer R is to +1 or -1, the more closely the two variables are related. Recall that the R-squared value is the square of the correlation coefficient.

e. Durbin-Watson statistic: quantifies the serial correlation of serial correlation of the errors in time series analysis and forecasting. D-W statistic is defined by:

Where ei is the ith error. D-W takes values within [0, 4]. For no serial

correlation, a value close to 2 is expected. With positive serial correlation, adjacent deviates tend to have the same sign; therefore D-W becomes less than 2; whereas with negative serial correlation, alternating signs of error, D-W takes values larger than 2. For a forecasting where the value of D-W is significantly different from 2, the estimates of the variances and covariances of the model’s parameters can be in error, being either too large or too small.

8.6 Forecasting softwares An interesting forecasting software survey appeared in December

2004 showed that the number of tools for planning and forecasting on the market is very large and their variety confusing (Yurkiewicz, 2004). Look at the forecasting softwares market, the level of maturity and stability of products and their features has reached “steady-state”. Programs such as: SAS, Minitab, NCSS, SCA, ADAPTA DLS-FBS, DrPro++, AGSS, Demand Solutions, Forecast Pro XE, PROC FORECAST, Futurmaster, AutoBox, Smart forecast, SPSS Trend, Statgraphics, Matlab, Statistica, UNISTAT.Minitab, NCSS, SAS and Systat are examples of this group.

( )

∑

∑

=

=−−

= n

ii

ii

e

ee

1

2

n

2i

21

StatisticW -D ( Eq. 8.21 )

( )( )

( ) ( )∑∑

∑

==

=

−−

−−=

N

i

N

i

N

1

2i

1

2i

1iii

FFXX

FFXXR ( Eq. 8.20 )


177

Typically, these programs include Box-Jenkins and exponential smoothing techniques as their core offerings, with different levels of automation and “ease of use”. Most current versions of these products have virtually identical forecasting features and capabilities. A newer branch of this market is the Microsoft Excel Add-Ins. Working on top of the spreadsheet engine, these products, typically macros, have the statistics and forecasting capabilities. These softwares have mainly segmented into two categories. Perhaps the largest is the stand-alone, dedicated statistics programs that offer forecasting capabilities as one of its features. A second broad category is stand-alone, dedicated forecast programs and these more advanced products generally offer many forecasting techniques, coupled with user features that make choosing the appropriate model, getting optimal parameters for that model, examining results, etc., easier than those found in general statistics programs.

The software’s capabilities, ease of use and accuracy are the primary attributes that users seek. Judging how easy a program is to use is problematical and open to debate. An automatic program is one in which the software, after scanning the data and doing statistical tests, tells the user which methodology is most appropriate to use, or the user manually chooses an alternative model. In either case, the program then proceeds to find the optimal parameters for the model, makes forecasts for some user-specified time horizon, displays plots of the data and the forecasts. Users without that statistical background may blithely rely on the program’s recommendation, treating the software as a “black box”. However, good automatic software should give the user clear information about why and how it made its recommendation.

Users expect the software to be accurate, but rarely do two programs using identical data, models and parameters get the same “optimal” parameters, and this, of course, leads to different forecasts. A general weakness of many of the products is that documentation is frequently short on mathematical or technical details.

Sometime series are too short or volatile to use, while others may have missing values or statistical outliers that could preclude using the program or causing poor forecasts. Some programs facilitate this process, automatically giving the time series plot and offering warnings about the data and suggestions for correction.

The typical user may have his or her data in an Excel spreadsheet, and while most programs claim that they can read such data and thus are Excel “compatible”, there are different degrees of compatibility. Others would not read an older Excel version spreadsheet, but wanted an earlier version of Excel. Graphics output varies. Some programs offer little user control of the plot, thus making cosmetic changes difficult.

These and other issues can be easy to resolve. However, resolving


178

some other issues may be harder. The infrequent forecast user wants to know details about the ease of learning and ease of use of the program. These products are frequently expensive, and the best way to answer these and other questions would be to download a “trial version” of the product. These versions are generally either the complete product limited to some time duration (15 or 30 days) or a certain number of runs, or have some type of crippling such as limited time series size, or not printing or saving data.

8.7 Water demand prediction technique at SCP Water demand prediction at SCP plays an important role in the

“Dynamic Regulation” control of the Canal de Provence. Indeed, on-demand water supply leads to large fluctuations in the canal flow which are difficult to forecast. On the contrary to the pressurized pipe networks which are more adapted to the on-demand water supply, the open canals are characterized by high response time, and present less flexibility since the storage volume are small. The “Dynamic Regulation” control is based on three different actions:

- Anticipatory action: this action is based on the forecast of water

requirements. According to the type of offtakes, flow forecasting can be either based on pre-established program, or by extrapolation of the trend for the coming hours using the average trends computed over the ten previous days. The forecasted flow at check structure are then calculated by introducing hydraulic delay from the intake to various offtakes and allow to determine target volumes for the different reachs of the canal for the next period of time.

- Corrective action: practically the exact balance between the inflow

and outflow in each reach cannot be achieved. This leads in the variations of volume in each reach which have to be counterbalanced by another action called corrective action. This corrective action consists in increasing the inflow in a reach if the actual volume is under the target volume and decreasing the inflow in the opposite case.

- Coordination action: the corrective action can be different for two

adjacent reachs and introduces a discrepancy between inflow and outflow in a reach. Thus, it is recommended to mitigate this imbalance by carrying forward the corrective action from one reach


179

96

96

1∑

== jij

i

QQ ( Eq. 8.23 )

i

ijij Q

Q k = ( Eq. 8.24 )

to the other upstream reachs, and this is called “coordination action” and it allows to better maintain the target volume. Finally, the flow to be delivered at the upstream of each reach is

given by the sum of the three actions described previously: The SCP’s operators at the control center developed their own

demand prediction tools based on their understanding of their own system being operated. These predictions carried out for a “statistical period (PS)” in general equals to 24 hours in the future. This period is divided into 96 timesteps because at SCP the average flows over a time interval of 15 minutes are archived and therefore we have 96 flow measurements a day. The predictions are carried out starting from “dimensionless curve” updated periodically at preset moments of the day. This curve is rebuilt repeatedly (around 10 times per day) using the archived flow data for a “statistical horizon” that is the previous ten days form the actual date (Viala, 2004).

For each statistical period Psi of the statistical horizon, where i from 1 to 10, and for each timestep j, where j from 1 to 96, we have the historical flows. The average flow is calculated for each Psi :

Then, for each statistical period Psi, we build the “dimensionless

curve” such that the flows Qij are divided by their average flow to define the ratio kij where:

Now, we create the “trend curve” such that the average of the kij

ratios is calculated for each timestep over the statistical horizon: This dimensionless curve gives the tendency of evolution of the flow

over the statistical period, and it will be used to predict the demand flow for

iQ

iQ

10

k k

10

1iij

j

∑== , j from 1 to 96 ( Eq. 8.25)

( Eq. 8.22 ) oncoordinaticorrectionpredictionreach QQQQ ++=


180

stab

stabadjust

jj

stabj

j

stab kQQ

kk

QQ =→==

∑∑==

4,

4

96

93

96

931

( Eq. 8.26 )

adjustjprediction QkjQ ×=)( ( Eq. 8.27 )

the coming statistical period. So, we define the “stabilization period Pstab” equals to 4 timesteps (i.e. 1 hour) preceding the actual date, and the average flow is then calculated over this period for only the last statistical curve, and we call this flow as “stabilization flow Qstab”. Also we calculate the average k of the dimensionless curve over this period. The ration of these two values is the “adjustment flow Qadjust” which used to adjust the dimensionless curve:

We multiply the dimensionless curve by Qadjust to produce the

prediction curve for the considered period of 24 hours: Figure 8.1 shows the recorded demand versus the predicted one for

“Toulon Est” network from midday 10/03/2006 to midday 13/03/2006. These recorded demands are measured by electromagnetic flowmeter installed at the head of the system. The demands characteristics of “Toulon Est” network have been introduced in Chapter 2 (see section 2.7). The predicted demands are computed using the above technique.

Figure 8.1 : Example of demand prediction at SCP – Toulon Est – 2006

Q (m

3 /s)

12:0

0:00

10

/03/

06

Time

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

00:0

0:00

11

/03/

06

00:0

0:00

12

/03/

06

00:0

0:00

13

/03/

06

12:0

0:00

13

/03/

06

Qreal Qprediction


181

8.8 Daily demand prediction technique implemented in FINESSE software

Demand prediction in FINESSE takes as input measured daily

demand profiles and produces as output a predicted daily demand. The demand predictor has an extensive data requirement but the prediction is fast. Typically, it takes longer to acquire measurement data that it does to analyze and predict demand. In On-line use, each day the demand prediction program is provided with the daily measured demands for the previous period (typically six weeks) and the demand prediction in turn produce a prediction for the next 24 hours based on this data. Prediction is strictly on a day-by-day basis, and it uses vertical prediction, where the demand at for example 08:00 on a given day is based on the demand at 08:00 on the preceding days. This is contrast to horizontal prediction where the prediction at 08:00 takes into account the demand at 07:45 if the prediction timestep is 15minutes for example.

The demand prediction program implemented in FINESSE is called “Graphical Interactive Demand Analysis and Prediction, GIDAP” (Coulbeck, 1989) and (SEEE, 1989). GIDAP is basically divided into two halves; Demand Analysis and Demand Prediction. Prior to prediction the actual data is first screened and smoothed to produce the equivalent useful data. The main function of GIDAP is to predict 24-hour or weekly demand profiles from current and recorded demand data. Demands profiles can consist of values at intervals as small as 15 minutes. The demand prediction process consists of several distinct stages concerned with the gradual refinement of raw data prior to prediction, as follows:

1. Data Screening. 2. Data Smoothing. 3. Data Forecasting. Special parameters are required at each stage of the prediction

process. Data screening requires suitable screening thresholds; data smoothing requires the maximum significant harmonic to be known and data forecasting requires knowing how daily profiles are categorized (Figure 8.2). These parameters can sometimes be obtained by inspecting the demand data with a little experience. The analysis techniques employed in GIDAP are described in detail in the following sections.

1. Data screening

GIDAP assumes that the actual demand data that it uses to predict

contains possible transmission and recording errors. These errors may


182

Raw Demand Data

Predicted Demand Data

Screening Thresholds

Maximum Significant Harmonic

Profile Categories

Data Screening

Data Smoothing

Data Forecasting

DEMAND ANALYSIS DEMAND PREDICTION

[ ] [ ] [ ]mn

mDnDFD tt

−−

=n ( Eq. 8.28 )

manifest themselves as unusually small or large data values, sudden peaks or dips in the data or missing values. The screening process applied to this raw demand data attempts to identify such errors. For effective data screening four thresholds are defined:

Figure 8.2 : GIPAD’s demand prediction stages

1. Lower demand threshold (DDMin) : data values below this threshold are considered to be too small and are rejected as transmission errors.

2. Upper demand threshold (DDMax) : data values above this threshold are considered to b too large and are rejected as transmission errors.

3. Maximum first difference (FDMax) : the first difference of a demand value defines the rate of change of demand represented by that value. The maximum first difference is defined such that if the first difference of a value exceeds it, then that value, then that value can be considered to be the result of an exaggerated rate of change in demand, and should be rejected. The first difference, FD[n], of the n’th data value is defined by:


183

[ ] [ ] [ ]nFDpFDmp

nSD −×−−

=2

2 ( Eq. 8.29 )

4. Maximum second difference threshold (SDMax): the second difference of a demand value is a measure of the ‘peakiness’ of that value, or the acceleration of demand represented by that value. The maximum second difference is defined such that if the second difference of a value exceeds it, then that value could be the result of a transmission error. The second difference, SD[n], of the n’th data value is defined by:

Where:

Dt[x] = demand value at position x, and day t n = position of current demand value m = position of last non-rejected demand value p = position of next acceptable demand value NT = number of demand values per day

The screening process takes each value in a demand profile in turn,

and tests it against each of the above threshold values; if the value fails the test on any one of the thresholds it is rejected and replaced by a predicted value. If the later value itself fails any of the same tests, then it is replaced again by a linear interpolation between adjacent non-rejected values. To be effective, the screening process requires the appropriate setting of each of the above mentioned thresholds.

2. Data smoothing

Data screening removes relatively coarse transmission errors but

overlooks small random fluctuations in demand present usually as high frequency low amplitude harmonics. These harmonics make no significant contribution to the underlying trends in the demand or to the basic shape of the demand profile, but nevertheless they can affect forecasts unless they are removed. The smoothing process attempts to remove such insignificants harmonic components to reveal the underlying demand information.

Basically, the screened demand profile is composed into its harmonic components, using a method based upon Fourier Analysis, called the Fast-Fourier-Transform, FFT. All harmonic components below a certain frequency are then recombined to form a smoothed version of the original profile. The assumption is that the components with the higher frequencies make no significant contribution to the profile and they are due instead to

NTpmn ≤< ,,0


184

( Eq. 8.32 )

random fluctuations in demand. Specifically, a continuous demand pattern represented by the infinite Fourier series:

It can be estimated by:

Where:

D(t) = demand value at time t ),(ˆ NHtD = estimate of D(t) summing NH harmonic

aj , bj = real harmonic coefficients

ja , jb = estimate of aj , bj NH = referred to the smoothing threshold, or the Highest

Significant Harmonic. NH represents that frequency, above which harmonic components

become insignificant. The value selected for NH in the above model affects the amount of random data allowed to pass through to the prediction phase. If NH is too low, then significant trend information is lost and prediction performance will decline. Conversely, if NH is too high, noisy data would be passed on, also adversely affecting the prediction performance.

3. Data forecasting

Data forecasting is based upon the Triple Exponential Smoothing

technique. This technique maintains estimates of current position, velocity and acceleration for each data value in a diurnal, which reflect the latest trends. These estimates are updated in the light of current smoothed data and then extrapolated forward one time period to produce the desired forecast. Days of the week can be grouped according to the statistical similarity of their average diurnal patterns, and therefore a separate set of estimates is maintained for each group or “category”.

When actual smoothed data becomes available for the period t, Dt , the predicted error for that period, E, is found as follows:

E = Pt – Dt

Where Pt is the predicted data or time period t.

( Eq. 8.30 )∑∑∞

=

∞

=

++=11

0 )2()2()(j

jj

j tSinbjtCosaatD ππ

( Eq. 8.31 ) ∑∑==

++=NH

jj

NH

jj jtSinbjtCosaaNHtD

110 )2(ˆ)2(ˆˆ),(ˆ ππ


185

( Eq. 8.34 )

If the day of the week corresponding to time period t is in profile category i, then the current position Sit, velocity Vit and acceleration Ait estimates of category I, are updated in the light of the current prediction error E, as follows:

Sit = Dt + ( 1 – α )3 * E Vit = Vit-1 + Ait-1 - 1.5 * ( 2 – α ) * α 2 * E Ait = Ait-1 – α 3 * E Where (α) is the smoothing constant. If the day of the week corresponding to the period t+1 is in category

j, then the forecast for the time period following period t, Pt+1, is found as follows:

Pt+1 = Sjt + Vjt + 0.5 * Ajt When actual data for time period t+1 becomes available, the above

process is repeated for the forecast for the time period t+2. The performance of the exponential smoothing depends largely upon the value selected for the smoothing constant a. This constant effectively controls the number of past realizations of the time series that are to influence the forecast. Small values for a give more weight to previous data values and therefore results in a slow response of the forecasting model to trends in the demand data. Large values for a give more weight to more recent values and cause model to respond more rapidly to change in demand.

GIDAP program configuration The correct functioning of demand prediction program is based upon

the appropriate setting of the above-mentioned parameters; screening thresholds, highest significant harmonic and smoothing constant. These values can be estimated, but they can also be derived automatically by supplying the demand prediction program with a certain amount of demand data and instructing it to configure itself. This usually requires about 6 weeks of data, mainly for the profile category analysis, but if the latter are known then as little as one day’s data is required as long as the data is good. In FINESSE this configuration is done automatically.

( Eq. 8.33 )


186

Improved FINESSE demand prediction: However, this version of the demand prediction is not very robust

and the prediction results were not very good when compared to some other techniques as it will be demonstrated in the next section. Accordingly, the DMU improved this demand prediction and now the user can select between single, double, or triple exponential smoothing, and also the smoothing constant can be set manually.

8.9 Comparison between short-term water demand forecasting techniques for water supply networks - case study : “Toulon Est” network system

One problem with each of these forecasting methods and techniques

is simple: How good is it?. The aim of this comparison mainly is to raise this question. The approach used here is to employ more than one prediction method and tool, and then to compare their prediction results with each other. As a secondary aim of this paper is also to show the effect of prediction period selected on the results of the prediction. The following techniques are used for the comparison purpose:

1- Weighted Moving Average (WMA), 2- Single Exponential Smoothing (SES), 3- Triple Exponential Smoothing (TES), 4- SCP Prediction Technique, 5- FINESSE demand predictor. 6- AutoRegression Integrated Moving Average (ARIMA),

8.9.1 Approach

A- Demand data source The source of raw demand data used in this comparison is the

recorded total water demand measured at the head of the “Toulon Est” distribution network for the years 2002 and 2003. The average demand over a time interval of 15 minutes is recorded in cubic meters per second, so we have 96 demand measurements a day.

B- Data pre-treatment

Since the historical demand data contains some missing and noise


187

values, the demand data will be screened and smoothed to estimate the missing one and remove the noise before passing to the prediction process. The screening process used here is just to eliminate the outlier data or extrapolate the missing one using moving average without losing any important information about the original demand profile. The screening is based on a relatively very coarse criterion that is: starting from a valid demand, the rate of change in system’s demand over 15 minutes will not exceed 30% and erroneous values and then the demand values are replaced by moving average demand for the last three measured demands.

Figure 8.3 : Example of original vs. smoothed demand - Year 2002

A spectral analysis has been also done for the measured demand and

the periodogram was drawn 0 (Figure 8.4). It was detected that the maximum period was at about wavelength = 96, where the wavelength corresponds to the number of measurements, thus the wavelength =96 means that the system’s periodicity is every 96 measurements, in others words, 24-hour water demand pattern. The spectrum shown in Figure 8.4 is for year 2002 only.

