suresh & chandru

7/27/2019 Suresh & Chandru

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ABSTRACT

In this thesis, the elimination of harmonics in a Cascaded Multilevel

Inverter (CMLI) by considering the non-equality of separated dc sources by

using Firefly Algorithm (FFA) is presented. Solving a nonlinear transcendentalequation set describing the harmonic elimination problem with non-equal dc

sources reaches the limitation of contemporary computer algebra software tools

using the resultant method.

The proposed approach in this thesis can be applied to solve the problem

in a simple manner, even when the number of switching angles is increased and

the determination of these angles using the resultant theory approach is not

possible. Results show that the proposed method does effectively eliminate a

great number of specific harmonics, and the output voltage is resulted in low

total harmonic distortion.


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TABLE OF CONTENTS

CHAPTER NO TITLE PAGE NO

ABSTRACT i

LIST OF TABLES iv

LIST OF FIGURES vi

1 INTRRODUCTION 1

1.1. PREAMBLE 1

1.2. LITERATURE REVIEW 3

1.3. SCOPE AND OBJECTIVE 6

2 PROBLEM FORMULATION 7

2.1. INTRODUCTION 7

2.2. MULTILEVEL INVERTER 8

2.3. CASCADED MLI 11

2.4. HARMONICS IN POWER SYSTEMS 19

2.4.1. Effects of Harmonics 20

2.4.2. Sources of Harmonics 20

2.4.3. Symptoms of Harmonics 21

2.5. HARMONIC OPTIMIZATION 22

3 FIREFLY ALGORITHM 26

3.1. FIREFLY IN NATURE 26

3.2. PSEUDO CODE OF THE FFA 28


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3.3. FLOWCHART FOR FFA 30

4 RESULTS AND DISCUSSIONS 31

4.1. INTRODUCTION 31

4.2. MATLAP/SIMULINK 31

4.3 MATLAP PLATFORM 32

4.4 SIMULINK 33

4.5. SIMULATION RESULTS 33

5 CONCLUSION 40

REFERENCES 41


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LIST OF FIGURES

FIGURE NO TITLE PAGE NO

2.1 MLI Topologies 92.2(a) Cascaded Multilevel Inverter 11

2.2(b) Cyclic Switching Sequence 12

2.2(c) Switching Strategies to generate 13

+3V dc at load

2.2(d) Switching Strategies to generate 13

-3V dc at load

2.2(e) Switching Strategies to generate 14

+2V dc at load

2.2(f) Switching Strategies to generate 14

+2V dc at load

2.2(g) Switching Strategies to generate 15

+V dc at load

2.2(h) Switching Strategies to generate 15

-V dc at load

2.2(i) Switching Strategies to generate 16

0 at load

2.3 Output of an 11 level Cascaded MLI 16

2.4 Seven level Topologies 18

2.5 Inverter output and load voltage 234.1 Circuit Diagram of MLI 35

4.2(a) Output phase voltage (M=0.6) 36

4.2(b) FFT analysis for phase voltage (M=0.6) 36

4.3(a) Output line voltage (M=0.6) 37


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4.3(b) FFT analysis for line voltage (M=0.6) 37

4.4(a) Output phase voltage (M=1) 38

4.4(b) FFT analysis for phase voltage (M=1) 38

4.5(a) Output line voltage (M=1) 394.5(b) FFT analysis for line voltage (M=1) 39

4.6(a) Output phase voltage (M=1.062) 40

4.6(b) FFT analysis for phase voltage (M=1.062) 40

4.7(a) Output line voltage (M=1.062) 41

4.7(b) FFT analysis for line voltage (M=1.062) 41


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LIST OF TABLES

FIGURE NO TITLE PAGE NO

2.1 Component requirement for different MLIs 10

4.1 DC Voltage Levels 33

4.2 Output Switching Angles 34


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Chapter 1

INTRODUCTION

1.1 PREAMBLE

Multilevel voltage-source inverters are suitable configuration to reachhigh power ratings and high quality output waveforms besides reasonable

dynamic responses. Among the different topologies for multilevel converters, the

Cascaded Multilevel Inverter (CMLI) has received special attention due to its

modularity and simplicity of control. The principle of operation of this inverter is

usually based on synthesizing the desired output voltage waveform from several

steps of voltage, which is typically obtained from DC voltage sources. There are

different power circuit topologies for multilevel converters. The most familiar

power circuit topology for multilevel converters is based on the cascade

connection of an s number of single -phase full-bridge inverters to generate (2s

+ 1) number of levels. However, from the practical point of view, it is somehow

difficult to keep equal the magnitude of Separated DC Sources (SDCSs) of

different levels. This is because of the different charging and discharging time

intervals of DC-side voltage sources.