C- Prediction period

The demand will be predicted for the coming day using certain

number of preceding days, this number refers to the “prediction period”.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

8-juin-02 9-juin-02 10-juin-02 10-juin-02

dem

and

(m3 /s

)

Original demand

Smoothed demand


188

T o u lo n -E s t D e m a n d F o r Y e a r 2 0 0 2

0 ,0 0 0

0 ,5 0 0

1 ,0 0 0

1 ,5 0 0

2 ,0 0 0

2 ,5 0 0

< 1

May

200

2 >

< 31

May

200

2 >

< 30

Jun

e 20

02 >

< 30

Jul

y 20

02 >

< 29

Aug

. 200

2 >

< 28

Sep

t. 20

02 >

< 29

Oct

. 200

2 >

Dem

and

(m3/

s)

Periodogram For T oulon-Est Demand (2002)

0 ,E+0 0

5 ,E+0 8

1 ,E+0 9

2 ,E+0 9

2 ,E+0 9

3 ,E+0 9

5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 1 1 0 1 1 5 1 2 0

Wave le ngth

Peri

od

W a ve le ngth = 96

For WMA, SES, TES, and FINESSE two prediction periods were selected: 21days (3 weeks) and 42 days (6 weeks). While for the SCP prediction technique only one prediction period has been selected, that is 10 days. For ARIMA, the prediction period is from the beginning of the year to the day before the day for which the demand will be predicted.

Figure 8.4 : Measured demand and the periodogram

D- Foreword prediction period The demand will be predicted 24hours foreword for every day for the

period from the 1st of May 2002 to the 31 October 2002, and from the 1st of May 2003 to the 31 October 2003, which means 184 days for each year. Because of the daily water demand behavior of this system, the prediction is vertical prediction, where the demand at for example 08:00 on a given day is based on the demand at 08:00 on the preceding days. The predicted demand will be compared to the measured one to evaluate the accuracy of the prediction using the criterion described soon.


189

E- Evaluating the accuracy of prediction We want a measure of how good the prediction is. The predicted

demand will be statically compared to the measured one. The “decisive factors” used in the comparison between different techniques in order to decide the “best” forecasting technique are:

- Mean Squared Error (MSE), - Mean absolute relative error (MARE), - R-Squared, - Correlation Coefficient.

F- Prediction tools The tools that were used to realize the prediction are briefly

described here for each technique:

1- Weighted moving average (WMA) In order to do the prediction by this technique, a macro was created

in MS Excel since the prediction techniques, such as WMA, are easy to implement on a spreadsheet. The mathematical equation used by WMA to predict the demand for the next 24 hours is simple:

Where: t = time period (t =1, 2, 3, …, T) T = prediction period or number of days used to predict demand Dt = actual demand at time period t PDt = predicted demand for time period t For the prediction period (T), two prediction periods were selected:

21days (3 weeks) and 42 days (6 weeks).

2- Single exponential smoothing (SES) This technique is also implemented in an Excel spreadsheet. The

mathematical equations used by SES to predict the demand for the next 24 hours are:

∑

∑

=

=+

×= T

1t

T

1tt

1t

t

DtPD ( Eq. 8.35 )


190

Where:

t = time period (t =1, 2, 3, …, T) T = prediction period or number of days used to predict demand N = number of demand measurements per day Dt = actual demand at time period t PDt = predicted demand for time period t Et = actual prediction error at time period t α = smoothing constant For the prediction period (T), two prediction periods were selected:

21days (3 weeks) and 42 days (6 weeks). One of the problems regarding the SES is setting its smoothing constants, alpha, to the appropriate values. Thus, a several values of alpha were used to predict the demand for the same 184 days, and then selecting the “optimal” value of alpha that one results statistically in predictions close to the measured demands.

The following values of alpha were used : α = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9. It was found that alpha optimal for year 2002 was α = 0.7, while for year 2003 alpha optimal was α = 0.5 and 0.6 (see Table 2.1). As a compromise, alpha was selected to be α = 0.6 for both years.

Table 8.1 : Alpha setting for SES

SES 2002 SES 2003 Alpha R-Squared

10-1 MSE 10-2

R-Squared 10-1

MSE 10-2

0.1 9.660 4.780 9.586 4.435

0.2 9.752 3.534 9.672 3.592

0.3 9.777 3.066 9.704 3.279

0.4 9.791 2.825 9.718 3.137

0.5 9.798 2.693 9.976 2.569

0.6 9.820 2.356 9.976 2.581

0.7 9.822 2.400 9.719 3.164

0.8 9.800 2.548 9.709 3.282

0.9 9.795 2.617 9.693 3.457

3- Triple exponential smoothing (TES)

The same as the WMA and SES, this technique is implemented in an

Excel spreadsheet. The mathematical equations used by TES to predict the

tt

ttt

tt

SPD - (1 D S D - PD Et

=Ε × )+=

=α ( Eq. 8.36 )


191

demand for the next 24 hours are:

Where:

t = time period (t =1, 2, 3,… T) T = prediction period or number of days used to predict demand N = number of demand measurements per day Dt = actual demand at time period t PDt = predicted demand for time period t Et = actual prediction error at time period t α = smoothing constant For the prediction period (T), two prediction periods were selected:

21days (3 weeks) and 42 days (6 weeks). Again, we should set the smoothing constant, alpha, to the appropriate values. The following values of alpha were used : α = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9. It was found that alpha optimal for year 2002 was α = 0.2, and for year 2003 alpha optimal was α = 0.2 (see Table 8.2). Thus, alpha was selected to be α = 0.2 for both years.

Table 8.2 : Alpha setting for TES

TEST 2002 TEST 2003 Alpha R-Squared

10-1 MSE 10-2

R-Squared 10-1

MSE 10-2

0.1 9.734 3.610 9.645 3.923

0.2 9.767 3.076 9.706 3.228

0.3 9.752 3.373 9.616 4.263

0.4 9.709 3.743 9.552 5.032

0.5 9.655 4.701 9.455 6.196

0.6 9.573 5.765 9.310 7.967

0.7 9.450 7.454 9.093 10.708

0.8 9.263 9.055 8.769 15.039

0.9 8.979 9.502 8.288 22.075

4- SCP prediction technique

This is also simple technique and was implemented in MS Excel

spreadsheet. We tried here to mimic the same procedure done at the control

ttt1t

t3

1-tt

t1-t1-tt

t3

tt

ttt

A5.0VSPDEAA

E ) - 2 ( 1.5 A V V

E ) - (1 D S

D - PD E

×++= × − =

× ××+=

×+=

=

+

2

α

αα

α

( Eq. 8.37 )


192

room of SCP as describe in section 8.7 of this chapter, where the prediction period is 10 days and the prediction is updated about four times a day, i.e. every 6 hours. However, we will use the same prediction period (10 days), the prediction will be updated every 6 hours (4 times /day), and then every 24 hours (1 times/day) to compare between the two updating frequencies.

5- FINESSE predictor module

The only thing we have to do here is to prepare the demand data in

appropriate format accepted by FINESSE predictor, where the data must be in a text (tab delimited) format. Then the importation of data inside FINESSE should be done manually for each day. For the prediction period, two prediction periods were selected, the same as for SES and TES: 21days (3 weeks) and 42 days (6 weeks). Both the old and the new versions of the FINESSE demand prediction will be tested. The new one will be used to predict the demand twice by using single exponential smoothing level and smoothing constant = 0.6, and then by using triple exponential smoothing level and smoothing constant = 0.2 for the same prediction periods: 21days (3 weeks) and 42 days (6 weeks).

6- Autoregression integrated moving average (ARIMA)

For ARIMA, because this technique is more complex than the above

techniques, we used statistical analysis software known as “NCSS” (Hintze, 2005), which provides the user with time-series analysis tools; including ARIMA model.

The first step is to determine the order of differencing needed to stationarize the series. From the autocorrelation and partial autocorrelation functions, any non-stationarity in the series can be identified. The ACF is shown in Figure 8.5 for demand series. From the ACFs for both years 2002 and 2003, it is clear that the ACFs decay very slowly, indicating non-stationary series, and there are peaks every 96 time lags. These peaks imply a seasonal effect of season length = 96, which correspond to a daily pattern since the data is measured every 15 minutes (this already shown in the periodogram in Figure 8.4). It is likely that the model will need to incorporate a first order consecutive difference and a 96 seasonal difference term. Therefore, the ACF and PACF of the model ARIMA (0,1,0)(0,1,0)96 were examined. These are shown in Figure 8.6 and Figure 8.7. The series are now stationarized after differencing. In light of these figures, a model consisting of a non-seasonal autoregressive parameter, two non-seasonal moving average parameters, and a seasonal moving average parameter was considered as an appropriate model. The ARIMA model is written as ARIMA (1,1,2)(0,1,1)96, and the parameter estimation there significance on


193

the model were done by the NCSS software as shown in Table 8.3. However, further terms were added to the model but were found to be unnecessary. The next step was to examine the residual of the time series, and this done by the examination of the ACF of the residual. The ACF is shown in Figure 8.8 for both years 2002 and 2003. The figure shows that the series is white noise.

Figure 8.5 : Autocorrelation function of demand series


194

Figure 8.6 : Autocorrelation and partial autocorrelation functions, 2002


195

Figure 8.7 : Autocorrelation and partial autocorrelation functions, 2003


196

Figure 8.8 : Autocorrelation function of residual


197

Model Estimation Section for Year 2002: Model: Regular(1,1,2), Seasonal(0,1,1), Seasons = 96 Parameter Parameter Standard T-Value Prob Name Estimate Error Level AR(1) 0.529 1.162E-02 45.503 0.000 MA(1) 0.283 1.178E-02 23.999 0.000 MA(2) -0.231 6.310E-03 -36.659 0.000 SMA(1) 0.974 1.021E-03 954.085 0.000 Model Estimation Section for Year 2003: Model: Regular(1,1,2), Seasonal(0,1,1), Seasons = 96 Parameter Parameter Standard T-Value Prob Name Estimate Error Level AR(1) 0.381 1.426E-02 26.735 0.000 MA(1) 0.077 1.407E-02 5.476 0.000 MA(2) -0.235 6.674E-03 -35.205 0.000 SMA(1) 0.959 1.382E-03 693.853 0.000

Table 8.3 : Parameter estimation

8.9.2 Comparison of the prediction results The measured and predicted demands for these techniques are

compared to each others using the NCSS software. The results of this comparison (R-Squared, correlation, MSE, and MARE) are summarized in Table 8.4 and Table 8.5 and Figure 8.9 and Figure 8.10 shown in the next pages. The techniques are ranked in the tables.

For year 2002, the SCP technique is statistically in the first rank and the best one that predict the demand for our system because it gives the maximum R-Squared and correlation, and the minimum MSE and MARE, and the prediction was better with 2-hour updating frequency (SCP-2h) than with 24-hour updating frequency (SCP-24h). The new FINESSE demand predictor is in the second rank. The ARIMA technique comes in the third rank, then SES, TES, WMA, and the old FINESSE demand predictor in the last rank that what shows us Table 8.4 and Figure 8.9.

For year 2003, the SCP technique is still statistically in the first rank, and the prediction was better with 2-hour updating frequency (SCP-2h) than with 24-hour updating frequency (SCP-24h). ARIMA technique comes in the second rank, then SES which upgraded to the third rank.


198

While the new FINESSE demand predictor downgraded to the fourth rank, then TES, WMA, and the old FINESSE demand predictor is the last one that what shows us Table 8.5and Figure 8.10.

For all cases, it is clear that the single exponential smoothing forecasts the demand better than the triple exponential smoothing. Moreover, the effect of the 21-day and 42-day prediction periods was almost negligible for SES, TES and FINESSE, and this applies to both years 2002 and 2003. Generally, the 21-day prediction period is fairly better, except for old FINESSE predictor for the year 2003.

In parallel, the same comparison has been made between the different methods but for only one day arbitrarily selected during the peak period demand of the year 2003 (July 31, 2003). As shown in Figure 8.11 and Table 8.6, one note that the SCP technique, with 2-hour updating frequency (SCP-2h), is still statistically in the first rank and the best one that predict the demand for our system because it gives the maximum R-Squared and correlation, and the minimum MSE and MARE.


199

Figure 8.9 : Prediction methods comparison – Year 2002

Table 8.4 : Results - 2002

Rank Method R-Squared Correlation MSE MARE1 SCP-2h 0.9641 0.9819 0.0059 0.0729

2 FIN21_New_S06 0.9575 0.9785 0.0070 0.0758

3 FIN42_New_S06 0.9466 0.9729 0.0088 0.0838

4 FIN21_New_T02 0.9407 0.9699 0.0102 0.0942

5 FIN42_New_T02 0.9295 0.9641 0.0122 0.1004

6 SCP-24 0.8888 0.9428 0.0185 0.1253

7 ARIMA 0.8828 0.9396 0.0206 0.1312

8 SES-21 0.8566 0.9255 0.0236 0.1400

9 SES-42 0.8566 0.9255 0.0236 0.1400

10 TES-21 0.8272 0.9095 0.0308 0.1584

11 TES-42 0.8256 0.9086 0.0310 0.1591

12 WMA-21 0.7240 0.8509 0.0458 0.2004

13 FIN21_Old 0.6832 0.8266 0.0532 0.2176

14 FIN42_Old 0.6827 0.8262 0.0533 0.2219

15 WMA-42 0.6265 0.7915 0.0633 0.2470

R-Squared2002

0.60

0.70

0.80

0.90

1.00

SCP-

2h

FIN

21_N

ew_S

06

FIN

42_N

ew_S

06

FIN

21_N

ew_T

02

FIN

42_N

ew_T

02

SCP-

24

AR

IMA

SES-

21

SES-

42

TES-

21

TES-

42

WM

A-2

1

FIN

21_O

ld

FIN

42_O

ld

WM

A-4

2

R-s

quar

edCorrelation

2002

0.70

0.80

0.90

1.00

SCP-

2h

FIN

21_N

ew_S

06

FIN

42_N

ew_S

06

FIN

21_N

ew_T

02

FIN

42_N

ew_T

02

SCP-

24

AR

IMA

SES-

21

SES-

42

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1

FIN

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ld

FIN

42_O

ld

WM

A-4

2

Cor

rela

tion

Mean-Squared-Error (MSE)2002

0.000.010.020.030.040.050.060.07

SCP-

2h

FIN

21_N

ew_S

06

FIN

42_N

ew_S

06

FIN

21_N

ew_T

02

FIN

42_N

ew_T

02

SCP-

24

AR

IMA

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21

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42

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21

TES-

42

WM

A-2

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42_O

ld

WM

A-4

2

MSE

Mean Absolute Relative Error (MARE)2002

0.05

0.10

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0.20

0.25

SCP-

2h

FIN

21_N

ew_S

06

FIN

42_N

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02

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2 SCP-24 0.7733 0.8794 0.0237 0.1249

3 ARIMA 0.7679 0.8763 0.0245 0.1264

4 SES-21 0.7435 0.8623 0.0261 0.1404

5 SES-42 0.7435 0.8623 0.0261 0.1404

6 FIN21_New_S06 0.7288 0.8537 0.0281 0.1447

7 FIN42_New_S06 0.7089 0.8420 0.0312 0.1512

8 TES-21 0.7074 0.8411 0.0324 0.1522

9 TES-42 0.7026 0.8382 0.0325 0.1523

10 FIN21_New_T02 0.7008 0.8372 0.0334 0.1544

11 FIN42_New_T02 0.6658 0.8160 0.0385 0.1649

12 WMA-21 0.5771 0.7596 0.0429 0.1928

13 FIN42_Old 0.5327 0.7298 0.0498 0.2115

14 FIN21_Old 0.5040 0.7099 0.0536 0.2177

15 WMA-42 0.4623 0.6799 0.0577 0.2309

R-Squared2003

0.400.500.600.700.800.901.00

SCP-

2h

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24

AR

IMA

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42

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R-s

quar

edCorrelation

2003

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0.000.010.020.030.040.050.06

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MSE


0.050.070.090.110.130.150.170.190.210.230.25

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24

AR

IMA

SES-

21

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42

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Figure 8.11 : Prediction methods comparison – July 31, 2003

Table 8.6 : Results - July 31, 2003 Rank Method R-Squared Correlation MSE MARE

1 SCP-2h 0.8656 0.9304 0.0015 0.0228

2 FIN21_Old 0.8255 0.9086 0.0082 0.0652

3 FIN42_Old 0.8112 0.9007 0.0114 0.0727

4 ARIMA 0.7464 0.8639 0.0062 0.0497

5 WMA-42 0.7424 0.8616 0.0133 0.0814

6 WMA-21 0.7090 0.8420 0.0054 0.0494

7 SCP-24 0.6739 0.8209 0.0036 0.0363

8 FIN42_New_S06 0.6456 0.8035 0.0058 0.0462

9 FIN21_New_S06 0.6393 0.7996 0.0062 0.0497

10 FIN42_New_T02 0.6099 0.7809 0.0073 0.0544

11 SES-21 0.6097 0.7809 0.0052 0.0460

12 SES-42 0.6097 0.7809 0.0052 0.0460

13 FIN21_New_T02 0.5845 0.7646 0.0103 0.0708

14 TES-21 0.5680 0.7537 0.0079 0.0612

15 TES-42 0.5635 0.7507 0.0079 0.0611

R-SquaredJuly 31, 2003

0.40.50.60.70.80.91.0

SCP-

2h

FIN

21_O

ld

FIN

42_O

ld

AR

IMA

WM

A-4

2

WM

A-2

1

SCP-

24

FIN

42_N

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FIN

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FIN

42_N

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02

SES-

21

SES-

42

FIN

21_N

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02

TES-

21

TES-

42

R-s

quar

edCorrelation

July 31, 2003

0.6

0.7

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0.9

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Mean-Squared-Error (MSE)July 31, 2003

0.000

0.004

0.008

0.012

0.016

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24SE

S-42

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Mean Absolute Relative Error (MARE)July 31, 2003

0.00

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Figure 8.12 : Measured vs. predicted demands(July 31, 2003)

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Hour

Dem

and

(m3/

s)

Dm WMA-21 WMA-42 SES-21

SES-42 TES-21 TES-42 FIN21_Old

FIN42_Old SCP-2h SCP-24 ARIMA

FIN21_New_S06 FIN42_New_S06 FIN21_New_T02 FIN42_New_T02

Figure 8.12 : Measured and predicted demand (July 31, 2003)


203

Lately, we also made the same comparison for the years 2004 and 2005. The technique for the old version of FINESSE was excluded here since it is not available any more. The results of this comparison were in agreement with what we obtained for years 2002 and 2003. The SCP technique is still in the first rank, the SES forecasts the demand better than the TES, and the effect of the prediction periods was almost negligible.