To control the output voltage and to eliminate the undesired harmonics in

multilevel converters with equal DC voltages, various modulation methods such

as sinusoidal Pulse Width Modulation (PWM) and space-vector PWM

techniques are suggested. However, PWM techniques are not able to eliminate

lower order harmonics completely. Another approach is to choose the switching

angles so that specific higher order harmonics such as the 5th, 7th, 11th, and13th are suppressed in the output voltage of the inverter. This method is known

as Selective Harmonic Elimination (SHE) or programmed PWM techniques in

technical literature. A fundamental issue associated with such method is to

obtain the arithmetic solution of nonlinear transcendental equations which


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contain trigonometric terms and naturally present multiple solutions. This set of

nonlinear equations can be solved by iterative techniques such as the Newton

Raphson method. However, such techniques need a good initial guess which

should be very close to the exact solution patterns. Furthermore, this methodfinds only one set of solutions depending on the initial guess. Therefore, the

Newton Raphson method is not feasible to solve the SHE problem for a large

number of switching angles if good initial guesses are not available.

A systematic approach to solve the SHE problem based on the

mathematical theory of resultant, where transcendental equations that describe

the SHE problem is converted into an equivalent set of polynomial equations and

then the mathematical theory of resultant is utilized to find all possible sets of

solutions for this equivalent problem.

This method is also applied to Multilevel Inverters with unequal DC

sources. However, applying the inequality of DC sources results to the

asymmetry of the transcendental equation set to be solved and requires the

solution of a set of high-degree equations, which is beyond the capability of

contemporary computer algebra software tools. In fact, the resultant theory is

limited to find up to six switching angles for equal DC voltages and up to three

switching angles for non-equal DC voltage cases.

More recently, the real-time calculation of switching angles with

analytical proof is presented to minimize the Total Harmonic Distortion (THD)

of the output voltage of multilevel converters. However, the presented analytical

proofs only validate to minimize all harmonics including triples and cannot beextended to minimize only non-triple harmonics that are suitable for three-phase

applications.

The harmonic elimination for multilevel converters by Genetic Algorithm

(GA) approach is only applied to equal DC sources and needs considerable


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computational time. Moreover, this method has not succeeded to find switching

angles for some modulation indices which have solutions. This thesis presents a

modern stochastic search technique based on Firefly Algorithm (FFA) to deal

with the problem for equal DC sources.In this thesis, the FFA approach is developed to deal with the SHE

problem with unequal DC sources while the number of switching angles is

increased and the determination of these angles using conventional iterative

methods as well as the resultant theory is not possible. In addition, for a low

number of switching angles, the proposed FFA approach reduces the

computational burden to find the optimal solution compared with iterative

methods and the resultant theory approach. The proposed method is used to

solve the asymmetric transcendental equation set of the harmonic minimization

problem of the Cascaded Multilevel Inverter.

1.2 LITERATURE REVIEW

MLIs have been drawing growing attention in the recent years especially in

the distributed energy resources area because several batteries, fuel cells, solar

cells or rectified wind turbines or micro turbines can be connected through a MLI

to feed a load or interconnect to the AC grid without voltage balancing problems.

In addition, MLIs have a lower switching frequency than standard PWM inverters

and thus have reduced switching losses. The development of MLI began in the

early 1980s when Nabae et al proposed the NPC pulse width modulated inverter.

Since then several multilevel topologies, namely the diode clamped MLI, theflying capacitors MLI and cascaded MLI have evolved and are applied in

adjustable speed drives, electric utilities and renewable energy systems. Among

the three MLI topologies, cascaded MLIs have more advantages than the other

two. Cascaded MLIs require less component count in producing the same output


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voltage levels. They do not require a large number of clamping diodes and flying

capacitors. They are easier to be modularized and soft switched and they do not

have the problem of neutral point voltage unbalancing.

Cascaded MLIs have been the subject of research in the last several years,where the DC sources were considered to be identical in that all of them were

batteries, solar cells, fuel cells etc. In, a MLI was presented in which the two

SDCS were the secondaries of two transformers coupled to the utility AC power.

Corzine et al have proposed a MLI using a single DC power source and capacitors

for the other DC sources.

A method was developed to transfer power from the DC power source tothe capacitor in order to regulate the capacitor voltage. A similar approach was

later proposed in Cascaded multilevel inverters using single dc source by

Du et al. These approaches required a DC power source for each phase. The scope

of this thesis has been restricted to the cascaded MLIs with SDCS for each H-

bridge cell which is typically produced by using transformer/rectifier combination.

The hot point in MLI research is its control strategies based on PWM.

During the past two decades, variety of multilevel PWM methods have

been proposed and researched which have significantly promoted the development

of the field. Three multilevel PWM methods most discussed in the literature are

Multilevel SVPWM, carrier based PWM and SHE.