2 ARIMA 0.9303 0.9645 0.0099 0.0861

3 SCP-24 0.8923 0.9446 0.0132 0.1009

4 SES-21 0.8523 0.9232 0.0161 0.1220

5 SES-42 0.8523 0.9232 0.0161 0.1220

6 FIN42_New_S06 0.8519 0.9230 0.0162 0.1251

7 FIN21_New_S06 0.8503 0.9221 0.0163 0.1254

8 FIN42_New_T02 0.8316 0.9119 0.0203 0.1419

9 FIN21_New_T02 0.8304 0.9113 0.0203 0.1423

10 TES-21 0.8256 0.9086 0.0217 0.1479

11 TES-42 0.8249 0.9083 0.0218 0.1480

12 WMA-21 0.6730 0.8203 0.0385 0.2245

13 WMA-42 0.5584 0.7473 0.0523 0.2835

R-Squared2004

0.50

0.60

0.70

0.80

0.90

1.00

SCP-

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AR

IMA

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SES-

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R-s

quar

ed

Correlation 2004

0.70

0.80

0.90

1.00

SCP-

2h

AR

IMA

SCP-

24

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21

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42

FIN

42_N

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0.000.010.020.030.040.050.06

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24

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MSE


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2 SCP-24 0.9417 0.9704 0.0201 0.1026

3 ARIMA 0.9303 0.9645 0.0290 0.1288

4 FIN21_New_S06 0.9025 0.9500 0.0335 0.1370

5 FIN42_New_S06 0.9004 0.9489 0.0344 0.1380

6 SES-42 0.8929 0.9449 0.0368 0.1408

7 SES-21 0.8929 0.9449 0.0368 0.1408

8 FIN21_New_T02 0.8927 0.9448 0.0377 0.1491

9 FIN42_New_T02 0.8916 0.9443 0.0382 0.1501

10 TES-21 0.8788 0.9374 0.0434 0.1588

11 TES-42 0.8779 0.9370 0.0435 0.1590

12 WMA-21 0.7945 0.8913 0.0703 0.2092

13 WMA-42 0.6316 0.7947 0.1264 0.2961

R-Squared2005

0.60

0.70

0.80

0.90

1.00SC

P-2h

SCP-

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AR

IMA

FIN

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R-s

quar

ed

Correlation 2005

0.75

0.80

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1.00

SCP-

2h

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AR

IMA

FIN

21_N

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tion


0.000.020.040.060.080.100.120.14

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8.9.3 Conclusion Data pre-treatment process, such as screening and smoothing, are

widely used as an effective and efficient time series mining tools. In this test the raw demand data was screened and smoothed to replace the missing data and remove the noise in the signal.

Prediction period is another issue that should be considered in the prediction. In this test, the effect of this issue was not quite evident for SES and TES techniques, and a little effect was observed for FINESSE. Anyway, when “data is money” from economic viewpoint, using less data to predict means less prediction costs. Thus, in some cases using a prediction technique that requires less data will positively be preferable in term of money.

As mentioned before, one of the problems regarding the exponential smoothing techniques is setting its smoothing constants, alpha, to the appropriate values. This parameter depends on the system demand and should be calibrated and updated from time to time.

An interesting result form this comparison is that the knowledge and the experience of the persons who manage and operate the networks at the SCP’s control room had permitted them to develop their own forecasting tools giving good forecasts for demands for the systems which they operate when compared to others known techniques such these presented here.

Finally, The morale of this comparison is neither to criticize nor to praise one of the these techniques but it’s rather to reveal that certain technique could be more appropriate for a system than others and vice versa depending mainly on the system itself. However, the persons who operate the system are the best one who can tell, based on their well understanding of the behavior of the system demand and water user, which technique (or techniques) is (are) appropriate(s) to predict the demand for the system.

10. CHAPTER 9 : Optimization of Water Distribution Networks

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CHAPTER 9

9. Optimization of Water Distribution Networks

9.1 Introduction Practical optimization is the art and science of allocating scarce

resources to the best possible effect. Optimization techniques are called into play every day in questions of industrial planning, resource allocation, scheduling, decision-making, etc. Many of large scale optimization techniques in general use today can trace their origins to methods developed during the World War II to deal with the massive logistical issues raised by huge armies having millions of men and machines. Any techniques that promised to improve the effectiveness of the war effort were desperately needed, especially in the face of limited numbers of people, machines, and supplies. The fundamentals of the first practical, large-scale optimization technique, the simplex method, were developed during the war. This simplex method was perfected shortly after the war when the first electronic computers were becoming available. In fact, the early history of computing is closely intertwined with the history of practical optimization. In the early years, the vast majority of all calculation on electronic computers was devoted to optimization via the simplex method (John, 2000).

New optimization techniques are arriving daily, often stimulated by fascinating insights from other fields. Genetic algorithms, for example, use an analogy to chromosome encoding and natural selection to evolve good optimization solutions. Optimization techniques play a role in training artificial neural networks used in artificial intelligence research for pattern recognition. Today, optimization methods are used everywhere in business, industry, government, engineering, and computer science because optimization problems arise just as regularly in these fields as they did during World War II (John, 2000) and (Simpson, 1994).

The process of optimization is shown schematically in Figure 9.1 (John, 2000). We typically begin with real problem, full of details and complexities, some relevant and some not. From this we extract the essential elements to create a model, and choose an algorithm or solution


207

technique to apply to it. In practical problems, the computer will carry out the necessary calculations. Moving from the algorithm or solution technique computer implementation is generally the province of numerical methods. Moving from computer implementation back to the algorithm or solution technique is called verification. The main idea is to make sure that the computer implementation is actually carrying out the algorithm as it is supposed to. Again, this will not be of great concern for users of well-tested commercial optimizers. We will be greatly concerned with the validation and sensitivity analysis, the process of moving between the algorithm or solution technique and the real world problem. Validation is the process of making sure that the algorithm or solution technique is appropriate for the real situation. Sensitivity analysis looks at the effect of the specific data on the results.

Figure 9.1 : Optimization process In most operational optimization methods, the optimization problem

is simplified through assumptions, discretization or heuristic rules. Such simplification makes it easier for specific optimization methods to determine the optimal solution, but introduces bias into the solution by excluding a large number of potentially good solutions. Genetic algorithms do not require such simplification measures, giving them a significant advantage in finding a near global optimal solution over most other optimization methods (Walski, 2003).

9.2 Optimization terminology

Objective function When optimizing a system or process, it is important to quantify how

good a particular solution is. A mathematical function called an objective function is used to measure system performance and indicate the degree to

Real word problem

Algorithm or solution technique

Computer implementation

Validation and sensitivity analysis

Analysis

Verification Numerical model


208

which the objectives are achieved. If multiple objectives exist, then there will be multiple objective functions.

The term optimization refers to mathematical techniques used to automatically adjust some details of the system in such a way as to achieve, for instance, the best possible system performance, or the least-cost design that achieves a specified performance level. The best or most advantageous solution (or solutions in multiobjective analysis) is called the optimal solution.

Decision variables In order to improve the performance of a system, the parameters that

can be changed must be known. These quantifiable parameters are called decision variables, and their respective values are to be determined. For example, in pipe-size optimization, the decision variables are the diameter for each of the pipes being considered. Any restrictions on the values that can be assigned to decision variables should be clearly stated in the optimization model. In the case of pipe sizes, each discrete pipe size available should be defined.

Constraints When judging systems and solutions, it is necessary to consider the

limits or restrictions within which the system must operate. These limits are called constraints. If one's objective is to attain a minimum-cost solution, for example, one must also consider the constraints on system performance and reliability. Constraints serve to define the decision space from which the objective function can take its values. The decision space is the set of all possible decision variables, and the solution space is the set of all possible solutions to the problem.

Constraints may be further classified as hard constraints, which may not be exceeded without failure or severe damage to the system, and soft constraints, which may be exceeded to a certain extent, although it is generally not desirable to do so. An example of a hard constraint is the maximum pressure that a pipe can withstand without jeopardizing the structural integrity of the system. A minimum pressure requirement for all water system nodes and a maximum permissible velocity for system pipes are possible soft constraints.

9.3 The Optimization process

The optimization involves:


209

a) The selection of a set of decision variables to describe the decision alternatives.

b) The selection of an objective or several objectives expressed in terms of the decision variables that one seeks to optimize (that is; minimize or maximize).

c) The determination of a set of constraints (both hard and soft), expressed in terms of the decision variables, which must be satisfied by any acceptable (feasible) solution.

d) The determination of a set of values (continuous or discrete) for the decision variables so as to minimize (or maximize) the objective function, while satisfying all constraints. In a more formal mathematical fashion, an optimization problem is

said to be given in the standard form if the above elements of the problem are presented as:

Objective function: Max f(x) Subject to constraints: X x0 h(x) and 0 g(x) ∈=≤ (Eq. 9.1)

Where:

f = objective function x = vector of decision variables f, g, h = functions of x X = set of all possible solutions When dealing with complex problems in practice, the experienced

engineer will of course adopt rules of thumb and use personal experience to focus on possible alternatives that are reasonably cost-effective, thereby dramatically reducing the decision space size.

Optimization is simply another type of modeling, and the logic that applies to the application of other computer models applies to optimization models as well. Optimization tools therefore should be used for supporting decisions rather than for making them - they should not substitute for the decision-making process (Goldman, 1998).

9.4 Water distribution networks optimization Given that water and energy are fundamentally important for the

health and vitality of any community, efficient energy management is important for water companies to meet government environmental targets and energy savings for economic reasons. For real-time control of water distribution networks, the aim should be to optimize the whole process for


210

both improved performance and operational-cost reduction, rather than one or the other.

Water distribution systems management is multidimensional. It embraces planning, design, construction, operation, and maintenance. Water distribution systems optimization has been a goal for many research and design projects in the water industry around the world, and can be broadly classified into two categories, namely design and operations. Design can include, for example, determining pipe diameters and locations of chlorine booster stations. Alternatively, water distribution systems operation is focused on the shorter time horizon, such as choosing trigger-levels in tanks for switching pumps on/off, and may also include chlorine dosing concentrations. More recently, water quality considerations have also been incorporated into water distribution systems optimization by requiring a minimum chlorine disinfection level throughout the system. Due to uncertainty in water distribution systems data, such as the demands and pipe roughness factors, reliability has also been incorporated into optimization. The objective has usually been to minimize cost, subject to hydraulic constraints, such as satisfying minimum pressure.

The efficient operation of such systems is a fundamental tool for extending the system’s service life as much as possible, thus ensuring a reliable service to the consumers while keeping electrical energy and maintenance costs at acceptable levels. Efficient operation requires knowledge of the system, supported by tools such as models for hydraulic simulation, optimization, and definition of rules, provides the operator with proper conditions for the rational operation of the system’s units. In this research work only the optimization of the operation of water distribution systems was dealt with.

Many water utilities spend 50% or more of their annual operating costs for electric power, of which more than 95% of the electric power budget may be associated with the cost of pumping (Pezeshk, 1996). Consequently, optimizing pump operations can generate significant savings that would be in the range of hundreds of thousands of euros annually.

The problem of finding the optimal operating strategy is far from simple: both the electricity tariff and consumer demand can vary greatly through a typical operating cycle; minimum levels of water have to be maintained in tanks to ensure reliability of the supply, and the number of pump switches in an operating cycle has to be limited to avoid excessive pump maintenance costs. Added to these factors the fact that the hydraulic behavior of water distribution systems is highly nonlinear, making computer modeling a complex and time-consuming process. Finally, the number of possible operating strategies becomes vast for systems with more than a few pumps and tanks.

In the planning, design and operating phases of a water system, there


211

are often many alternatives for each component of the system (Pérez, 2001). To illustrate the size of the optimization problem, consider a simple network design example in which only 10 pipes must be sized. If we assume that there are 10 discrete diameters to choose from for each pipe, then theoretically, the total number of possible design alternatives is 1010.

With the aid of a hydraulic network model, the modeler adopts a trial-and-error approach to produce a few feasible solutions, which can then be priced. The main reason to rely on any model in a decision-making process is to provide a quantitative assessment of the effects of management decisions on the system being considered. A model also provides an objective assessment as opposed to subjective opinions of system behavior. Thus, models should be used in support of decision-making.

Optimization, as it applies to water distribution system modeling, is the process of finding the best, or optimal, solution to a water distribution system problem. Examples of possible problems are the design of new piping or determination of the most efficient pumping schedule. This section provides a general overview of the optimization process, including key terminology and principles.

9.5 Applications of optimization in water distribution networks Many real-world engineering design or decision-making problems

need to achieve several objectives: minimize risks, maximize reliability, minimize deviations from desired (target) levels, minimize cost (both capital and operational), and so on. Various problems from water distribution modeling practice can be formulated as optimization problems. This section provides a brief overview of the main areas where optimization has been applied to water distribution management problems (Walski, 2003).

Automated calibration Before hydraulic network models can be used for predictive purposes

with any degree of confidence, they need to be calibrated against field data. Optimization can automate the process of adjusting the parameters of the network model by using a measure of the match between modeled and observed values as the objective. In other words, optimization in this case is aimed at determining the pipe roughness and nodal demand, which will minimize the difference between modeled and observed values (see Chapter 7).


212

Operational optimization Pump operating costs make up a large proportion of the expenses of

water utilities. It is therefore important to plan the operation of pumps to minimize energy consumption while maintaining the required standard of service and reliability. For water distribution systems, the objective function is normally defined to minimize the operational cost of the system over a period of time (typically 24 hours), and the decision variables are the times for which each pump is run.

Design/Expansion Design of new water distribution networks or expansion of existing

ones is often viewed as a least-cost optimization problem with pipe diameters being the decision variables. Pipe layout, connectivity, and imposed head and velocity constraints are considered known. Obviously, other elements (such as service reservoirs and pumps) and other possible objectives (reliability, redundancy, and water quality) exist that could be included in the optimization process. However, difficulties with including reservoirs and pumps and with quantifying additional objectives for use within the optimization process have historically kept most optimization researchers focused on pipe diameters and the single objective of least cost (Walski, 2003).

Rehabilitation Improvements in a water distribution system's performance can be

achieved through replacing, rehabilitating, duplicating, or repairing some of the pipes or other components (pumps, tanks, and so on) in the network, and also by adding completely new components. It is likely that funding will be available to modify or add only a small number of components to a network at any one time. The multiobjective optimization problem is therefore formulated to choose which components to add or improve (and how to improve them) in order to maximize the benefits resulting from the system changes, while minimizing the costs, possibly subject to budget constraints.

9.6 Optimization methods Optimization search methods range from analytical optimization of

one variable; to linear, nonlinear, and dynamic programming approaches. The most sophisticated search methods mimic various natural processes in


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their approaches; these techniques are called adaptive search methods. Adaptive methods known as genetic algorithms mimic the natural selection process and have been successfully applied to distribution network optimization (Walski, 2003).

The hydraulic simulation model is used to implicitly solve for the hydraulic constraints that define the flow phenomena (continuity and energy balance) each time the search method needs to evaluate these constraints. The search process starts by generating one or more initial solutions. Each solution is then tested by solving the hydraulic simulation model to compute the flows and pressures in the system. Based on the cost and performance (minimum pressure at nodes, minimum/maximum velocities, travel times, and so on), the solution is assessed and the search method generates a new test solution. The procedure is repeated until some convergence criterion is reached.

Analytical Optimization Analytical optimization techniques are often introduced in calculus

courses. These techniques usually deal with unconstrained problems for which one is trying to obtain the optimal solution to a problem that consists of an objective function alone (that is, without constraints imposed on the solution). The problem of unconstrained optimization of a function of more than one variable (the multivariate case) is concerned with finding the correct combination of the values of the variables to obtain the best value of the objective function. The criteria used for selecting the combination of variables are similar to those used for single-variable functions but require more complex mathematical techniques (Walski, 2003). Analytical optimization methods do not usually work well for network problems because of the large number of elements involved (pipes, valves, tanks, pumps, etc).

Linear programming Linear programming (LP) refers to the class of optimization

problems in which both the objective function and constraints in (Eq. 9.1) are linear functions that is, the variable's exponent is 1. The knowledge that the optimal solution of a LP problem is an extreme point motivates a special iterative procedure for reaching the optimum called the simplex method. Starting from a feasible extreme point, the simplex method changes the variables to move to an adjacent extreme point where the objective function has a larger value. Movement therefore occurs on the edge of the feasible region along a selected constraint line that is connected to the current extreme point. The procedure selects the next extreme point


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on the basis of the largest gain in the objective function value. It continues in this way until an extreme point is reached for which no further improvement in the objective function is possible (Hillier, 1995) and (Wagner, 1975).

One of the greatest advantages of LP over nonlinear programming (NLP) algorithms is that if the optimum exists, LP is guaranteed to find it. Thanks to the advances in computing of the past decade, problems having tens or hundreds of thousands of continuous variables are regularly solved. LP makes it possible to analyze the final solution and find its sensitivity to changes in parameters. However, the assumption of linearity is often not appropriate for real engineering systems, and it is certainly not appropriate for water distribution system optimization. Linear programming techniques work well for pipe sizing problems involving branched systems with one-directional flow (Walski, 2003).

Nonlinear programming Nonlinear programming (NLP) problems have the same structure as

the general optimization problem given in (Eq. 9.1). However, nonlinear programming refers to the class of optimization problems for which some or all of the problem functions, f(x), g(x), and h(x), are nonlinear with respect to the variables. NLP models more realistically capture certain characteristics of system relations but introduce significant computational difficulties. Nonlinear problems become even more difficult to solve if one or more constraints are involved. Some NLP problems are further complicated by the existence of decision variables that can only take one integer values. Discrete pipe sizes are an example of this. Optimization problems that combine continuous and integer values are referred to as mixed-integer problems and require a special set of techniques such as the Simple Branch-and-Bound (SBB) method (Hillier, 1995). Because of the nonlinear nature of head loss equations and cost functions, various nonlinear programming methods have been used for pipe sizing optimization and optimal pumps scheduling.

Dynamic programming Dynamic Programming (DP) is a procedure for optimizing a

multistage decision process in which a decision is required at each stage. The technique is based on the simple principle of optimality of Bellman (Bellman, 1957), which states that an optimal policy must have the property that regardless of the decisions leading to a particular state, the remaining decisions must constitute an optimal sequence for leaving that state. This technique is appropriate for problems that have the following


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characteristics:

a) The problem can be divided into stages with a decision required at each stage;

b) Each stage has a number of system states associated with it; c) The decision at one stage transforms that state into a state in the next

stage through a state transformation function; d) Given the current state, the optimal decision for each of the

remaining states does not depend on the previous states or decisions. Consider the following example, which illustrates the basic

principles behind the DP method. Assume that the operation of a water distribution system needs to be optimized over a 24-hour period under known demand conditions. If a day is divided into 24 periods, then the decision of how much water to pump into the central reservoir to meet demands and minimize the cost of pumping is made at 24 stages. The reservoir volume will go through different states during the 24 hours (for example, the reservoir could be full initially, then empty, and then refill). Therefore, the system state or the state variable is defined as the states of the reservoir (that is, the reservoir volume). The decision in the example is the volume pumped into the reservoir, and the state transformation function is the continuity equation relating the storage in one time period to the storage in the previous time period. Dynamic programming works well as long as the number of decision variables is very small.