Carrara et al have successfully extended the basic two level sinusoidal

PWM techniques to MLI and have shown three different ways to position the

carrier waves. Calais et al analyzed the multicarrier PWM methods for a single

phase five level inverter. Most of the modulation methods developed for MLIs are

based on multiple carrier arrangements with PWM. The carrier can be arranged

with vertical shifts (phase disposition, phase opposition disposition and alternative

phase disposition PWM).


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SHE is also extended for MLIs. A different approach to the problem of

harmonic elimination for PWM waveform generation was used in. This approach

is based on the use of Walsh series expansion of PWM waveforms rather than

Fourier series. Walsh series were also applied for optimum PWM pattern ininduction motor. It is shown that the Walsh coefficients of a PWM waveform are

not only a function of PWM waveform angle but also of Walsh subinterval within

which the angle lies. It is pointed out that the algorithm has the restriction that

within a given interval, only one angle is allowed to vary and if there exists a

solution that requires two or more angles to vary in the same selected interval,

then such a solution cannot be detected by the method shown.

Chiasson et al used the mathematical theory of resultants to compute the

optimum switching angles. The expressions involved were high order polynomials

that could not be solved when the number of levels in the MLI became large. The

switching times (angles) are chosen appropriately such that a desired fundamental

output is generated and specifically chosen harmonics of the fundamental are

suppressed. In particular, the harmonic elimination approaches in produces a

system of non-linear transcendental equations that requires the Newton-Raphson

matrix method for its solutions.

SHE methods such as Newton-Raphson method and elimination by the

theory of resultant are complicated and time consuming. There are a few examples

of applications of GA for power electronics in the literature but only recently has

GA been applied to Multilevel Inverters. FFA a global search technique for

optimizing problem in is applied for optimizing the switching angles of MLIs in

this work.


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1.3 SCOPE AND OBJECTIVE

In this thesis, Firefly Algorithm is proposed for the solution of selective

harmonic elimination problem. In this thesis work, Firefly Algorithm is used to

find the switching angles of the Multilevel Inverter to minimize particular order harmonics. The proposed method is tested on an 11-level cascaded Inverter. The

results of the proposed Firefly Algorithm technique show the elimination of

selected harmonics in the output voltage of the Multilevel Inverter.


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Chapter 2

PROBLEM FORMULATION

2.1 INTRODUCTION

The problem of eliminating harmonics in inverter has been focus of research

for many years. If the switching losses in an inverter are not a concern (i.e.

switching on the order of a few kHz is acceptable) then the sine-triangle PWM

method and its variants are very effective in controlling the inverter. This is

because the generated harmonics are beyond the bandwidth of the system being

actuated and therefore these harmonics do not dissipate power. Multilevel

inversion is a control strategy in which the output voltage is obtained in steps thus bringing the output closer to a sine wave and reducing the THD. The multilevel

VSI is popularly used in high power industrial applications such as AC power

supplies, static VAR compensators, drive systems etc. The outputs of MLIs are in

stepped form, resulting in reduced harmonics compared to a square-wave inverter.

To reduce the harmonics further, different multilevel SPWM and SVPWM

schemes are suggested in the literature; however these PWM techniques increase

the control complexity and switching frequency.

On the other hand, for systems where high switching efficiency is of utmost

importance, it is desirable to keep the switching frequency much lower. In this

case, another approach is to choose the switching times (angles) such that a

desired fundamental output is generated and specifically chosen harmonics of the

fundamental are suppressed. This is referred to as selective harmonic elimination

or programmed harmonic elimination as the switching angles are chosen or

programmed to eliminate specific harmonics.

SHEPWM has been intensively studied in order to achieve low THD. The

common characteristic of the SHEPWM method is that the waveform analysis is

performed using Fourier theory. The selective harmonic elimination problem is


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formulated as a set of transcendental equations that must be solved to determine

the time (angles) in an electrical cycle for turning the switching devices on and off

in a full H-bridge inverter so as to produce a desired fundamental amplitude while

eliminating particular order harmonics. These transcendental equations are mostlysolved using iterative numerical techniques like Newton-Raphson method to

compute the switching angles.

This method is derivative dependent and may end in local optima; however

a judicious choice of the initial values alone guarantees convergence. As an

alternative solution to the harmonic optimization problem, Firefly Algorithm

(FFA) technique is presented in this work. FFA solves the same problem with asimpler formulation and with any number of levels without extensive derivation of

analytical expressions.

2.2 MULTILEVEL INVERTERS

MLIs easily produce high-power, high-voltage output with the multilevel

structure because of the way the device voltage stresses are controlled in the

structure. Increasing the number of voltage levels in the inverter without requiring

higher ratings on individual devices can increase the power rating. The unique

structure of multilevel VSI allows them to reach high voltages with low harmonics

without the use of transformers or series connected synchronized switching

devices. As the number of voltage levels increases, the harmonic content of the

output voltage decreases significantly.