Genetic Algorithms The theory behind Genetic Algorithms (GAs) was proposed by

Holland (Holland, 1975) and further developed in the 1980s by Goldberg (Goldberg, 1989) and others. These methods rely on the collective learning process within a population of individuals, each of which represents a search point in the space of potential solutions. Various applications have been presented since the first works, and GAs have clearly demonstrated their capability to yield good solutions even in the complicated cases of multi-peak, discontinuous, and non-differentiable functions. The following are the steps in a standard GA run:

1. Randomly generate an initial population of solutions. 2. Compute the fitness of each solution in the initial population. 3. Generate a new population using biologically inspired operators:

reproduction (crossover) and mutation. 4. Compute fitness of the new solutions.


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5. Stop if the termination condition is reached, or repeat steps 3 through 5 to produce successive generations.

Genetic algorithms belong to a class of nondeterministic algorithms

that draws on Darwinian evolution theory (Savic, 1997). This search strategy allows GAs to converge rapidly on an optimal or near-optimal solution while only analyzing a fraction of the number of possible solutions. Although they are not guaranteed to find the global optimum, GAs are generally good at finding "acceptably good" solutions to problems "acceptably quickly." Where specialized techniques exist for solving a particular problem, they are likely to outperform GA in both speed and accuracy of the final result. GAs can be computationally intensive when objective function evaluation requires significant computational resources such as those required for the hydraulic analysis of a large water distribution model.

9.7 FINESSE scheduler for optimal operational scheduling FINESSE software has an environment for performing enhanced

hydraulic modeling including optimal scheduling and other optimization tasks. This calculates optimal control schedules for pumps and valves, and for water production, with respect to specified system constraints, for example reservoir levels. The input data are similar to that of the simulator but also include constraints, electricity tariffs and simulated hydraulics. The scheduler, as with all tools in FINESSE, is general purpose in that it takes any data model of a network in FINESSE and if the model is feasible it calculates the optimal schedules (WSS-DMU, 2003). The scheduler has solved other networks such as Kilham (UK), Yorkshire Grid (UK), South Staffordshire water supply system (UK) and Aix Nord/Trévaresse (France) networks (Tischer, 2003). However, FINESSE Pump Scheduler considers only Hazen-Williams equation to calculate the elements headloss. Darcy-Weisbach equation is not considered for the moment in the Scheduler.

9.7.1 Mathematical principles and problem formulation

Optimal scheduling calculates operational schedules for pumps,

valves and treatment works for a given period of time, typically 24 hours, and can be classified as an optimal control problem. Generally speaking, the formulation of the optimal scheduling problems comprises three components (Tischer, 2003), (Walski, 2003), (Ulanicki 1997) and (Yu, 1994):


217

- Objective function - Network model - Operational constraints

They have to be expressed in the language of mathematical

equations. The optimization problem consists in searching the space of input schedules to minimize the cost over a given horizon while satisfying constraints on the output flows and heads. The problem formulation will involve many equations and many variables.

1) Objective function

The objective function typically includes energy cost for pumping

and treatment cost for producing a given mass of water. The formula for the energy cost should include a pump efficiency factor. The pumping cost depends on the electrical tariff. There are different pricing options proposed by electrical boards. The tariff is a function of time so there are cheaper and more expensive periods.

The optimization problem will be considered over a given time horizon. The operational cost can be expressed by the following equation (Eq. 9.2) containing the two terms corresponding to a unit tariff charge and the treatment cost respectively; other costs can be added as required.

( ) ( ) ( )( ) ( )( ) ( ) ( ) )2.9.(

,00

Eqdttqtdttctqthtgqt

s

f

p

f

Jj

t

t

js

jsjj

jj

Jj

t

t

jp ∑ ∫∑ ∫

∈∈

×+Δ

×= γη

γφ

Where:

o Ф = total operational cost o Jp = set of indices for pump stations o Js = set of indices for treatment works (sources)

o ( ) ( )( ) ( )( )tctq

thtgqjj

jj

,ηΔ = electrical power consumed by a j pump station at any

point of time o g q jΔh j = mechanical power required to increase the head of the

pump flow qj by Δh j , g is the gravity constant o η(qj

, cj) = pump efficiency, depends on the pump flow qj and the

control variable cj . The latter vector can represent number of pumps

on and/or pump speed. Typically η(qj , cj) is a quadratic function of qj

o jsq = water treatment work flow (sources)

o )(tc j = number of pumps-on and/or pump speed o (t)j

pγ = unit electricity tariff o (t)j

sγ = volumetric treatment cost for j treatment works


218

2) Network model The hydraulic model has been formulated in Chapter 5 (see section

5.3) :

( ) ( )tqhSdt

dhrr

r 1−−=

( ) )()( tqtqRh =Δ

dtq −=Λ )(

⎥⎦

⎤⎢⎣

⎡ Δ=ΓΔ

0h

h

The fundamental requirement in an optimal scheduling problem is

that all calculated variables satisfy the hydraulic model equations. The network equations are non-linear and play the role of equality constraints in the optimization problem. In the simulation task the operational schedule were known, in the optimal scheduling task the schedules for pumps, valves, and water production (treatment works schedules) are unknown and they are called decision variables.

3) Operational constraints

The operational control constraints reflect requirements for a

physical system to remain in a feasible state. They include:

• Constraints on operational variables, e.g. maximum number of pumps in a pump station.

• Treatment work requirements reflecting production technology such as: limited flow rate, limited change rate, limited total production.

• Reservoir levels lower and upper bounds. • Pressure requirements at critical nodes.

These constraints are linear and are very easy to handle by numerical

algorithms. The major task for operational control is to keep the system states within their assigned limits (feasible region). Practical requirements are translated from grammatical statements into mathematical equalities and inequalities. The control variables such as number of pumps-on, pump speed; or valve positions are constrained by lower and upper bounds determined by the construction of the control components:

(Eq. 9.3)


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cmin ≤ c(t) ≤ cmax (Eq. 9.4) Constraints on the control variable corresponding to water

production reflect the properties of the water treatment processes. These may be instantaneous constraints:

qs

min ≤ qs(t) ≤ qsmax for ∈t [ t0,tf ] (Eq. 9.5)

The reservoir levels (water network state variables) are constrained

in order to prevent the reservoirs from emptying or overflowing. These may also be used to maintain adequate reserve storage for emergency purposes:

hr

min ≤ hr(t) ≤ hrmax for ∈t [ t0,tf ] (Eq. 9.6)

Similar constraints must be applied to the heads at critical connection

nodes in order to maintain required pressures throughout the water network:

hc

min ≤ hc(t) ≤ hcmax for ∈t [ t0,tf ] (Eq. 9.7)

4) Decision variables

The network scheduling problem consists in searching the space of

decision variables to minimize the objective function over a given time horizon, whilst satisfying the constraints. The decision variables are operational schedules c(t) for the control elements (e.g. pumps and valves), and water production schedules )(tqs . For given control schedules ( )(),( tqtc s ) the network model equations can be solved and the values of all internal variables evaluated. This enables the calculation of the cost (value of the objective function Ф), and also the validation that all operational constraints are satisfied. Decision variables such as pump speed, valve position and pump flow are naturally continuous while others such as the number of pumps switched on are integer.

9.7.2 Transformation of the network scheduling problem into a

non-linear programming problem In order to solve the above optimization equations (objective

function, network model equations, and operational control constraints) numerically, the problem is converted into a non-linear programming problem using time discretization. The time horizon ],[ 0 ftt is replaced by a


220

discrete grid },...,,,{ 210 Ktttt where fK tt = and kk ttt −=Δ +1 is a timestep. The time grid can be referred to as }...,,2,1,0{ K . The integrals in the objective function (Eq. 9.2) are replaced by finite sums in (Eq. 9.7):

( ) ( ) ( )( ) ( )( ) )8.9.()()(

, 00Eqtkqkt

kckqkhkgqk

sp Jj

Kk

k

js

js

Jj

Kk

kjj

jjjp ∑∑∑ ∑

∈

=

=∈

=

=

Δ××+Δ×Δ

×= γη

γφ

The differential equation describing reservoir storage is discretized

using a simple Euler scheme in (Eq. 9.9):

( ) ( ) ⇒−= − tqhSdtdh

rrr 1

)9.9.(1,...,1,0)()()1( 1 EqKkforkqStkhkh rrr −=×Δ−=−+ − The algebraic equations (Eq. 9.3) are transformed by direct

replacement of the continuous argument (t) by the discrete variable (k). Thus (Eq. 9.8) is an objective function of the non-linear programming problem, (Eq. 9.3) and (Eq. 9.9) represent equality constraints, and [(Eq. 9.4), (Eq. 9.5), (Eq. 9.6), and (Eq. 9.7)] represents inequality constraints. In this interpretation, each equation is a collection of constraints for each timestep k=0,…,K-1, so the total number of constraints is equal to the number of equations multiplied by a number of timesteps. Similarly, the number of variables is multiplied by the number of timesteps, and subsequently the decision vector has the following structure:

In the transformed non-linear programming problem all variables are

decision variables and are iterated during the numerical procedure.

9.7.3 The equation-oriented programming language Substantial progress was made in the 1950s and 1960s with the

development of algorithms and computer codes to solve large mathematical programming problems. The number of applications of these tools in the 1970s was less than expected, however, because the solution procedures formed only a small part of the overall modeling effort. A large part of the time required to develop a model involved data preparation and transformation and report preparation. Each model required many hours of analyst and programming time to organize the data and write the programs

)10.9.()]1(),1(),1(),1(),1(),1(

...,),0(),0(),0(),0(),0(),0([

EqKqKqKhKhKqKc

qqhhqcxT

rTT

rT

csT

Tr

TTr

Tc

Ts

T

−−−−−−

=


221

that would transform the data into the form required by the mathematical programming optimizers. Furthermore, it was difficult to detect and eliminate errors because the programs that performed the data operations were only accessible to the specialist who wrote them and not to the analysts in charge of the project (Brooke, 1992).

There are very efficient modeling environments and solvers for resolving large-scale non-linear programming problems. The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming and optimization. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large scale modeling applications, and allows to build large maintainable models that can be adapted quickly to new situations. GAMS is available for use on personal computers, workstations, mainframes and supercomputers (Brooke, 1992), (Brooke, 1998), and (Ulanicki, 1997).

The GAMS programming language is a declarative language in that it declares what the problem is, rather than how to solve it. The GAMS compiler and a “Solver” automatically accomplish the latter task. The GAMS program is automatically compiled to a form that can be executed by numerical solvers. The results from the numerical solver are automatically returned and GAMS outputs the results.

CONOPT is a non-linear programming solver, which is based on the Generalized Reduced Gradient algorithm or originally in French “Gradient Réduit Généralisé” (GRG) first suggested by Abadie and Carpentier and was presented in English in 1969 (Abadie, 1969). Details on the algorithm can be found in Drud (1985 and 1992). Generalized Reduced Gradient is the generalization of Wolfe's reduced gradient method to a set of non-linear constraints. Hence it has the advantage of performing iterations in a reduced state space. Some variables are changed freely by the algorithm (super-basic variables) and some are calculated from the equality constraints of the problem (basic variables). The gradient is calculated only with respect to the super-basic variables. GRG algorithms are efficient for models with few degrees of freedom (Ladson, 1986) and (Drud, 1992). CONOPT can solve the optimal scheduling problem in reasonable operational time for medium-to-large sized networks (Drud, 1996).

The FINESSE scheduler for optimal scheduling problem and solution of different optimization tasks is based on the GAMS modeling language and the CONOPT solver. GAMS has been integrated into FINESSE by using a Dynamic Link Library (Tischer, 2003). The modeling environment includes previously prepared templates for different types of tasks. In order to solve a specific network the templates are filled with data from the data store. The optimal scheduling problem can be solved for any network topology. Because there is plenty of existing network models, as


222

GINAS input data files (Coulbeck, 1985) and (Ulanicki, 1999), the software is equipped with an auxiliary module to import existing models into the Data Store. If a model contains too many pipes it can be automatically simplified by a special network simplification.

The scheduler is general purpose. If a specific network is to be solved then modeling code is generated from the network data model stored in the FINESSE database. The optimization procedure is initiated by the user by operating the user interface. Data is transferred from FINESSE to the GAMS manager via the FINESSE data interface library. The GAMS manager produces the GAMS source file containing a complete and concise formulation of the problem for the specific network. The GAMS executable is then called to compile and execute the source file. The GAMS software environment itself controls the solver via its solver interface. When the solution is completed GAMS outputs the results into an output file according to instructions given in the source file. This output file is read by the GAMS manager and translated back to FINESSE via the FINESSE Data Interface Library (DMU-WSS, 2003).

9.7.4 Selection of a starting point

An important requirement for non-linear programming is the

selection of a starting point for numerical iterations. Non-linear programming belongs to a class of “hill climbing” local search algorithms and the starting point should be as close as possible to the final solution. All variables shown in the vector (Eq. 9.10) have to be initialized. Since GAMS and CONOPT solver are integrated into FINESSE environment with a common data structure, the simulator is used to provide an initial starting point for the network scheduler. This facilitates the solution of the initialization problem in a very efficient manner. The user provides an initial guess for water production (qs(t)) and pump schedules (c(t)), which are simulated and the hydraulic results passed to the scheduler as a starting point. In operational use, the initial schedules can be taken from historical data (Drud, 1994) and (Ulanicki, 1999).

9.7.5 Continuous relaxation of the network scheduling problem

Problems containing both continuous and integer variables are called

Mixed-Integer problems. The Mixed-Integer problems and the algorithms for solving them will briefly be presented in the next section. Examples of such problem in water distribution network are: optimal design of water distribution network (Hossein, 2006), optimal operation schedules of a water distribution network (Bounds, 2005), and discrete-time operative planning problem when operating schedules are specified typically in


223

hourly intervals (Burgschweiger, 2004). The FINESSE Pump Scheduler can produce both continuous and

discrete schedules. Decision variables such as pump speed, valve position and pump flow are naturally continuous while others such as the number of pumps switched on are integer. The energy savings are mainly obtained through reservoirs that enable the shifting of pumping between expensive and cheap tariff periods. The reservoirs can be filled during the cheap tariff periods and used to offset pumping during expensive periods.

The change in a reservoir volume over some period of time (timestep) is governed by its net inflow/outflow during that period, which in turn affects the average flow pumped during the period. Using this practical observation it is assumed that the integer decision variables can vary continuously within constraints. The scheduler in FINESSE initially assumes that the problem is a purely continuous one to calculate the optimal pump flows. The non-linear programming algorithm efficiently solves this relaxed continuous optimization problem. The relaxed optimal continuous solution is cheaper than any optimal discrete solution (Фc < Фd). The discrete solution that is found in the neighborhood of the continuous solution is assumed to be close to the optimal discrete solution (Ulanicki, 1999).

In the later version of FINESSE, a discrete scheduler is employed in order to translate the continuous solution into an integer solution for local operational use. As a starting point, the reservoir trajectories are taken from the continuous solution. For each tariff period, a Simple Branch-and-Bound algorithm (SBB) is applied to follow the original reservoir trajectories as closely as possible. However, the SBB solver is not available at the SCP.

SBB is a GAMS solver based on a combination of the standard branch-and-bound method known from mixed integer linear programming and nonlinear programming solvers supported by GAMS. Initially, the Relaxed Mixed Integer Nonlinear Programming (RMINLP) model is solved using the initial values provided by the modeler. SBB will stop immediately if the RMINLP model is unbounded or infeasible or fails. If all discrete variables in the RMINLP model are integer, SBB will return this solution as the optimal integer solution. Otherwise, the current solution is stored and the Branch-and-Bound procedure will start (SBB User Manual) and (John, 2000). The SBB method is the basic workhorse technique for solving integer and discrete problem. The method is based on the observation that the enumeration of integer solution has a tree structure. The main idea of Branch-and-Bound is to avoid growing the whole tree as much as possible. The name of the method comes from the “branching” that happens when a node is selected for further growth and the next generation of children of that node is created. The “bounding” comes from the bound on the best value attained by growing a node is estimated.


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9.7.6 Solution approaches to integer programming problems (IP) LP and NLP problems assume continuity of the solution region

where decision variables can equal whole numbers or any other real number. However, in engineering problems fractional solutions are not always acceptable. Integer programming (IP) requires a subset of the decision variables to take on integer values. IP also permits modeling of fixed costs, logical conditions, discrete levels of resources and nonlinear functions. Problems containing integer variables fall into several classes. A problem in which all variables are integer is a pure IP problem. A problem with some integer and some continuous variables, is a Mixed IP problem (MIP). A problem in which the integer variables are restricted to equal either zero or one is called a zero-one IP problem. There are pure zero-one IP problems where all variables are zero-one and mixed zero-one IP problems containing both zero-one and continuous (McCarl, 1997). IP problems are notoriously difficult to solve due to their combinatorial nature and potential existence of multiple local minima in the search space (Vladimir, 2003). They can be solved by several very different algorithms. Today, algorithm selection is an art as some algorithms work better on some problems.

After the invention of LP and NLP, those examining LP relatively quickly came to the realization that it would be desirable to solve problems which had some integer variables (Dantzig, 1960). This led to algorithms for the solution of pure IP problems. The first algorithms were cutting plane algorithms as developed by Dantzig, Fulkerson and Johnson (Dantzig, 1954) and Gomory (Gomory, 1958). Land and Doig subsequently introduced the branch and bound algorithm (Land, 1960). More recently, implicit enumeration (Balas, 1965), decomposition (Benders, 1962), lagrangian relaxation (Geoffrion, 1974) and heuristic (Zanakis, 1981) approaches have been used. Unfortunately, after 20 years of experience involving literally thousands of studies none of the available algorithms have been shown to perform satisfactorily for all IP problems (Von Randow, 1982). However, certain types of algorithms are good at solving certain types of problems. The section below briefly reviews these approaches.

A) Rounding

Rounding is the most naive approach to IP problem solution. The

rounding approach involves the solution of the problem as a LP problem followed by an attempt to round the solution to an integer one by dropping all the fractional parts; or by searching out satisfactory solutions wherein the variable values are adjusted to nearby larger or smaller integer values.


225

Rounding is probably the most common approach to solving IP problems. In general, rounding is often practical, but it should be used with

care. One should compare the rounded and unrounded solutions to see whether after rounding: a) the constraints are adequately satisfied; and b) whether the difference between the optimal LP and the post rounding objective function value is reasonably small. If so, the formal IP algorithms are usually not cost effective and the rounded solution can be used. On the other hand, if one finds the rounded objective function to be significantly altered or the constraints violated from a pragmatic viewpoint, then a formal IP exercise needs to be undertaken (McCarl, 1997).

B) Cutting planes

The first formal IP algorithms involved the concept of cutting planes.

Cutting planes remove part of the feasible region without removing integer solution points. The basic idea behind a cutting plane is that the optimal integer point is close to the optimal LP solution, but does not fall at the constraint intersection so additional constraints need to be imposed. Consequently, constraints are added to force the non-integer LP solution to be infeasible without eliminating any integer solutions. The cutting plane algorithm continually adds such constraints until an integer solution is obtained. Several points need to be made about cutting plane approaches. First, many cuts may be required to obtain an integer solution. Second, the first integer solution found is the optimal solution. This solution is discovered after only enough cuts have been added to yield an integer solution. Consequently, if the solution algorithm runs out of time or space the modeler is left without an acceptable solution (this is often the case). Third, given comparative performance in comparison with other algorithms, cutting plane approaches have faded in popularity (Dantzig, 1954) and (Gomory, 1958).

C) Branch-and-Bound

The second solution approach developed was the branch and bound

algorithm. Branch and bound, originally introduced by Land and Doig, pursues a divide-and-conquer strategy. The algorithm starts with a LP solution and also imposes constraints to force the LP solution to become an integer solution much as do cutting planes. However, branch and bound constraints are upper and lower bounds on variables. The branch and bound solution procedure generates two problems (branches) after each LP solution. Each problem excludes the unwanted non-integer solution, forming an increasingly more tightly constrained LP problem. There are several decisions required. One must both decide which variable to branch


226

upon and which problem to solve (branch to follow). When one solves a particular problem, one may find an integer solution. However, one cannot be sure it is optimal until all problems have been examined. The branch and bound approach is the most commonly used general purpose IP solution algorithm (Beale, 1977) and (Lawler, 1966). It is implemented in many codes including all of those interfaced with GAMS. However, its use can be expensive. The algorithm does yield intermediate solutions which are usable although not optimal. Often the branch and bound algorithm will come up with near optimal solutions quickly but will then spend a lot of time verifying optimality (Land, 1960).

D) Lagrangian relaxation

Lagrangian relaxation (Geoffrion, 1974) is another area of IP

algorithmic development. Lagrangian relaxation refers to a procedure in which some of the constraints are relaxed into the objective function using an approach motivated by Lagrangian multipliers. The main idea is to remove difficult constraints from the problem so the integer programs are much easier to solve. The trick then is to choose the right constraints to relax and to develop values for the Lagrange multipliers leading to the appropriate solution. Lagrangian Relaxation has been used in two settings: to improve the performance of bounds on solutions; and to develop solutions which can be adjusted directly or through heuristics so they are feasible in the overall problem (Fisher, 1981). An important Lagrangian Relaxation result is that the relaxed problem provides an upper bound on the solution to the unrelaxed problem at any stage. Lagrangian Relaxation has been heavily used in branch and bound algorithms to derive upper bounds for a problem to see whether further traversal down that branch is worthwhile.

E) Benders decomposition

Another algorithm for IP is called Benders Decomposition. This

algorithm solves mixed integer programs via structural exploitation. Benders developed the procedure, thereafter called Benders Decomposition, which decomposes a mixed integer problem into two problems which are solved iteratively - an integer master problem and a linear subproblem. The success of the procedure involves the structure of the subproblem and the choice of the subproblem. The procedure can work very poorly for certain structures. The real art of utilizing Benders decomposition involves the recognition of appropriate problems and/or problem structures which will converge rapidly. The most common reason to use Benders is to decompose large mixed integer problem into a small,


227

difficult master problem and a larger simple linear program. This allows the solution of the problem by two pieces of software which individually would not be adequate for the overall problem but collectively are sufficient for the resultant pieces. In addition, the decomposition may be used to isolate particular easy-to-solve subproblem structures (Benders, 1962).

F) Heuristics

Many IP problems are combinatorial and difficult to solve by nature.

In fact, the study of NP complete problems (Papadimitrou, 1982) has shown extreme computational complexity for problems such as the traveling salesman problem. Such computational difficulties have led to a large number of heuristics. These heuristics (Zanakis, 1981) are used when the quality of the data does not merit the generation of exact optimal solutions; a simplified model has been used, and/or when a reliable exact method is not available, computationally attractive, and/or affordable. Arguments for heuristics are also presented regarding improving the performance of an optimizer where a heuristic may be used to save time in a branch and bound code, or if the problem is repeatedly solved. Many IP heuristics have been developed, some of which are specific to particular types of problems. Generally, heuristics perform well on special types of problems, quite often coming up with errors of smaller than two percent. Heuristics also do not necessarily reveal the true optimal solution, and in any problem, one is uncertain as to how far one is from the optimal solution.

G) Structural exploitation

Years of experience and thousands of papers on IP have indicated

that general-purpose IP algorithms do not work satisfactorily for all IP problems. The most promising developments in the last several years have involved structural exploitation, where the particular structure of a problem has been used in the development of the solution algorithm. Such approaches have been the crux of the development of a number of heuristics, the Benders Decomposition approaches, Lagrangian Relaxation and a number of problem reformulation approaches. Specialized branch and bound algorithms adapted to particular problems have also been developed (Fuller, 1976) and (Glover, 1978). The application of such algorithms has often led to spectacular results, with problems with thousands of variables being solved in seconds of computer time (Geoffriones, 1974). The main mechanisms for structural exploitation are to develop an algorithm especially tuned to a particular problem or, more


228

generally, to transform a problem into a simpler problem to solve.

H) Other solution algorithms and computer algorithms The above characterization of solution algorithms is not exhaustive.

A field as vast as IP has spawned many other types of algorithms and algorithmic approaches. Genetic algorithms (GA) are powerful tools for solving IP problems (Vladimir, 2003). These methods do not require gradient or Hessian information. However, to reach an optimal solution with a high degree of confidence, they typically require a large number of analyses during the optimization search. Performance of these methods is even more of an issue for problems that include continuous variables. Several studies have concentrated on improving the reliability and efficiency of GAs. Hybrid algorithms formed by the combination of a GA with local search methods provide increased performance when compared to a GA with a discrete encoding of real numbers or local search alone (Seront, 2000).

Integer Programming softwares: Recent developments in integer–programming software systems

have tremendously improved our ability to solve large–scale instances. Today, instances with thousands of integer variables are solved reliably on a personal computer and high quality solutions. The basis of state–of–the–art integer–programming systems is a linear–programming based Branch–and–Bound algorithm (Atamturk, 2005). The most known software packages available for solving IPs are listed here. Complete coverage of these softwares is far beyond the scope of this thesis and the interested reader could consult:

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Categories/intprog.html

IP softwares list: 1. CPLEX : linear, quadratically constrained and mixed integer

programming. 2. SBB : Simple Branch-and- Bound Solver -GAMS 3. Excel and Quattro Pro Solvers : spreadsheet-based linear, integer

and nonlinear programming. 4. FortMP : linear and mixed integer quadratic programming. 5. LAMPS : linear and mixed-integer programming. 6. LINDO Callable Library : linear, mixed-integer and quadratic

programming. 7. LINGO : linear, integer, nonlinear programming with modeling

language.


229

8. MILP88 : mixed-integer linear programming. 9. MINTO : mixed-integer linear programming. 10. MIPIII : mixed integer programming. 11. MPSIII : linear and mixed integer programming (includes OML,

WHIZARD, and DATAFORM). 12. OML : linear and mixed-integer programming. 13. OSL : linear, quadratic and mixed-integer programming. 14. PROC LP : linear and integer programming. 15. Q01SUBS : quadratic programming for matrices. 16. QAPP : quadratic assignment problems. 17. What'sBest : linear and mixed integer programming. 18. WHIZARD : linear and mixed-integer programming. 19. XPRESS-MP : from Dash Associates-linear and integer

programming.

9.7.7 Discretization by post-processing of continuous solution The FINESSE Pump Scheduler does assume that the number of

pumps switched on can vary continuously between constraints. For example, 3.73 pumps switched on would be an acceptable solution. However, the continuous solution can be transformed into a discrete solution by simple post-processing. The idea behind the post-processing approach that I will present in the next paragraphs to discretize the continuous pump schedules, is that for every timestep the continuous number of pumps turned on is rounded up or down and, thus, the nearest discrete solution is chosen such that the deviation from the optimal reservoir trajectory is smallest.

Owning to the fact that the optimal pump schedule is continuous solution; therefore, any discrete solution will be less optimal, either in terms of total cost, or in terms of hydraulic behavior of the system. We assume that the best discrete solution in terms of hydraulic behavior lies in the neighborhood of the continuous solution.

When we round the continuous number of pumps up or down, for a given timestep, one parameter (or more) in the system must be therefore adjusted to eliminate the effect of the rounding on the hydraulic behavior of the system. In other words, the pump’s head and total discharge must be as those of the continuous solution for the given timestep. Here, I will illustrate how one can transform the continuous solution into discrete solution for the pump schedule by adjusting one of these parameters:

- Valve aperture, - Pump speed, or - Timestep length


230

1. Discretization by: Valve aperture adjustment In this approach, when we round the number of pumps up or down,

we adjust the valve aperture (or opening) mounted just at the outlet of the pumping station (Figure 9.2). When we round up the pump curve will move upward and since we attempt to maintain the discharge obtained by the continuous solution, hence, we decrease the valve aperture to increase system headloss and shift the system curve upward such that the two curves intersect at the same discharge obtained by the continuous solution but the pump head will increase. Conversely, when we round down the pump curve will move downward and to maintain the discharge obtained by the continuous solution, we increase the valve aperture to reduce system headloss and shift the system curve downward such that the two curves intersect at the same discharge obtained by the continuous solution but the pump head will decrease.

The criterion for rounding up or down is the change in the valve aperture (∆vv) such that whichever rounding results in smallest ∆vv will be selected as the discrete solution. This means the deviation from the pump optimal head is therefore smallest. The discretization procedure is shown in 0. This procedure is repeated for each timestep.

Figure 9.2 : Discretization by valve aperture adjustment

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350

1.0 Pump

2.0 Pumps

2.7 Pumps

3.0 Pumps

Sys tem Curve_2.7

Sys tem Curve_3.0

Sys tem Curve_2.0

upvhΔ

downvhΔ

3.0 pumps 2.7 pumps 2.0 pumps 1.0 pump

Qc

Hc

Qcont , Hcont

Pump Valvehv, vv Qcont

vQp k = h

852.1

vvv ⎟⎟

⎠

⎞⎜⎜⎝

⎛aperture valve:v

t coefficien valve:k headloss, valve:h

V

vv

Hup

HdownH (m

)

Q (l/s)


231

Figure 9.3 : Valve adjustment approach

From Continuous solution Ncont = number of pumps Qcont = total discharge Hcont = pump head

contvh = valve headloss

contvv = valve aperture

Input

Nup =Round-up(Ncont)

c NQb

NQa H

up

cont

2

up

contup +⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

contupupv HHh −=Δ

upv

contv

upv hhh Δ+=

( ) 54.0upv

cont

vupv h

Qkv =

upv

contv

upv v-vv =Δ

Ndown =Round-down(Ncont)

c NQb

NQa H

down

cont

2

down

contdown +⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

downcontdownv HHh −=Δ

downv

contv

downv hhh Δ−=

( ) 54.0downv

cont

vdownv h

Qkv =

contv

downv

downv v-vv =Δ

Calculations

discvdisc vand N

Output

Nup or Ndown?

downv

discvdowndisc

upv

downv

upv

discvupdisc

upv

downv

v vandN N then v v if

v vandN N then v v if

==Δ<Δ

==Δ>Δ

Discretization


232

2. Discretization by: Pump speed adjustment: Instead of adjusting the valve aperture one can adjust the pump speed

(RPM) to discretize the pump continuous schedule. If the pump speed is fixed then the discretization by valve aperture adjustment is the best choice. The advantage of the pump speed adjustment approach is that both pump discharge and head for discrete solution will be the same as those for the continuous solution (Figure 9.4).

When we round up the pump curve will move upward and since we attempt to maintain the pump discharge and head obtained by the continuous solution, hence, we decrease the pump speed (RPM) to shift the pump curve downward such that the pump and system curves intersect at the same discharge and head obtained by the continuous. On the other hand, when we round down the pump curve will move downward and since we attempt to maintain the pump discharge and head obtained by the continuous solution, hence, we increase the pump speed (RPM) to shift the pump curve upward such that the pump and system curves intersect at the same discharge and head obtained by the continuous.

The criterion for rounding up or down is the change in the pump speed (or speed ration Sr) such that whichever rounding results in smallest ∆Sr will be selected as the discrete solution. This means the deviation from the pump optimal speed is therefore smallest. The discretization procedure is shown in Figure 9.5. This procedure is repeated for each timestep. However, before all we have to derive the equation from which the speed ratio (Sr) is calculated.

Figure 9.4 : Discretization by pump speed adjustment

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300 350

2.7 Pumps_Sr=1

System Curve

2Pump_Sr=1.075

3Pumps_Sr=0.955

Hpump

Qpump

H (m

)

Q (l/s)

3Pumps_Sr=0.955

2Pumps_Sr=1.075

2.7Pumps_Sr=1

System curve nominalRPM

RPMspeed nominal Pumpspeed operating Pump Sr ==


233

Speed ration (Sr) - Pump equation at nominal speed (RPMnominal) is approximated by quadratic equation:

cQbQaH ++=⇒ nominalnominal2

nominal - If N pumps are configured in parallel, the pump equation will be:

cN

QbN

QaH +⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=⇒ nominal

2nominal

- If the pump operates at speed RPM different form RPMnominal :

22

nominal nominal nominalnominal

:1999) Nelik,(

SrRPM

RPMH

HandSrRPM

RPMQ

Q

LawAffinity

=⎟⎟⎠

⎞⎜⎜⎝

⎛===⇒

Then the pump equation is written like this:

cSrN

Qb

SrNQa

SrH

+⎟⎟⎠

⎞⎜⎜⎝

⎛×

+⎟⎠⎞

⎜⎝⎛

×=⇒

2

2

22

SrcSrNQb

NQaH ×+×⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=⇒

-We rewrite this equation for Sr:

0ˆˆˆ 2 =++⇒ cSrbSra

HNQac

NQbbcaWhere −⎟

⎠⎞

⎜⎝⎛===

2

ˆ,ˆ,ˆ:

- By solving this quadratic equation we obtain:

acabbSr

ˆ2ˆˆ4ˆˆ 2 −±−

=

- Then we calculate Sr when the number of pumps is rounded up and when it is rounded down. The approach is shown in Figure 9.5.


234

Figure 9.5 : Pump speed adjustment approach

discdisc RPM and N Output

Nup or Ndown?

updiscupdisc

downdiscdowndisc

updiscupdiscmin

downdiscdowndiscmax

RPMRPM andN N then Sr Sr If Else

RPMRPM andN N then Sr Sr If ElseRPMRPM andN N then RPM RPM If Else

RPMRPM andN N then RPM RPM If

==Δ>Δ

==Δ<Δ

==<

==>

updown

updown

down

up

Discretization


contup

con

up

cont

HN

tQac

NQbb

ca

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

=

=

2

ˆ

ˆ

ˆ

acabbSrup ˆ2ˆˆ4ˆˆ 2 −±−

=

upcontup SrSrSr −=Δ

nominalRPMSrRPM upup ×=


contdown

con

down

cont

HN

tQac

NQbb

ca

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

=

=

2

ˆ

ˆ

ˆ

acabbSrdown ˆ2ˆˆ4ˆˆ 2 −±−

=

contdowndown SrSrSr −=Δ

nominalRPMSrRPM downdown ×=

Calculations

Ncont = number of pumps Qcont = total discharge Hcont = pump head a, b, c = pump coefficients

contRPM = pump operating

contSr = speed ratio

nominalRPM = pump nominal speed RPMmax= pump maximum speed RPMmin= pump minimum speed

From Continuous solution Input


235

3. Discretization by: Timestep adjustment: The pump optimal schedule is calculated for a given period of time,

typically one day or one week with regular timestep Ts. Instead of adjusting the valve aperture or pump speed, we can discretize the pump schedule by adjusting the timestep, for example, if Ncont=2.7 pumps turned on for a given timestep (Ts) can be realized by a combination of 2 and 3 pumps switched over the timestep. The time lap for which the 2 pumps will be turned on and the time lap for which the 3 pumps will be turned on are calculated such that the discharged volume of water during the Ts, by a combination of 2 and 3 pumps switched over the timestep, equals to the discharged volume of water when 2.7 pumps are ON, and also the pump head should be the same in both cases as much as possible.

In general, over the timestep (Ts), the pumps are operated such that we turn on Nup=Round-up (Ncont) pumps for a certain time (tup) less than or equal (Ts), then we turn on Ndown=Round-down(Ncont) for the rest of the timestep (tdown=Ts-tup). As mentioned previously, tup and tdown are calculated such that the volume of water delivered to the system and the pump head during the timestep Ts equal that of the continuous solution. -The discharged volume is calculated like this:

downdownupupcont tqtqTsQ ×+×=×= volumeDischarged Where: Qcont = pumps total discharge obtained from the continuous solution qup = pumps total discharge when Ncont rounded up qdown = pumps total discharge when Ncont rounded down - And since the pump head assumed to be the same:

contcont

downdowncont

cont

upup

down

down

up

up

cont

cont

QNNqandQ

NN

q

Nq

Nq

NQ

×=×=⇒

=== pumpper Discharge

- And the sum of tup and tdown must be equal to timestep Ts:

downup ttTs +=

- We solve for tup and tdown :


236

( ) ( ) TsNNtandTsNNt contupdowndowncontup ×−=×−=

- If Ts =1 hour then tup will be equal to the decimal portion of the Ncont. The discretization procedure is shown in Figure 9.6.

Figure 9.6 : Timestep adjustment approach

It is clear that the discretization by adjusting timestep of the

optimization will produce solution with irregular timesteps. - Yet, the post-processing approachs are useful heuristics but depend

on either a local valve at the pump discharge, the pump being able to vary its speed, or the pump being durable with rapid switching for small timesteps.

Output

( )( ) TsNNt

TsNNt

contupdown

downcontup

×−=

×−=

Discretization



Calculations

From Continuous solution Ncont = number of pumps Qcont = total discharge Ts =regular timestep

Input

( Nup , tup )

( Ndown, tdown )


237

9.7.8 Remarks on GAMS/CONOPT Solver for optimal operational scheduling

In the following section I will consider two network examples and

use the Pump Scheduler to optimize them. The objective here is to check how good the GAMS/CONOPT solver is for solving an optimization problem. Some interesting remarks have been observed and they are presented hereafter.

1. Network configuration

Let’s consider the following network model created in FINESSE as

shown in Figure 9.7:

Figure 9.7 : Network configuration example 1 The scheme in Figure 9.7a is the original network, and the scheme in

Figure 9.7b is exactly the same network except that we added “dead-end” pipe at the suction side of the pumping station as indicated by the arrow on the scheme. However, this dead-end pipe has a negligible length and diameter and thus it does not change a bit the hydraulic operation of the network. I attempted to find the optimal pump schedule for this network using Pump Scheduler interface. The starting point (reservoirs levels,

(a) (b)

dead-end pipe


238

pumps and valves settings) is the same for both configurations. The optimization done here is continuous; this means that the number of pumps in operation can be any real number from 0 to nmax, and thus, for example, 2.3 pumps in operation is feasible.