The MLIs synthesize a near sinusoidal voltage from several DC voltage

sources. As the number of levels increases, the synthesized output has more steps,

resembling a staircase wave that approaches a desired sinusoidal waveform. As

the number of levels increases, the output voltage that can be spanned by

summing multiple voltage levels also increases.


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MLIs have many attractive features like high voltage capability, reduced

common mode voltages, near sinusoidal outputs, low dv/dt and smaller or even no

output filter, making the inverters suitable for high power applications.

Figure 2.1 MLI topologies (a) Diode clamped MLI (b) Flying capacitor MLI

(c) Cascaded MLI

The MLIs can be classified into three types as shown in Fig. 2.1:

i) Diode Clamped Multilevel Inverter

ii) Flying Capacitors Multilevel Inverter iii) Cascaded Multilevel Inverter


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Table 2.1 Comparison of component requirements for different MLIs

Inverter

Configuration

Diode clamped

MLI

Flying capacitors

MLI

Cascaded

MLI

Main switching

Devices2(m-1) 2(m-1) 2(m-1)

Main diodes 2(m-1) 2(m-1) 2(m-1)

Clamping

diodes(m-1)(m-2) 0 0

DC buscapacitors

(m-1) (m-1) (m-1)/2

Balancing

capacitors0 (m-1)(m-2)/2 0

Table 2.1 compares the power component requirements among three types

of MLIs having m levels in the output. This table shows that the same number of main switches and main diodes are needed by the inverters to achieve the same

number of m voltage levels in the output.

Clamping diodes are not needed in flying capacitor and cascaded inverter

configurations while balancing capacitors are not needed in diode clamped and

cascaded inverter configurations. Implicitly, the cascaded MLI requires the least

number of components to achieve given number of voltage levels and hence a

sample cascaded seven level inverter is taken for study in this work.


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2.3 CASCADED MULTILEVEL INVERTER

The power circuit (Fig.2.2 (a)) consists of a cascade of N independent

single-phase inverters. These are of full-bridge configuration with SDCS, which

may be batteries, fuel cells or solar cells and are connected in series. Each FBIunit can generate a three level output: +V DC, 0 or VDC by connecting the DC

source to the AC load by different combinations of the four switches of each FBI.

Using the top FBI as the example, turning on S 11 and S 41 yields +V DC output.

Turning on S 21 and S 31 yields -V DC output. Turning off all switches yields 0 volts

output. The AC output voltage at other FBIs can be obtained in the same manner.

The number of voltage levels at the load generally defines the number of FBIs incascade. The number of FBI units or DC sources N is (m-1)/2 where m is the

sum of zero level and the number of positive and negative levels in MLI output.

Each switching component turns ON and OFF only once per cycle i.e. at the line

frequency.

Figure 2.2 (a) Cascaded Multilevel Inverter


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The main features of cascaded Multilevel Inverters are:

For real power conversions from DC to AC, the cascaded inverters need

separate DC sources. The structure of SDCS is well suited for various

renewable energy sources such as fuel cell, photovoltaic cell and biomass. It can generate almost sinusoidal output voltage while switching only one time

per fundamental cycle.

It can eliminate transformers of multi-pulse inverters used in conventional

utility interfaces and static VAR compensators.

Figure 2.2 (b) Cyclic switching sequence of a sample seven level inverter


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Figure 2.2 (b) shows the cyclic switching sequence for a sample MLI. The

switching strategies to generate +3V DC ,-3 V DC ,+2 V DC, -2 V DC ,+ V DC,- V DC ,0 at

load are displayed in Fig. 2.2 (c) Fig. 2.2 (i). The Multilevel Inverter s load

voltage V a0 (Fig. 2.22(a)) is equal to the sum of the output voltages(Va1,Va2, .VaN) of the individual FBI units.

Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

LOAD

S13 S23

S33 S43

Vdc

Vdc

Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

LOAD

S13 S23

S33 S43

Figure 2.2 (c) Switching strategies to

generate +3V dc at load

Figure 2.2 (d) Switching strategies to

generate -3 V dc at load


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Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

L

O

A

D

S13 S23

S33 S43

Vdc

Vdc

Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

L

O

A

D

S13

S23

S33 S43

Vao

Fig.2.2 (e) Switching strategies to Fig.2.2 (f) Switching strategies to

generate +2V DCat load generate -2V DC at load


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Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