For the original network in Figure 9.7a, the GAMS/CONOPT solver was not able to find the optimal solution and instead an “Infeasible Solution” was found and the total costs were 11.247 k€, and it took 3 seconds to find this solution. For the second network in Figure 9.7b the solver, however, was able to find the optimal solution and the total cost was 6.228 k€, and it took 8 seconds to find this optimal solution. If one tries to change the location of the dead-end pipe the Solver will find optimal solution if and only if the dead-end pipe is connected to one of the three nodes that have a black mark in the center as shown on Figure 9.7b.

Let’s take also another network example and do the same thing as in the above example. The scheme in Figure 9.8a is the original network, and the scheme in Figure 9.8b is exactly the same network except that we added “dead-end” pipe to the reservoir and at the suction side of the pumping station as indicated by the arrow on the scheme. For both configurations and the same starting point (reservoirs levels, pumps and valves settings), the GAMS/CONOPT was able to find optimal solution for both of them but the optimal solution was not the same solution for each. The total costs for the network in Figure 9.8a were 542.0 €, and the total costs for the network in Figure 9.8a were 174.0 €. If one tries to change the location of the dead-end pipe, the Solver will find the 174.0 €-optimal solution when the dead-end pipe is connected to any node in the network except for the node immediately at the discharge side of the pump where the 542.0 €-optimal solution is found.

Figure 9.8 : Network configuration example 2

dead-end pipe

(a) (b)


239

In spite of the fact that the two networks are hydraulically the same but it seems that they are mathematically not the same for GAMS/CONOPT Solver.

In parallel, these network models were sent to WSS at DMU to reexamine them and they have made some investigations into FINESSE and the scheduler. It was found that the main problem is that we are using an old version of GAMS and CONOPT (1999) at SCP. While at DMU they are currently using a later version of GAMS and CONOPT (2003). This means that they cannot reproduce our results exactly. They got infeasible solutions for the networks in Figure 9.7a and Figure 9.7b. However, when they modified the starting point of the pump stations then they got an optimal solution and the cost was 6.228 k€ for both networks in Figure 9.7a and Figure 9.7b (the dead-end pipe had no effect), this is exactly the same cost we got here by the old version of GAMS and CONOPT when the dead-end pipe is added.

For the networks in Figure 9.8a and Figure 9.8b they did get optimal solutions without modifying the starting point, and the cost was of 174.0 k€ for the network in Figure 9.8a, and it was of 161.4 € for the network in Figure 9.8b. In this case even the results of the new version of GAMS and CONOPT were affected by the dead-end pipe. However, they got the same optimal solution that we got by the old version of GAMS and CONOPT when the dead-end pipe is added (174.0 €). The dead-end pipe does not affect the hydraulic operation of the network and should have zero flow and zero head difference but this may not be true during the optimization because there may be a numerical inaccuracy.

2. Starting points

Not only the network configuration affects the performance of the

GAMS/CONOPT Solver but also the starting points, i.e. the initial hydraulic conditions including: reservoirs levels, valves apertures, number of on-pumps, have an effect on the optimal solution. For the same networks in Figure 9.7 and Figure 9.8 I tried different starting points by changing randomly the valves apertures and I got sometimes “optimized solution”, sometimes “infeasible solution”, sometimes “GAMS execution error”, and sometimes “Error in solution”. At some starting points where an optimal solution is found for network in Figure 9.7b the total costs were not the same, for example: 6.228 k€ , 6.237 k€, and 6.582 k€, and for the network in Figure 9.8a : 151.0 k€, 174.0 k€, 187.0 k€, 195.0 k€, 275.0 k€.

For the network in Figure 9.7 I, however, tried to find an optimal solution without using the Pump Scheduler but instead I used the simulation and the trail-and-error technique and I reached an optimal discrete solution where the total costs were about 5.516 k€, and this is


240

obviously cheaper than the costs found by GAMS/CONOPT Solver (6.228 k€). Then, I used this solution as starting point to initialize the Solver, and the Solver was able to find an optimal solution and the total cost was about 5.767 k€; this solution is cheaper than the solutions obtained previously but even though it is still higher than the solution obtained by trial-and-error technique. Moreover, for this starting point the Solver was able to find the 5.767 k€-optimal solution for the network in Figure 9.7 with and even without adding the dead-end pipe.

3. Multi-optimal solutions

As has been shown here above, the water network has multi-optimal

solutions according to GAMS Solver, and an optimal solution depends on the system configuration and the starting point. This is a non-convex optimization and such a problem may have multiple feasible regions and multiple locally optimal points within each region. Even that the starting point is very close to an optimal solution, the Solver might diverges from the optimal solution.

4. Optimization Timestep

The optimization timestep were 3-hours for which all above optimal

solutions were found. But, when the optimization timestep was reduced to 1-hour it was hard to obtain an optimal solution for the network in Figure 9.7, while the Solver still was able to find optimal solution even when the timestep was reduced to 1-hour for network in Figure 9.8.

5. Valve aperture

The discrete optimization searches an optimal discrete solution such

that the number of pumps in operation is necessarily integer number, but on the other hand the valve aperture is allowed to be continuous and it lies between 0 and 1. However, this solution is feasible providing that the valves are fully automated, otherwise, this solution is infeasible and it will be hard to actuate the valves continuously.

11. CHAPTER 10 : Development Program and the Reversible Pump-Turbine Plant

241

CHAPTER 10

10. Development Program and the Reversible Pump-Turbine Plant of

Trapan Dam

10.1 Introduction

The development program proposed in the general study of hydraulic operation and management of “Toulon Est” network performed upon the decision of SCP to improve safety and reliability of the water-supplying service for the eastern zone of the region of Toulon city (Engineering Division-SCP, 2002). The primary objective is to maintain the possibility of supplying the priority customers in the case of unavailability of water from Les Laures or in the case of pipe bursting on the main pipeline between Les Laures and Trapan dam and, consequently, the infrastructures of the “Canal de Provence” upstream of the divisor of Les Laures will be out of service for a long time. It is also a question of allowing the organization of maintenance operation programmed during the off-peak period of water consumption, and in particular the cleaning activities of the Montrieux gallery. It appeared necessary to extend safety in case of a serious incident intervening on one of the sections of the main pipeline between Les Laures and Gratteloup. This objective implies the construction of a pumping station at Trapan dam to mobilize the volume of this dam, which could be associated with new water tank to be built to the right side of Le Col Gratteloup (Figure 10.2).

The second objective is to generate electrical energy by the possibility of equipping the station of Trapan with a reversible pump-turbine unit, and of associating it with the Gratteloup tank to maximize net head for the turbine. The unit associated with the Gratteloup tank also offers opportunity of realizing a third objective that is to increase the system supply flow to satisfy new eventual demands. This objective is added to the agenda with the increase in the subscription of the SIDECM intervened in 2002.


242

10.2 Optimization of pumping stations at SCP Before speaking about the optimization of the pumping station of

Trapan, I will briefly introduce here the optimization procedure applied at the SCP’s control center. As most of water agencies and companies, the SCP has requirements for an effective operation policy for the pumping stations. The operation policy for a pumping station represents a set of temporal rules or guidelines (pump operating times) that indicate when a particular pump or group of pumps should be turned on and off over a specified period of time, typically 24 hours. The optimal pump policy is the schedule of pump operations that will yield the lowest operating cost while satisfying the desired operational performance of the water system: maintaining an adequate pressure range and meeting water turnover and storage requirements.

In order to optimize the energy costs, contractual constraints must be considered when setting an operation policy for the pumping station. These are the contractual subscriptions and constrains of EDF that correspond to a maximum number of pumps turned on according to the EDF tariff period.

EDF’s Scenario allows defining the tariff periods. For SCP, we always use the same scenario. This scenario is cyclic, it is the same whatever the day: Peak period is from 06:00 to 22:00, and Off-peak period is from 22:00 to 06:00. Also, the year is divided into two large periods; the winter period and the summer period. Winter period is from 1st November to 31st Mars, and Summer period is from 1st April to 31st October. In addition to this scenario, signals are sent from the field, they inform of the tariff period seen locally by the station to check permanently that the pump scheduling program is well coupled with the field and to identify inconsistencies. Generally speaking, at SCP there are two modes for the optimization of pumping station operation:

A. Optimization based on the water demand forecast For this optimization mode, the operating flow of the considered

station is calculated from water demand forecasts and, hence, the volumes of water which will be consumed from the downstream tank during a tariff period are calculated. Two tariff periods are distinguished:

- Off-peak period: during this period the objective is to deliver the

maximum volume at the end of the period. - Peak period: during this period the objective is to deliver the

minimum volume at the end of the period while maintaining the volume of security in the tanks.


243

In general manner, optimization always uses the minimum necessary number of pumps to be turned on. The optimization algorithm can be described as follows:

1. Creating the forecast scenario according to the statistics of the

downstream tanks (continuous flows), 2. Recovering the available drawdown volume of the tanks (the

difference between the high and the actual water level in the tank), 3. Distributing this drawdown volume between the upstream pumping

stations, 4. Calculating, at the stations level, the optimization scenarios

according to the available drawdown volume, to tariff period, and to the pumping station constraints (allowed nominal discharge). This algorithm is a backtracking testing the various possible adjustments until obtaining a solution fulfilling these criteria. B. Optimization based on the tank’s water level In this mode, the control of the pumping station flow can

nevertheless be carried out in a local way without using forecasts. In this case, the pumping station is directly controlled depending on the water level in the downstream tank. Such a control can be carried out directly by using automated controllers.

The principle is then the following. Thresholds of water levels will trigger the start-up or the switch-off of the pumps. This system allows maintaining, roughly, the water level in the tank within a certain limit. A lower level or a high level is used according to whether we want to empty the tank or we want to store water in the tank. During the off-irrigation period in winter, the operation is based on the high level such that we refill the tank during the off-peak tariff period of EDF (in the night), and based on low level to empty the tank during peak tariff period of EDF (in the day). During the peak water demand, it is necessary that the tank level is permanently maintained at the high level.

10.3 The Pump – Turbine plant of Trapan

Two installation options are proposed for the equipment of the plant at Trapan: - Installation of two pumps of the same characteristics in parallel. - Installation of three pumps in parallel with the possibility of delaying the installation of the third pump.


244

The technical solution suggested hereafter results from the first research near manufacturers which made it possible to be ensured of the existence in the market of equipment adapted to the case studied here, but which also showed the choice is very restricted. Pre - consultation was launched near five suppliers of pumps concerning the supply of a machine that fulfills in the best possible conditions the desired objectives in terms of pumping and turbining. Only one manufacturer could present a material answering the arising problem. The pump - turbine unit proposed is a standard reversible pump "SULZER" and no particular adaptation is necessary for turbine-mode. It concerns a model of pump that was developed for severe particular applications such as the pumping out of mine with heads of 400 m, and of boiler supply with temperatures of 100C°. For the moment, SCP does not purchase this unit.

The optimal hydraulic operation points and hydraulic characteristics of this pump - turbine unit are summarized in Table 10.1 and Figure 10.1:

Table 10.1 : Optimal operating points

Mode Pump Turbine

Discharge (l/s) 256 345

Net charge (m CE) 177 240

Nominal speed (tr/mn) 1,525 1,525

Efficiency (%) 84 83


245

Figure 10.1 : Hydraulic characteristics of the pump - turbine unit


246

10.4 Gratteloup water tank

The functions of a new water tank to be built at Le Col Gratteloup are: A. Increase the system flow

It is a question of building at Gratteloup a complementary volume to the volume already available in the existing tanks to improve the compensation of the daily demand of the whole networks upstream of the Gratteloup and to increase thus the system flow available downstream. B. Energy production

The Gratteloup tank will participate in the energy production because it will allow increasing the net head available to the turbine by allowing the disconnection of all the networks located downstream of Trapan. The volume necessary corresponds to the daily demand asked at La Môle in winter that should be stored in the tank during the night; i.e. during the off-peak period of electricity tariff (8 hours from 22h to 6h) to maintain the continuity of the service for the networks during the turbine-mode period (peak period of electricity tariff). If we consider only the flow subscribed for normal use by the SIDECM, that is 330 l/s, this volume is approximately 4,750 m3 if the water turbining is limited to 4 hours per day (peak period only), and of 19,000 m3 if the water turbining intervenes during the totality of the peak period (16 hours).

At this stage, we consider that the volume reserved for the turbining will be at least 5,000 m3, to go up to approximately 20,000 m3 according to the selected option and if we wish to maximize the energy production. 10.5 Piping and fittings

The supply in pumping mode and the rejection in turbining (Figure 10.5) will be ensured by a single siphon (Figure 10.3). It is a pipeline of 900 mm in diameter and length of 200 m approximately. It will be laid on the bottom of the dam and its upper end at water level of 43 m. The end of the siphon will be equipped with a strainer. It is admitted that the station will not be able to operate in pump and turbine mode at the same time insofar as we do not consider the doubling of the siphon; as well as of the pump discharge pipe until the connecting point on the main supply pipe (about 170 m pipes and fitting). A deep well of 7.5 m is dug near the dam on the left bank at the high point of the siphon. Then, this well will


247

accommodate a balloon connected to a vacuum pump laid out at the high point of the siphon for pump priming. The water level adjustment in Trapan can be done by a winch installed on the banks with a system with cable and pulley. An articulation is considered on the last section of the siphon equipped with a mobile joint making it possible the pipe intake to vary between the minimum and maximum allowable levels of Trapan (43 m and 56 m respectively). A system of vertical guide will have to be set up for this section of mobile pipe.

The pipe connecting the station to the dam will end up in the suction well equipped with a general isolation valve. This collector well will include three taps for the pump-turbine groups (including one closed by a flange corresponding to the reservation for the third group) corresponding to the 600 mm-suction pipes of the groups with for each group an electrically motorized valve. This valve will allow the change of the unit-operating mode: pump or turbine. The valves will have hydraulic controls and security mechanism. The securization will be ensured by a counterweight that guarantees the full cut of the flow within approximately 20 seconds in the case of power outage of EDF, it is pump-overspeeding protection. A water hammer protecting tank will be connected to the end of the suction well.

The connection of the station and the main supply pipe is done by a pipe in 700 mm diameter and 120 m in length at point located at about fifty meter approximately before the arrival on the pressure dissipater tank (Figure 10.4). The installation of isolation valve will allow the isolation of the section Laures - Trapan to pump only towards Gratteloup tank.


248


Elev

atio

n (

m N

GF)

Les Laures Dissipator (295 m NGF) Figure 10.2 : Hydraulic profile of Toulon Est network


Elev

atio

n (

m N

GF)

Les Laures Dissipator (295 m NGF)


249

Figure 10.3 : 900mm-pipeline profile connecting the station to Trapan

Figure 10.4 : 700mm-pipeline profile connecting the station and the main supply pipe


250

Figure 10.5 : General view of the project

Trapan Dam

Siphon intake

Pumping Station

Pumping Direction

Turbining Direction


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10.6 Electrical equipments

The electrical motor-generator will be of the Asynchronous type. It will be in a standard way as well driving motor as generator with the possibility of reversing the sense of rotation. Each motor (two motors for first phase and future one for the future third group) will have a rating power of 1,000 kW. It is also considered two transformers of electrical power. Each one will function like a step-down transformor in pumping mode, and each one will also be able to function like a step-up transformor in turbine-mode, thus these two transformors will have to be reversible. Lastly, each unit of the reversible pump-turbine will be controlled by such a reversible variable speed transmission. 10.7 Operating points of pump-turbine plant

After this general presentation of the development program of “Toulon Est” and the pump-turbine plant of Trapan, we now will analyze and simulate the different possible scenarios of the station operation in order to determine the operating points (discharge and head) in turbine mode and in pump mode. However, some part of this analysis was carried out before by the Engineering Division-SCP in the framework of the project brief and the development program of Toulon Est. We thus will redo this analysis but with FINESSE software.

A- Turbine mode

This mode is about the electrical energy production by turbining water coming from Les Laures by gravity by exploiting the volume available in Trapan dam. The objective of the following analysis is to identify the operating point of the turbine.

To find the operating point of the station in turbine mode we will trace initially the system curve. The system curve is the difference in altitude between the divisor at Les Laures and the Trapan dam “less” the headloss in the main supply pipe. It depends on the turbine flow and the derived water demands. Hydraulic conditions and hypothesis

In this operating mode, only one turbine will be in function at

constant speed, which is the nominal speed of the machine (1,525 rpm). We define two system curves; maximum head curve and minimum head curve.


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- Maximum head: corresponds to the difference between the high water level in Les Laures (295 m) and the low water level in Trapan (45 m), less the headloss calculated with the optimistic hypothesis of roughness (ε =0.5 mm). To maximize the head available at Trapan, it is provided that all the tanks between Les Laures and Trapan are insolated, that no water demand takes place on the main supply pipe, and that the delivery of La Môle (point M) does not withdraw. The net head available at Trapan is thus maximal. - Minimum head: corresponds to the difference between the low water level in Les Laures (293 m) and high water level in Trapan (57 m), less the headloss calculated with the pessimistic hypothesis of roughness (ε =3.0 mm), and with a flow delivered on the way taken equal to 50 l/s and transported up to approximately 5 km downstream from Golf Hôtel to represent the winter demand, which can not be provided from a tank during the turbining periods. The net head available to Trapan is thus minimal.

The two cases are modeled and simulated using FINESSE. Only the following components are kept and modeled in FINESSE to trace the curves: - Les Laures divisor modeled as fixed head reservoir. - Trapan dam modeled as fixed head reservoir. - Main supply pipe from Les Laures to Trapan.

The two system curves issued from this simulation and the characteristic curve of the turbine provided by the manufacturer are overlapped and the intersections of both give the operating points. While referring to the graph below (Figure 10.6) we find that the nominal operating points of the turbine are:

- Maximum head: The flow is 341 l/s (1,227 m3/h), the head available at Trapan is 235 m, and the efficiency is 83% (from Figure 10.1). - Minimum head: The flow is 322 l/s (1,166 m3/h), the head available at Trapan is 215 m, and the efficiency is 82% (from Figure 10.1).


253

Figure 10.6 : Turbine operating points

This analysis shows that the operating points of the turbine are naturally almost at its best performance.

B- Pump mode

The first function which the pump-turbine station will have to provide is that maintaining water supply of the customers located between the divisor of Les Laures and Trapan dam in the case of unavailability of water from Les Laures or in the case of pipe bursting on the main pipeline between Les Laures and Trapan. In view of the system current hydraulic state, there is no any possibility of emergency supply. From the point of view of system safety, we can consider that the station will also allow minimizing the incidents risks because it will make it possible or more convenient the maintenance interventions. Currently certain operations prove to be impossible because of the duration of the water cuts; it is particularly the case for Montrieux gallery cleaning, the guard valves on the gallery at Les Laures, and the sectional valves equipping the main supply pipe, and also the pipes flushing operations.

The pumping station will function according to three distinct modes which we will be modeled separately hereafter. It will be equipped with three pumps in parallel, but in the first phase only two groups will be installed.

Hea

d (m

)

Flow (l/s)

50

100

150

200

250

300

150 200 250 300 350 400 450 500 550 600

Turbine V = 1525rpmcharge nette maxicharge nette mini

Turbine V=1525rpm Head_Maxi Head_Mini


254

1) Pumping to Les Laures

It is the case of pumping water to Les Laures in emergency cases; we pump water back from Trapan to Les Laures divisor. Hydraulic conditions and hypothesis

In this operating mode we will simulate the operation of the station by changing at the same time the number of operating groups and the rotation speed of the pumps. We define two system curves; maximum head curve and minimum head curve. - Piezometric conditions maximal: corresponds to the difference between high water level in Les Laures (295 m) and low water level in Trapan (45 m), plus the headloss calculated with the pessimistic hypothesis of roughness (ε =3.0 mm). All the tanks between Les Laures and Trapan are isolated. - Piezometric conditions minimal: corresponds to the difference between low water level in Les Laures (293 m) and high water level in Trapan (57 m), plus the headloss calculated with the optimistic hypothesis of roughness (ε =0.5 mm), and with all the tanks between Les Laures and Trapan are isolated.

Only the following components are kept and modeled in FINESSE to trace the curves: - Les Laures divisor modeled as fixed head reservoir. - Trapan dam modeled as fixed head reservoir. - Main supply pipe from Les Laures to Trapan.


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Table 10.2 : Pumping to Les Laures

Piezometric conditions maximal 1 Pump 2 Pumps 3 Pumps

Speed (rpm) Q ( l/s) H (m) θ (%) Q ( l/s) H (m) θ (%) Q ( l/s) H (m) θ (%)

1,000 # # # # # # # # #

1,100 # # # # # # # # #

1,200 # # # # # # # # #

1,300 # # # # # # # # #

1,400 # # # # # # # # #

1,500 # # # # # # # # #

1,600 38 250 23 66 251 20 84 252 17

1,700 207 259 78 295 269 65 330 274 53

1,800 272 266 83 435 291 77 483 301 66

1,900 327 273 83 524 310 81 608 331 73

2,000 375 281 82 603 329 83 714 361 77

Table 10.3 : Pumping to Les Laures

Piezometric conditions minimal 1 Pump 2 Pumps 3 Pumps


1,000 # # # # # # # # #

1,100 # # # # # # # # #

1,200 # # # # # # # # #

1,300 # # # # # # # # #

1,400 # # # # # # # # #

1,500 # # # # # # # # #

1,600 136 239 64 210 243 53 250 245 44

1,700 243 244 82 410 260 77 475 268 68

1,800 303 249 84 516 273 82 639 293 77

1,900 356 254 82 607 288 83 754 315 80

2,000 403 259 80 690 302 83 858 338 82


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This analysis shows that (Table 10.2 and Table 10.3): - The pump rotation speed must be approximately equal or higher than 1,600 rpm so that water reaches the divisor at Les Laures. - The maximum efficiency obtained at speeds between 1,800 rpm and 2,000 rpm. - According to characteristics of the main pipe Laures-Trapan and also according to water-hammer protection analysis (Engineering Division-SCP, 2002) the maximum operation pressure should not exceed the authorized maximum pressure 300 m (30 bars). We see that the maximum speed is approximately 1,800 rpm to fulfill this constraint. 2) Pumping to Gratteloup:

It is the case of pumping water to the new tank at Gratteloup in order to increase the flow available downstream of Gratteloup. Hydraulic conditions and hypothesis

In this operating mode we carry out the simulation as in Les Laures case, and we define also two system curves; the maximum head curve and the minimum head curve.

- Piezometric conditions maximal: corresponds to the difference between high water level in Gratteloup (assumed level: 170 m) and low water level in Trapan (45 m), plus the headloss calculated with the pessimistic assumption of roughness (ε =3.0 mm). - Piezometric conditions minimal: corresponds to the difference between low water level in Gratteloup (160 m) and high water level in Trapan (57 m), plus the headloss calculated with the optimistic assumption of roughness (ε =0.5 mm).

Only the following components are kept and modeled in FINESSE to trace the curves: - Trapan dam modeled as fixed head reservoir. - Gratteloup tank modeled as fixed head reservoir. - Discharge pipe towards La Môle. This analysis shows that (Table 10.4 and Table 10.5): - The pump rotation speed must be approximately equal or higher than 1,100 rpm so that water reaches the Gratteloup tank.


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Table 10.4 : Pumping to Gratteloup


Speed (rpm) Q (l/s) H (m) θ (%) Q (l/s) H (m) θ (%) Q (l/s) H (m) θ (%)

1,000 # # # # # # # # #

1,100 # # # # # # # # #

1,200 154 127 79 272 131 75 323 134 66

1,300 221 129 84 397 138 83 517 147 80

1,400 274 131 81 494 145 83 645 160 83

1,500 321 134 77 579 153 81 758 173 84

1,600 364 136 72 658 161 79 861 187 83

1,700 405 139 68 732 170 76 960 202 82

1,800 444 142 64 803 179 74 1,053 218 81

1,900 482 145 60 872 189 71 1,144 235 80

2,000 519 148 57 939 199 69 1,233 252 79

Table 10.5 : Pumping to Gratteloup

Piezometric conditions minimal 1 Pump 2 Pumps 3 Pumps


1,000 # # # # # # # # #

1,100 150 104 81 278 107 79 370 110 75

1,200 214 106 83 400 112 84 542 119 83

1,300 267 107 79 497 116 82 675 127 83

1,400 312 108 74 583 121 78 794 137 82

1,500 355 110 68 663 126 74 903 146 80

1,600 395 111 64 739 132 71 1,007 157 78

1,700 434 113 59 812 138 67 1,107 169 76

1,800 471 115 56 883 144 64 1,203 180 74

1,900 509 117 52 952 151 62 1,298 192 72

2,000 545 119 49 1,019 158 60 1,390 205 70


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3) Pumping to Golf Hôtel:

This case corresponds to the recycling of turbined water into Golf Hôtel tank. Hydraulic conditions and hypothesis

In this operating mode we carry out the simulation as in the above cases, and we define also two system curves; the maximum head curve and the minimum head curve. - Piezometric conditions maximal: corresponds to the difference between high water level in Golf Hôtel (171 m) and low water level in Trapan (45 m), plus the headloss calculated with the pessimistic assumption of roughness (ε =3.0 mm). - Piezometric conditions minimal: corresponds to the difference between low water level in Golf Hôtel (164 m) and high water level in Trapan (57 m), plus the headloss calculated with the optimistic assumption of roughness (ε =0.5 mm).

Only the following components are kept and modeled in FINESSE to trace the curves: - Trapan dam modeled as fixed head reservoir. - Golf Hôtel tank modeled as fixed head reservoir. - Discharge pipe towards Golf Hôtel. This analysis shows that (Table 10.6 and Table 10.7): - The pump rotation speed must be approximately equal or higher than 1,100 rpm so that water reaches the Golf Hôtel tank.


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Table 10.6 : Pumping to Golf Hôtel



1,000 # # # # # # # # #

1,100 # # # # # # # # #

1,200 142 130 77 203 134 64 229 137 52

1,300 208 135 83 336 149 80 386 156 70

1,400 259 139 82 422 162 83 503 177 77

1,500 304 145 79 496 175 84 594 196 80

1,600 345 150 76 565 190 83 678 218 82

1,700 385 156 72 630 205 82 756 240 83

1,800 422 162 69 692 222 81 832 264 83

1,900 458 168 66 752 239 80 904 289 83

2,000 494 175 64 811 257 79 975 315 84

Table 10.7 : Pumping to Golf Hôtel

Pumping to Golf Hôtel B - Piezometric conditions minimal 1 Pump 2 Pumps 3 Pumps


1,000 # # # # # # # # #

1,100 131 109 77 200 112 67 233 114 56

1,200 198 112 84 341 122 82 426 130 77

1,300 251 115 81 433 131 84 543 145 81

1,400 296 118 77 513 141 83 645 160 83

1,500 338 122 73 587 151 81 739 176 84

1,600 378 125 69 657 162 79 826 193 83

1,700 419 129 64 723 173 77 912 212 83

1,800 453 133 61 788 185 75 994 231 83

1,900 489 138 58 851 198 73 1,074 252 82

2,000 524 142 56 912 212 72 1,152 274 81


260

Figure 10.7 : Operation of the Trapan pumping station at different conditions

100

150

200

250

300

0 200 400 600 800 1000 1200 1400Discharge (l/s)

Hea

d (m

)

Gratteloup_mini

Gratteloup_maxi

Golf Hôtel_mini

Golf Hôtel_maxiLes Laures_mini

Les Laures_maxi

1pump_1800

2pumps_1800

3pump_1800

1pump_15252pumps_1525

3pumps_1525

1pump_3000

2pumps_30003pumps_3000


261

10.8 NPSH (Net Positive Suction Head)

Pump has a maximum aspiration capacity which is the value of the vacuum that it can produce. This characteristic varies according to the type and the design of the pump. Theoretically, the maximum height of aspiration, in a cavity where prevails the absolute vacuum, is equal to the atmospheric pressure, i.e. 10.33 m at sea level. It decreases gradually when altitude increases. This height is also limited by the physical properties of pumped liquid.

NPSH is simply a measure permitting to quantify the total suction head at the pump inlet to avoid pump cavitation. Thus, the NPSH is defined as the absolute pressure at the pump inlet expressed in meters of liquid, plus the velocity head, minus the vapor pressure of the liquid at pumping temperature, and corrected to the elevation of the pump centerline. NPSH is always positive.

NPSH Required (NPSHr) This is the minimum head required to stop the pump from caviating.

NPSHr is a function of the pump design and is determined based on actual pump test by the vendor. Pump manufacturer's curves normally provide this information. The NPSHr is independent of the liquid density. The NPSHr varies with speed and capacity within any particular pump.

NPSH Available (NPSHa)

NPSHa represents the pressure of the liquid over the vapor pressure at the pump inlet and is determined entirely by the system preceding the pump, and it depends on:

- Atmospheric pressure at the suction liquid level (Patm = 10.3 m). - Total headloss (friction plus fitting) in the pump suction pipe (Psuc). - Vapor pressure of the pumped liquid (Pvap= 0.1252 m at 10°C, Pvap=

0.2387 m at 20°C). - Static suction pressure i.e. the vertical distance between the impeller

centerline and the suction liquid level (Pz).

NPSHa = Patm – Pvap – Psuc - Pz

NPSH for “Toulon-Est” pumping station

The curve of Figure 10.8 shows us the NPSH available versus the


262

pump total flow. We saw that in the case of pumping towards Les Laures the maximum rotation speed is approximately 1,800 rpm and the flow through one pump is 300 l/s. At this operating point the NPSHr is approximately 17 m and the total flow should not thus exceed 900 l/s (from Figure 10.1). In all cases the flow is limited voluntarily to 300 l/s by group for reasons of NPSHa.

The Net Positive Suction Head available to the pump inlet must be above the Net Positive Suction Head required to prevent damage caused by cavitation.

Figure 10.8 : NPSH – Toulon Est pumping station 10.9 Reversible pump-turbine plant: operation principles and

scenarios

Here, we will present the operation principles and scenarios of the future station according to the general study and the development program of Toulon Est.

1) Emergency Operation

It is the main motive of the project, which corresponds to pumping back from Trapan dam up to Les Laures divisor. We speak of course about pumping mode only. Several cases can arise:

16.6

16.7

16.8

16.9

17.0

17.1

17.2

17.3

17.4

17.5

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300

Débit (lps)

NPS

H d

ispo

nibl

e (m

CE)

NPS

Ha

(m)

Flow (l/s)


263

A. Pipe bursting at Les Laures level The pumping station must be able to pump back up to divisor. It is

the operation obtained by one or two pumps at 1,800 rpm where the flow available to Les Laures is around 270 l/s to 300 l/s (1 pump) or 450 l/s to 510 l/s (2 pumps) with no demand taken out on the way.

It had been considered the successive isolation of the tanks by closings the valves on the main pipe to limit the pumping head and to fill the tanks the ones after the others. It had been also suggested the possibility of limiting the pumping head to the highest tank, which is Fenouillet, located approximately 80 m below Les Laures. But to simplify the operation, the following rules are considered:

• Starting the first pump with 1,800 rpm at first level, that is the high level of Les Laures.

• Starting the second pump with 1,800 rpm at a second level, that is the low level of Les Laures.

• Controlling the filling flows of each tank by means of the equipments that already exist and recently renovated. Choices will have to be made knowing that the maximum flow provided by the station in this configuration is of 500 l/s.

B. Pipe bursting at any level between Les Laures and Trapan dam

The tanks located upstream the burst can be supplied by gravity from

Les Laures. Downstream, the station must ensure the supply of the tanks (and possible customers). In this case the pumping head is adjusted by the variable speed drive.

C. Pipe bursting at Les Laures and at some level between Les

Laures and Trapan This case would justify the implementation of a device controlling

the tanks emptying flows, those remaining only the sources of water. It would be then possible to manage these tanks and allow the filling of the one by the other to prevent for example that a tank is emptied quickly whereas the others still have reserve.

2) Normal operation: pumping-turbining

The principles held in “Toulon Est” general study are to turbine in winter when the energy bought by EDF is most expensive and to recycle water by pumping in summer when the cost of purchase of electricity for


264

SCP is the least expensive. This means that we fill the dam in winter and we empty it in summer. The main problem which is opposed to turbine permanently is that recycling would become impossible because the turbined volume would be greater than the pumped volume. Moreover it is held in the general study in order to optimize the energy generation the pumping head is limited up to Golf Hôtel tank. Recycling is done then by the various flows taken out the dam: - Flow taken out by the CEO. - Flow pumped to the Golf Hôtel tank. - Flow pumped to La Môle.

The considered control is, of course, different according to whether we are in pump mode or in turbine mode.

Turbine mode

Standard operation will be to ensure a constant rotation speed equal the nominal speed of the machine, 1,525 rpm in turbine mode. The variable speed drive of the concerned machine will generate the nominal tensions and frequencies of the engine: 690 V, 50 Hz. The evolution of turbined flow will then follow roughly the head-flow curve of the turbine. In fact in this case, the variable speed drive acts only as an intermediary between EDF and the engine. The variable speed drive provides thus engine protection, speed control which must be constant, and harmonics filtering.

In turbine mode, we expect to isolate the tanks between Les Laures and Trapan. The net head available at Trapan is maximum and thus controlled. If for various reasons the head do not follow any more the expected system curves, for example when necessary to fill any of the tanks, there is a possibility of adapting the rotation speed of the turbine to remain permanently at maximum efficiency. In a very simple way, the variable speed drive then do not generates any more 50 Hz but a slightly lower frequency; produces an operation curve (head vs. flow) slightly higher and more adapted in term of output efficiency at low turbined flow. In this case the variable speed drive ensures a real speed variation.

Pumps mode

Pumping under normal operation corresponds mainly to recycling

part of turbined water in winter and where necessary to the increase in the system flow of the supply pipe between Trapan and La Môle. Within the framework of pumping, it is a matter of making place for the next turbining season. Volume to be pumped is estimated at 0.7 Mm3. It is estimated in


265

function of the rainfall and the evaporation losses each year in Trapan. Pumping is done mainly towards the Golf Hôtel tank and possibly towards the delivery point at La Môle when this asks for water.

When the flow must be pumped toward the two branches (Golf Hôtel and La Môle), the basic solution is to maintain a constant water level in the Golf Hôtel tank which is slightly higher in terms of system curve than La Môle.

But we are then confronted with the supply of small possible flows which would be asked by La Môle. When the high level of Golf Hôtel tank is reached, the station stops and the difference in elevation between the water level in Golf Hôtel and Gratteloup is too weak to guarantee the supply of La Môle. The station not being able to provide a flow lower than 150 l/s, this simple operation is not a solution.

Another constraint is the pressure at Gratteloup: the latter is the limiting factor for supply pipe flow between Trapan and La Môle. In the case of the reinforcement of the flow of this pipe, the station will have to maintain a minimum pressure at Gratteloup (1.0 bar).

The solution suggested is as follows. The principle is the organization each summer an "emptying campaign" for Trapan, corresponding to an approximate period of one month during which the valve on the main pipe at point G (Figure 10.2) is closed (the connecting point to Mont Redon tank). The upstream section to this valve is supplied by gravity and the downstream section by the pumping station for only Golf Hôtel tank. The interest is to limit the valve operation to one closing and one opening per season, and surely to at least limit the pumping head to the Golf Hôtel tank. The operation is as follow:

• Closing the existing sectional valve (motorized and remote-controlled) at point G to pump only in Golf Hôtel and to isolate the tanks upstream to this point.

• Controlling an optimal pressure at the point H, departure towards

Golf Hôtel, by the pumping station.

• Controlling the valve at the departure towards Golf Hôtel (recently renovated) to flow close to 200 l/s.

- The station should not stop at the high water level in Golf Hôtel to be able to provide the possible small demands (between 0 and 150 l/s) asked by La Môle. The 200 l/s flow is informative and corresponds to the summer continuous emptying flow of Golf Hôtel in 2002. It also corresponds to the minimum flow provided by a pump at maximum efficiency. In absolute terms, we fix the minimum flow that can be provided by the station to 150 l/s, knowing that efficiency


266

loss can be observed.

- Any higher flow asked by La Môle can be provided by the station and thus simplifies the operation insofar as the volume in Trapan is recycled more quickly.

- In this configuration, the maximum flow that can be provided by the

station is about 610 l/s, covering the contractual flow of La Môle (410 l/s) and supplying the Golf Hôtel (200 l/s).

• Safety: in the case of station breakdown, the valve at point G can

always be reopened. In addition we hold the possibility of pumping towards the other tanks in case of too low flow asked by the Golf Hôtel networks.

• Booster mode: in the case of pressure drop beyond a certain limit at

Gratteloup, this pressure sent back to the pumping station which will have to control a pressure setting at Gratteloup.

3) The Choice of Trapan useful volume

Useful volume of Trapan is that will be used within the framework of pumping-turbining between a minimum and maximum water level in Trapan. The conclusion of the general study showed that the larger this volume; the more we favor the energy balance between the income of the generator driven by the turbine and the expense of the motor-driven pump. However, the larger this volume; the more the operating constraints increase, the more the quality of water in the dam is uncertain; from where the obligation to find a compromise between various parameters. The general study clarifies here below the procedure leading to this compromise: 1- The lowest water level in normal operation is 47 m, and the highest water level is 57 m. By taking one meter on these two levels for safety, the minimum and maximum dam water levels are 48 m and 56 m. The corresponding useful volume is 1.7 Mm3 (at Level of 56 m) – 0.4 Mm3 (at level of 48 m) = 1.3 Mm3. 2- The average net inflow (rainfall – evaporation – leakage) is estimated at about 0.3 Mm3 a year as described in the general study. We thus obtains the useful volume of 1.3 Mm3 – 0.3 Mm3 = 1.0 m3.