L

O

A

D

S13 S23

S33 S43

Vdc

Vao

Vdc

Vdc

S11 S21

S31 S41

S12 S22

S32 S42

LOAD

S13 S23

S33S43

Vdc

Figure 2.2 (g) Switching strategies to

generate +V dc at load

Figure 2.2 (h) Switching strategies to

generate V dc at load


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V dc

V dc

S 11 S 21

S 31 S 41

S 12 S 22

S 32 S 42

L

O

A

D

V o

S 13 S 23

S 33 S 43

V dc

Figure 2.2 (i) Switching strategies to generate 0 volts at load

Figure 2.3 Output of an 11 level Cascaded Multilevel Inverter


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The use of transformers presents advantages particularly in terms of voltage

matching, protection and insulation. The transformer increases the cost and

reduces the overall efficiency of the compensator. These transformers1) are the most expensive equipment in the system

2) will produce about 50% of the total losses of the system

3) will occupy a large area of real estate, about 40% of the total system

4) will cause difficulties in control due to DC magnetizing and surge over

voltage problems resulting from saturation of transformers and

5) are unreliable.

MLIs are an attractive option for a transformer-less series voltage sag/swell

compensator. The number of possible voltage levels at the output generally

defines the Multilevel Inverter topologies. The relatively low harmonic content of

the unfiltered output voltage, compared to conventional inverters, is also an

attractive feature. The voltage levels needed for compensation are provided in this

work by a sample single phase seven level inverter structure consisting of three H- bridge inverters connected in series. The individual bridges are switched at line

frequency when voltage step control is employed. Hence switching losses are

reduced resulting in high efficiency and therefore operating costs of the

compensator are low.

The cascaded Multilevel Inverter has a separate DC source (V DC) for each

individual FBI. Each FBI unit can generate a three-level output +V DC or -V DC. The

Multilevel Inverter output voltage V a0 in Fig. 3.2 is equal to the sum of the output

voltages of the individual FBI units (V a1, V a2,Va3) and can be controlled to

produce a staircase waveform similar to that in Fig. 2.3.


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Fig. 2.4 Sample Cascaded 7 level topology

The cascaded inverter structure is simple since no real power needs to be

supplied other than the losses. The DC sources are floating and no transformer isrequired for coupling to the transmission system. For each FBI unit, the current

rating is the nominal current of the transmission system.

The AC output rating and therefore the DC source rating depend upon the

total compensation voltage required, the number of converters and the sharing of


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the load voltage among individual units. One of the main advantages of this

topology, compared to other multilevel topologies, is the fact that the maximum

number of levels is only limited by isolation constraints. Its robustness and ease of

control are also advantages.

2.4 HARMONICS IN POWER SYSTEMS

One of the biggest problems in power quality aspects is the harmonic

contents in the electrical system. Harmonic in power circuits is created by non-

sinusoidal loads which are integer multiples of the supply frequency. The rapid

growth of power electronics has greatly increased the number and size of theseloads, with the utility and their control. Harmonics are unnecessary high frequency

voltages or currents flowing in a power system.

Generally, harmonics may be divided into two types:

1) Voltage harmonics

2) Current harmonics

Current harmonics are usually generated by harmonics contained in supply

voltage and depend on the type of load such as resistive load, capacitive load and

inductive load. Both harmonics can be generated by either the source or the load.

Harmonics generated by load are caused by non-linear operation of devices

including power converters, arc-furnaces, gas discharge lighting devices etc. Load

harmonics can cause the overheating of the magnetic cores of transformer and

motors. On the other hand, source harmonics are mainly generated by power

supply with non-sinusoidal voltage. Voltage and current harmonics imply power

losses, EMI and pulsating torque in AC motor drives. There are several methods

to indicate the quantity of harmonic contents of a periodic wave. One among them

is THD which is mathematically given by


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1

2n

2n

H

HTHD

and defined in terms of the amplitudes of the harmonics H n at frequency n 0 where 0 is frequency of the fundamental component whose amplitude is H1 and

n is an integer. Since any periodic waveform can be shown to be the

superposition of a fundamental and a set of harmonic components, by applying

Fourier transformation, these components can be extracted. The frequency of each

harmonic component is an integral multiple of its fundamental.

2.4.1 Effects of Harmonics

Sudden increase in demand reduced capacity utilization and increased

energy losses.

Increase in neutral current, overheating of motor windings, overloading of

diesel generator sets, fire hazards due to burning of over-heated cables.

Saturation of transformers, frequent damage to switchgears and controls. Amplification of harmonic currents in capacitor banks and frequent failure

of capacitors.

Inaccurate and excess recording by power/energy meters. Interference with communication equipment. Nuisance, tripping of circuits and interruption in production flow.

2.4.2 Sources of Harmonics

Non-linear loads like thyristors/IGBT based drives/Variable Frequency

drives

Induction heating furnaces

Arc furnaces


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Battery Charging Rectifiers

UPSs

SMPSs

PCs

Electronic chokes in lights.

2.4.3 Symptoms of Harmonics

Blinking of incandescent bulbs

Flickering of fluorescent tubes

Fuses blowing for no apparent reason

Motor failures due to overheating

Excessive neutral current.