267

3- The study on the water quality in the dam brings more elements on the validity of these hypotheses.

• Raising Trapan water level

The operation of the unit as turbine will be possible in the beginning of November, which at that time corresponded to the seasonal peak period tariff of EDF, where the level of Trapan will have to be at 48 m. The objective is to deliver at the end of March the million m3 through the turbine. The turbining will take place 6 hours per day until end of Mars, from 9:00 AM to 12:00 PM and from 5:00 PM to 8:00 PM. Thus, we get entirely benefit from the sale of energy during peak period.

The tanks which will be isolated during these time bounds will run out whereas until now the levels were maintained constant. It was verified for each tank that the volumes taken by the networks during these hours, in particular from 9:00 AM to 12:00 PM, could be provided.

Refilling the tanks will be ensured by gravity from Les Laures during the off-peak period, where there is non-turbining, and controlled by the installations renovated recently at each departure point to the tank.

• Lowering Trapan water level

In summer at the beginning of April to the end of October, the water level must be lowered up to 48 m. The preceding studies show that the CEO Company downstream Trapan takes on average 0.6 Mm3 per year mainly during this period.

The flow to be recycled by pumping is thus: 1.0 Mm3 (turbined) + 0.3 Mm3 (average net inflow) – 0.6 Mm3 (CEO water demand) = 0.7 Mm3. This volume will then be pumped towards La Môle or Golf Hôtel (the pumping conditions are similar), in certain manner since the summer continuous flow taken only by the networks downstream from Golf Hôtel is 200 l/s. Pumping will be carried out according to the principle of the "emptying campaign" exposed previously.

• Winter water demand available for turbining

According to the flow records at the cenral room (CGTC) provided by Les Laures flowmeter during December for the previous years illustrating the quantity of the total water demand in winter for Toulon Est, we observe a daily demand greater than 200 l/s, that is at least 2.6 Mm3/year. A fraction of this volume could be turbined in addition to the volume available in Trapan. It is then possible to optimize the energy production by turbining each day more time and by pumping the same day


268

the additional volume. In fact, we turbine a significant volume of the demand in winter during peak period, and recycling this volume during off-peak period in the night.

4) Influence on Trapan water quality

In spite of the absence of the results of the water quality study, the

various operating modes of the station are re-examined below by analyzing their impact on the water quality.

• Turbine mode

During the turbining, the water level in Trapan rises up from 48 m to 56 m, the only constraint is not to suspend the sediments which rest on the bottom. In this optics it is interesting to raise the end of the siphon as the water level in the dam rises up and to maintain a constant height between the end of the siphon and the water level, height which will have to be sufficient to prevent surface current form being created.

• Pump mode

During the water pumping in summer, the level drops down regularly to 48 m. The intake pipe must follow this drop. The intake level will be optimized by taking into account the main water quality constraints in the summer: - A strong temperature variation exists between the surface and the

bottom. The water temperature at the CEO Company should not exceed 25°. This temperature is reached regularly in summer near to the surface.

- Another strong gradient exists, but in the opposite direction, regarding

the dissolved metals content and in particular the manganese which is a major constraint because it is difficult to be treated. The manganese content is null on the surface and increases with the depth.

• Emergency mode

Under emergency operating conditions, pumping is subjected to the

same constraints as in pumping under normal conditions. Only the pumping head and the extent of the supplied networks increase. The pumping under normal condition is limited by the minimum admissible water level of 48 m in Trapan. In emergency mode, this minimum admissible water level could


269

be violated implying high difficulties management.

Water quality improvement

In addition to the operation modes discussed here, we consider simply that it is possible to implement a pumping and turbining during the summer aiming only at improving water quality of Trapan subjected to the constraints mentioned previously. The principle is as follow: By turbining: bringing fresh water and its dissolved oxygen and thus: -Reducing the manganese content. -Limiting water temperature variations in every day. By pumping: tacking out surface water from Trapan and thus: - Recycling the volume brought by turbining. - Improving water quality by mixing.

Finally the considered operation in this case does not bring any

additional constraint in comparison to the normal pumping-turbining operation exposed previously. We consider a simplified pumping-turbining such that: - It is not necessary to close all the tanks between Les Laures and Trapan to optimize the turbining. - It is not necessary, and voluntarily we do not consider optimizing pumping towards Golf Hôtel tank. The considered operation is to maintain one or two pumps at 1,800 rpm to reach the maximum height and the maximum flow of 300 l/s or 600 l/s. No valve operation on the main pipe is thus necessary. 10.10 Reversible pump-turbine plant scheduling using FINESSE

Pump Scheduler (CONOPT/GAMS) One of the most difficult problems encountered in the optimization

of the network of “Toulon Est” is the presence of the turbine. This new hydraulic element was not included in the earlier versions of FINESSE and it has been thus implemented into the later version of FINESSE modeling environment by DMU upon our request within the framework of the technical assistance contract and for the purpose of this research work. However, this did not completely solve the problem and this is because of that:


270

B. The pump - turbine unit proposed is a standard reversible pump "SULZER" model and there will be three units in parallel, but in the first phase only two units will be installed, and they will share the same suction pipe. This means that the pump and turbine are physically the same element and we change the operating mode by reversing the rotation direction of the impeller, and this type of operations is programmatically complex to be modeled and to be optimized too. In FINESSE, the pump-turbine unit of “Toulon Est” is modeled by adding two elements connected in parallel, one for the pump and the other for the turbine, and in fact this does not represent the real system. From optimization point of view, using the GAMS/CONOPT Solver to solve this system; the solver will possibly find a solution such that the pump and the turbine are turned on in the same time where part or all of the pumped water reenters the turbine, and also where part or all of the turbined water will reenter the pump as shown in Figure 10.10. This because of the characteristic of EDF electricity tariff (Table 10.9) where the selling price from EDF is less than the buying price to EDF.

C. We also want to manage the operation of the water tanks, pump-turbine

plant, and the Trapan dam over the year not over 24 hours (or one week).

D. In addition, as we introduced the future operation scenarios of this

pumping station in section (10.8), the pump-mode under normal operation corresponds to pumping water mainly up to Golf Hôtel tank at Point H (Figure 10.9) and possibly towards the supply point at La Môle when this asks for water, and thus the system upstream Point H will be isolated and no water will be available from Les Laures to the system downstream Point H. Contrary to the turbine-mode, Les Laures is the main source of water to the turbine and thus it can not be isolated from the system.

In fact, if we suppose that the real system consists of pump and

turbine as two separated elements like the system in Figure 10.9 and the water from Les Laures is available, and then we look for the optimal solution of this system. In this case, there is no need to any optimizer to solve the problem because the optimal solution is simply that the pumping station is shut down and the turbine is turned on along the optimization period and the reservoirs filled up with water coming from Les Laures upstream the system, and thus we produce energy and earn money.

However, the Toulon Est model shown in Figure 10.9 includes pump and turbine and the FINESSE Pump Scheduler has been used to schedule the pump-turbine unit and infeasible solution was found with pumping and


271

turbining in the same time, or sometimes “GAMS execution error” message was obtained at the end of the optimization for different starting points, and as we have seen in the previous chapter (section 9.7.6); GAMS/CONOPT Solver is sensitive to the selected starting point.

Figure 10.9 : FINESSE model for “Toulon Est”

Figure 10.10 : Pumping and turbining in the same time Nevertheless, we split the model in Figure 10.9 into two models; one

for the pump and the other for the turbine, and we will try to estimate the power absorbed by the pump and the power recovered by the turbine under normal operation conditions. We need to know the system water demands and thus we use here the average demands (rounded up to the nearest ten) recorded during the summer of 2005 as shown in Table 10.5:

Pump Turbine

Qpump Qturbine

Qsystem

Qtrapan

Qpump Qturbine

Pump Turbine

Qpump Qturbine

Qsystem

Qtrapan

Qpump Qturbine

(a) (b)


272

Table 10.8 : 2005 Summer Demand for Toulon Est

Point 2005 Summer Demand (l/s) Point B - CEO 100 Point C - PIERRASCAS 200 Point E 150 Point F - FENOUILLET 100 Point G - MONT REDON 100 Point H - GOLF HOTEL 250 Point K 60 Point T - TRAPAN 80 Point M - LA MÔLE 270

And we added around thirty liters per second derived along the

mainline for the non-recorded demand. Also, we need to know the electricity tariff. The electricity tariff used for development program and the general study of hydraulic operation of “Toulon Est” will be used as in Table 10.6. In fact, this tariff is only an informative one because the electricity tariff for this project is not yet defined for the moment.

Table 10.9 : EDF Electricity tariff (€/kWhr)

Period Selling price from EDF Buying price to EDFPeak (06:00 - 22:00) 0.13 0.19

Off-peak (22:00 - 06:00) 0.04 0.06

10.10.1 Pump-mode As mentioned previously, the pump-mode under normal operation

corresponds to pumping water mainly up to Golf Hôtel tank at Point H and possibly towards Gratteloup tank as show in Figure 10.11a where only the pump and the system downstream point H were kept.

A good starting point has been selected to initiate the optimization process and, for this starting point, the number of pumps turned on is discrete. In the pump constrains the minimum number of pumps is set equal to 0 and the maximum number of pumps is set equal to 2.

The Pump Scheduler was used to optimize the simple system in Figure 10.11a and, nevertheless, it was not able to find optimal solution. On the other hand, the system shown in Figure 10.11b is the same as in Figure 10.11a except that we added a dead-end pipe to the node at point T as indicated on the schema, and the Pump Scheduler was used again to optimize this system and the same starting point was used. Even though the two systems are, hydraulically, the same the Scheduler was able to find an optimal solution in the second case. Fore this obtained optimal solution the


273

number of pumps turned on is continuous solution since we do not have the SBB Solver (Figure 10.12).

Figure 10.11 : Toulon Est in pump-mode under normal operation

Figure 10.12 : Pump control – Pump optimal continuous solution

(a)

(b)

Dead-end pipe


274

The volume of water pumped from Trapan was around 36,000 m3/day and the pump absorbed power was around 15.57 MWhr/day, and since the total volume of water that would be pumped from Trapan is about 0.7 Mm3/year, then the total power absorbed is:

However, the operation costs in the case of continuous solution were

around 1.77 k€ while they were around 1.78 k€ in the case of discrete solution. This problem of “dead-end pipe” was previously introduced in Chapter 9.

10.10.2 Turbine-mode

The standard operation will be to ensure a constant rotation speed

equal the nominal speed of the machine, 1,525 rpm in turbine mode, and we expect to isolate the tanks between Les Laures and Trapan as explained in section 10.8. The Schema in Figure 10.13a represents the system in turbine-mode, and the Gratteloup tank, which has a volume of 20,000 m3, can assure continuous water supply to La Môle of 270 l/s for 20 hours.

We selected a good starting point to initialize the optimizer and the number of turbine turned on is always one. In the turbine constrains the minimum number of turbines is set equal to 1 and the maximum number of turbine also is set equal to 1. This means that the turbine is turned on all the time to maximize the power production.

As in the pump-mode, the optimizer was not able to find an optimal solution for the system in Figure 10.13a, even though it was able to find an optimal solution for the same system when adding the dead-end pipe as shown in Figure 10.13b.

For this optimal solution, the optimal “costs” were around 2.48 k€, and the turbined water into Trapan dam was around 23,000 m3/day and the turbine recovered power was around 15.50 MWhr/day, and since the total volume of water that would be turbined into Trapan dam is about 1.0 Mm3/year, then the total power recovered is:

MWhr/year 673.90 MWhr/day 15.50/daym 23,000 /yearm 1,000,000

3

3

≈×

MWhr/year 302.75 MWhr/day 15.57/daym 36,000 /yearm 700,000

3

3

≈×


275

Figure 10.13 : Toulon Est in turbine-mode under normal operation We will consider another scenario for the turbine-mode such that the

tanks between Les Laures and Trapan are not isolate as shown in Figure 10.14. As before, we selected a good starting point and, however, no optimal solution was found. Here, we did not add dead-end pipe but rather the valve and the pipe, which are pointed out by the arrows as shown in Figure 10.14, are switched round with each other, and then an optimal solution was obtained.

In this scenario, the optimal “costs” were around 2.35 k€, and the turbined water into Trapan dam was around 22,300 m3/day and the turbine recovered power was around 14.60 MWhr/day, and thus the total power recovered is:

MWhr/year 654.70 MWhr/day 14.60/daym 22,300 /yearm 1,000,000

3

3

≈×

And this is clearly less than the power recovered when the tanks

were isolated.

(b)

(a)

Dead-end pipe


276

Figure 10.14 : Toulon Est in turbine-mode and water tanks between Les Laures and Trapan are not isolated

Finally, these eventual scenarios that present the future operation of

the pumping station show us that the power recovered by the turbine can be significantly higher than the power absorbed by the pumps, and thus this means that the benefits form selling the generated power will, at least, recover the pumping costs.

Optimal solution when these two elements are switched round!

12. CHAPTER 11 : Summary and Conclusions

277

CHAPTER 11

11. Summary and Conclusions

11.1 Summary In this research work we dealt with the operation management and

optimization of water distribution networks. The water quality issue was out of the scope of this work.

The operation management and optimization of water distribution networks led us to approach other relevant topics such: modeling and simulation methods and software (Chapters 3, 4, and 5), SCADA system (Chapter 6), network calibration (Chapter 7), water demand prediction (Chapter 8), and optimization principles and methods (Chapter 9). Indeed, each one of these topics has vital role in the efficient management and operation of the water distribution network. We need modeling and simulation tools to construct a model which can be considered as an abstraction and simplified representation of the hydraulic behavior of the real system and must be calibrated to ensure that the model simulated performance reasonably agrees with real system performance over a wide range of operating conditions. Also, we need to know the system water production or demand which is the driving force behind the hydraulic dynamics occurring in water distribution systems, and we need rules, guides, and tools to manage, improve, and optimize the system operation. SCADA system, if one exists, will help the manager to follow the state of the system in real-time and remotely initiate the operation of system elements such as pumps and valves from a single central location. This, in turn, will reduce operational staffing levels through automation or remote control, leading to efficient management of the system.

At Canal de Provence Company in France, where this research work was carried out, a water supply network was selected as a case-study where a new reversible pump-turbine plant will be constructed. This network is known as “Toulon Est” network and presented in Chapter 2, and the new reversible pump-turbine plant was introduced in Chapter 10. FINESSE software was used as our main modeling, simulation, prediction, and optimization tool.


278

11.2 General conclusions

Before the commencement of the overall management and optimization process of an existing water distribution system, the system is in its initial state that is the “As-is” and “Non-optimized” state, and by the end of this process the system will come to its final aimed state that is the “To-be” and “Optimized” state. In order to bring the system to this final state, this process includes carrying out some tasks such as: making plan and strategy, consultation, data collection, model building, model calibration and validation, understanding customers water requirements and predicting system future water demand, installation of new SCADA system or improving an existing one, looking for feasible and economical solutions and executing them, decision-making, etc. Each one of these tasks is a challenge for the manager. At each stage, there are difficulties and obstacles and thus the manager has to make decisions to successfully accomplish the task. As we saw in this work, mathematicians, hydraulic engineers, and programmers have made an appreciative effort and have developed different methods, algorithms, softwares, and tools to accomplish the same task. This multitude means that the path to be followed to reach the final state is not unique and thus nobody guarantees that the final solution is unique since each methods, algorithms, and tools has its own assumptions, and complexity and accuracy levels. The key decision which must be made at the very start of the process is whether or not to use the hydraulic network modeling software as the right tool for providing answers to problems faced in managing water distribution systems. However, the manager must make a choice which leads him to the final state with feasible, satisfactory, and economical solutions.

Concerning FINESSE software, this study was a useful opportunity,

not only for SCP but also for DMU, to try and test this software and its modeling, simulation, prediction, and optimization tools at SCP. During this work some bugs in the software have been identified and the demand prediction module was improved, and new element was added, that is “turbine”. One of the obstacles of using FINESSE is lack of documentation and its “help file” is not complete and, hence, the user always needs to contact the software developer at DMU to request help on using the software tools. However, some problems have been encountered during the use of FINESSE for “Toulon Est” network, for example the turbine, where this element was not integrated into FINESSE and then it was added upon our request for


279

the purpose of this study. Even though, this was not enough to fulfill our needs since the pump and the turbine are physically the same unit but in FINESSE they are modeled as two separated elements. Yet, the usefulness of this software at SCP is doubtful.

Another problem is related to the “Pump Scheduler”. The problem is

that at SCP we are currently using an old version of GAMS and CONOPT (1999) and it seems that this version is not efficient in some cases as such are those that were presented in Chapter 9 and Chapter 10. A more recent version of GAMS and CONOPT (2003) used at DMU also showed difficulties in finding a feasible and optimal solution sometimes proving that this non linear optimization problem is a difficult one and that the available algorithms and software may not fulfill our requirements yet.

In this thesis, a calibration approach has been presented, and we

described the use of EPANET software and Excel VBA macro in search of the best set of pipe roughness coefficients. This tool is an automatic trial-and-error calibration approach and provides reasonable solutions as well. It performs very well with the small size network but in large size network the time required to find an optimal solution is often very long. However, this tool maybe needs to be improved to reduce the time required to find a solution, and it would be great if the nodes demand factors can be calibrated too. Also, this calibration work shows how difficult is the calibration process of the hydraulic model for water pipe network; even for a simple network like “Toulon Est” network.

According to the comparison study made between FINESSE demand

prediction and other prediction techniques, including those used at the SCP, the DMU-WSS has improved the demand prediction and the new version gives better results than the old one and allows the user to choose either single, double, or triple exponential soothing, but it cannot automatically set the smoothing constant for the case at hand and thus the user must either accept the default value or he already must know the right smoothing constant for the case at hand. The knowledge and the experience of the persons who manage and operate the networks at the SCP’s control center had permitted them to develop their own forecasting tools giving good forecasts for demands for the systems which they operate when compared to others known techniques such as those presented in this work.


280

Finally, since this research work comes within the framework of the Franco-Jordanian technical cooperation the knowledge acquired in this domain will be transferred when I go back to Jordan to improve the situation of water distribution in the country that is one of the ten countries most threatened by the water shortage in the world and is facing a chronic imbalance in the water supply-demand equation. The operating cost of urban water in a country, having semi-arid climate and water resources limited and difficult to exploit, is very high.

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14.

« Et Nous avons fait de l’eau toute chose vivante »

«And We made every living thing of water »

thesis all chapters en 26 october 06

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