Neutral conductor and terminal failures

Failure of electromagnetic loads

Overheating of metal enclosures

Power interference on voice communication

2.5 HARMONIC OPTIMIZATION

The output voltage for a sample cascaded seven level Inverter is shown in

Fig.2.4 for m=7 where m=number of steps in the positive and negative side after

including the zero levels also. Switching angles to eliminate 5 th,7th,11 th and higher


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order are designed usually assuming that the peak fundamental output voltage is a

desired fraction of its maximum value. For any Cascaded Multilevel Inverter, the

output voltage is

Where

Due to the quarter wave symmetry along the x-axis in load voltage of

Fig.2.3, both Fourier coefficients A 0 and A n are zero. B n is defined as

Bn

4V dc [2

1

k 1sin(nt)d(t) +2

2

k 2sin(n t)d(t) +. +2

N

k Nsin(n t)d( t)]

N

1 j j

dc ncosn4V

(2.2)

which gives the instantaneous output voltage v a0 as

tv a0 N

n1 j

j jdc ncosk

n4V

1 tnsin (2.3)

Where

Equation (3) provides the generalized Fourier series expansion of the outputvoltage. If the peak output voltage must equal to the carrier peak voltage

= (m-1) V DC. Thus the modulation index M is

dccr

ac

cr V1m

VVV

M(peak)

(peak)

(peak)

(2.4)


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Load voltage

V 1 +V 2 +V 3

V 1 +V 2

V 1

V 1 +V 2 +V 3

V 1 +V 2

V 1

Inverter III Output

Inverter II Output

Inverter I Output

V 1

V 2

V 3

1 2 3

2

Figure 2.5 Inverter outputs and load voltage in a sample seven level inverter

Two predominating techniques in choosing the switching angles 1, 2 ,.. N

are to:

1) Eliminate the lower frequency dominant harmonics or

2) Minimize the THD.

The more popular and straight forward of the two techniques is the first,

that is to eliminate the lower dominant harmonics and filter the output to remove

the higher residual frequencies. Here the choice is also to eliminate the lower

frequency harmonics. The goal here is to choose the switching angles 0 1


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2


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employed for minimization of harmonics in order to reduce the computational

burden associated with the solution of the non-linear transcendental equation of

the conventional SHE method. An accurate solution will be guaranteed with FFA

even for a higher number of switching angles than other techniques would be ableto calculate for a given computational effort. Hence FFA seems to be promising

methods for applications when a large number of DC sources are sought in order

to eliminate more low-order harmonics to further reduce

the THD.


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Chapter 3

FIREFLY ALGORITHM

3.1 FIREFLY IN NATURE

Fireflies or glowworms are the creatures that can generate light inside of

it. Light production in fireflies is due to a type of chemical reaction. This process

occurs in specialized light-emitting organs, usually on a firefly's lower abdomen.

It is thought that light in adult fireflies was originally used for similar warning

purposes, but evolved for use in mate or sexual selection via a variety of ways to

communicate with mates in courtships. Although they have many mechanisms,

the interesting issues are what they do for any communication to find food and to

protect themselves from enemy hunters including their successful reproduction.

The pattern of flashes is often unique for a particular species of fireflies.

The flashing light is generated by a chemical process of bio luminescence.

However, two fundamental functions of such flashes are to attract mating

partners or communication, and to attract potential victim. Additionally, flashing

may also serve as a protective warning mechanism. Both sexes of fireflies are

brought together via the rhythmic flash, the rate of flashing and the amount of

time form part of the signal system. Females respond to a male s unique pattern

of flashing in the same species, while in some species, female fireflies can mimic

the mating flashing pattern of other species so as to lure and eat the male fireflies

who may mistake the flashes as a potential suitable mate. The light intensity at a

particular distance from the light source follows the inverse square law. That is

as the distance increases the light intensity decreases. Furthermore, the air

absorbs light which becomes weaker and weaker as there is an increase in the

distance. There are two combined factors that make most fireflies visible only to

a limited distance that is usually good enough for fireflies to communicate each


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other. The flashing light can be formulated in such a way that it is associated

with the objective function to be optimized. This makes it possible to formulate

new meta-heuristic algorithms.

The firefly algorithm (FFA) is a meta-heuristic algorithm, inspired by the

flashing behaviour of fireflies. The primary purpose for a firefly's flash is to act

as a signal system to attract other fireflies. Now this can idealize some of the

flashing characteristics of fireflies so as to consequently develop firefly inspired

algorithms. For simplicity in describing our new Firefly Algorithm (FFA) [30],

there are the following three idealized rules. On the first rule, each firefly attracts

all the other fireflies with weaker flashes. All fireflies are unisex so that onefirefly will be attracted to other fireflies regardless of their sex. Secondly,

attractiveness is proportional to their brightness which is inversely proportional

to their distances. For any two flashing fireflies, the less bright one will move

towards the brighter one.

The attractiveness is proportional to the brightness and they both decrease

as their distance increases. If there is no brighter one than a particular firefly, it

will move randomly. Finally, no firefly can attract the brightest firefly and it

moves randomly. The brightness of a firefly is affected or determined by the

landscape of the objective function. For a maximization problem, the brightness

can simply be proportional to the value of the objective function. Other forms of

brightness can be defined in a similar way to the fitness function in genetic

algorithms. Based on these three rules, the basic steps of the firefly algorithm(FFA) can be summarized as the pseudo code shown below.


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3.2 PSEUDO CODE OF THE FFA

Begin FFA Procedure;

Initialize algorithm parameters:

MaxGen: the maximal number of generations

: the light absorption coefficient

r: the particular distance from the light source

d: the domain space

Define the objective function of f(x), where x =(x 1, ........, x d)T

Generate the initial population of fireflies or x i (i=1, 2... n)

Determine the light intensity of I i at x i via f (x i)

While (t I i), move firefly i towards j; End if

Attractiveness varies with distance r via exp [- r2];

Evaluate new solutions and update light intensity;

End for j;

End for i;

Rank the fireflies and find the current best;


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End while;

Print the results;

End procedure;

In the firefly algorithm there are two important issues of the variation of

light intensity and the formulation of the attractiveness

where r or r ij is the distance between the i th and j th of two fireflies.

0 is the attractiveness at r = 0 and is a fixed light absorption coefficient. The

distance between any two fireflies i and j at x i and x j is the Cartesian distance

as follows:

( ) where x ik is the k

th component of the i th firefly ( x i). The movement of a

firefly i is attracted to another more attractive (brighter) firefly j , is

determined by

( ) where the second term is due to the attraction while the third term is the

randomization with being the randomization parameter. For most cases in the

implementation,

[ ]


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YES

START

Read inverter data & FFA

data(nf,alpha, beta0,del,irmax)

For all fireflies initialize randomly ij = rand (0 to /2)

For all i=1 to nf j=1 to ns

Iter = 1

Evaluate objective function for all

firefliesFi = f( i1, i2, ins)

Rank the fireflies based on their objective function such that thefirefly with minimum value of objective function is ranked #1

nij =

ij

A

=

B

YES

NO

NO

is Iter >itermaxIter=Iter+

B

Print the first fireflyas the best solution.

STOP

beta = beta0 * exp( - gamma *2

For all j=1 to nsij = [ ij(1- beta)]+[n kjbeta]+[alpha(rand -0.5)]

is k >i

k=k+

i=i+1

A

=

Find distance between fireflies iand k

r = [ ]

is i >nf

YES

3. 3 FLOW CHART FOR SOLVING SHE PROBLEM USING


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Chapter 4

SIMULATION RESULTS

4.1 INTRODUCTION

The nonlinear transcendental equation considering the non-equality of the

DC sources are solved by using Firefly Algorithm (FFA) technique. The

proposed algorithm is coded in MATLAB platform. The proposed algorithm

gives the global optimum switching angles for the 11 level Cascaded Inverter.

The 11 level Cascaded Multi Level Inverter used in this work was simulated in a

MATLAB/SIMULINK platform. Fast Fourier Transform (FFT) of the output

phase voltage and line voltage are plotted and given.

4.2 MATLAB/SIMULINK

MATLAB/SIMULINK is one of the most successful software packages

currently available. It is a powerful, comprehensive and user friendly software

package for simulation studies. A very nice feature of SIMULINK is that it

visually represents the simulation process by using simulation block diagram.Especially, functions are then interconnected to form a SIMULINK block

diagram that defines the system structure.

Once the system structure is defined, Parameters are entered in the

individual subsystem blocks that correspond to the given system data. Some

additional simulation parameter must also be set to govern how the computation

is carried out and the output data will be displayed. The block diagram of a

sample five level Cascaded Multilevel Inverter is shown in the figure.


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4.3 MATLAB PLATFORM

The MATLAB platforms consist of five main parts. They are,

a) Development Environment

It incorporates a set of tools and facilities, which allows the use of

MATLAB function and files. Most of these tools are of graphical user interface

in nature. It includes the MATLAB desktop, a command window a command

history, editor, debugger and browsers for viewing help, the workspace, files and

the search path.

b) The MATLAB Mathematical function library

This is a vast collection of computational algorithms ranging from

elementary functions, like sum, sine, cosine, and complex arithmetic to more

sophisticated functions such as matrix inverse, Eigen values, basset functions,

and Fast Fourier Transforms (FFT).

c) The MATLAB language

This is a high level matrix/ array language with control flow statement that

serves to process functions, data structure, input/output, besides it includes

object oriented programming.

d) Graphics

MATLAB has extensive facilities for displaying vectors and matrix as

graphs, besides annotating and printing the graphs. It includes high level


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function for two-dimensional and three dimensional data visualization, image

processing, animation and presenting graphics.

4.4 SIMULINK

SIMULINK is an interactive tool for modeling, simulating and analyzing

dynamic, multi domain systems. It lets the user to accurately describe, simulate,

evaluate and refine a system s behavior through standard and custom block

libraries. SIMULINK models serve to access MATLAB, providing flexible

operation and an extensive range of analysis.

4.5 SIMULATION RESULTS

To obtain an insight on the proposed optimization technique, a MATLAB

simulation is carried out. The eleven level Cascaded Multi-level Inverter is

simulated using MATLAB/SIMULINK block sets. The harmonic elimination

problem of the Multi-Level Inverter was solved considering the non-equality of the DC sources. The magnitudes of the DC voltage levels in the experiment are

considered as follows,

Table 4.1 DC voltage levels used in this thesis work.

VDC1 VDC2 VDC3 VDC4 VDC5

120 94 85 82 76


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Table 4.2 Output switching angles obtained using FFA and PSO.

Modulation

index (M)

SWITCHING ANGLES THD

%1 2 3 4 5

0.6FFA 36.8110 48.960 59.618 70.869 83.984 6.82

PSO 36.236 51.509 67.473 87.761 86.885 9.03

1FFA 7.6400 15.341 26.058 36.920 57.174 4.79

PSO 26.174 45.868 57.055 65.102 75.331 5.71

1.062FFA 4.8004 11.920 21.932 29.054 43.194 4.14

PSO 15.066 35.628 52.760 61.478 79.370 6.66

The above results are given with the following parameters of FFA and

PSO. The calculated switching angles by the FFA method and the corresponding

resulted objective function values are plotted with respect to the modulation

index (M) in Fig. 4.1 and 4.2. By changing the dc-side voltage, the switching

pattern has to be recalculated but, if not, there will be considerable harmonics in

the output voltage waveform. The simulink circuit diagram is shown below.


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Figure 4.1 Circuit diagram for multilevel inverter


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The output voltage waveform for different modulation indices and the

corresponding Fast Fourier transform (FFT) analysis are shown in fig(4.4 to 4.9).

The output phase voltage of the eleven level Cascaded Multi Level Inverter for

the optimum switching angle is given below.

Figure 4.2 (a) Output phase voltage (M=0.6) (b)FFT analysis for phase voltage

(M=0.6)

From the FFT plot of the phase voltage, it is observed that the 5 th, 7 th, 11 th,

13 th order harmonics are effectively minimized. THD is 43.92% with 3 rd order

harmonic dominating more than 40% of fundamental.


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Figure 4.3 (a) Output line voltage (M=0.6) (b) FFT analysis for line voltage

(M=0.6)

From the FFT plot of the line voltage, the triplen harmonics are

eliminated. Thus the total harmonic distortion further reduces. THD is 6.82%.


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Figure 4.4 (a) Output phase voltage (M=1) (b) FFT analysis for phase voltage

(M=1)


13 th order harmonics are effectively minimized. THD is 10.24%.


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Figure 4.5 (a) Output line voltage (M=1) (b) FFT analysis for line voltage (M=1)




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Fig-4.8 (a)output phase voltage (M=1.062) (b)FFT analysis for phase voltage

(M=1.062)


13 th order harmonics are effectively minimized. THD is 10.24%.


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Fig-4.9 (a)output line voltage (M=1.062) (b)FFT analysis for phase voltage(M=1.062)




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Chapter 5

CONCLUSION

Inverters are used to convert DC input voltage to AC output voltage of

desired magnitude and frequency. MLI structures have been developed toovercome short comings in solid-state switching device ratings, so that they can be

applied to high voltage electrical systems. Cascaded type MLIs are taken for study

in this work since they have been the subject of research in the last several years,

where the DC sources are batteries, solar cells etc., SHE is implemented in chosen

cascaded MLI by pre-calculating the switching angles of devices such that

particular orders of harmonics are minimized. By employing Firefly Algorithmtechnique and by using MATLAB, the formulated non-linear asymmetric

transcendental equations are solved to find the switching angles for minimizing

the harmonics.

The simulation results for output voltage and THD for the proposed

technique is evaluated. The principle of operation of a sample seven level inverter

non-carrier PWM technique for one phase is explained. Thus the harmonics in

the output voltage of the Cascade Multilevel Inverter by considering the non-

equality of separated DC sources is eliminated by using firefly algorithm. The

simulation results are provided for an under modulation (M=0.6), critical

modulation (M=1) and over modulation (M=1.062) an 11-level cascaded H-

bridge inverter to validate the accuracy of the computational results.


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