1

CONTENTS

Page

DECLARATION ii

ACKNOWLEDGEMENTS iii

ABSTRACT iv

CONTENTS v

LIST OF TABLES

LIST OF FIGURES

LIST OF ABBREVIATION

CHAPTER I INTRODUCTION

1.1 Project Background

1.2 Project Objectives

1.3 Outline of Thesis

CHAPTER II THEORY OF STATCOM HARMONIC STUDIES

2.1 Distortion in power networks

2.2 Sources of harmonics

2.2.1 Harmonic generation

2.2.2 Sources of Harmonics

2.3 Power Electronic interface/device

2

2.3.1 Line Commutated Converters

2.3.2 Pulse-Width Modulated Converters

2.4 Harmonic mitigation in PWM technique

2.4.1 Delayed triangular carrier in SPWM

2.4.2 Selective Harmonic Elimination

2.5 Presentation of harmonic data

2.5.1 Displays of individual harmonics

2.5.2 Displays of groups of harmonics

2.5.3 THD

CHAPTER III RESEARCH METHODOLOGY

3.1 Introduction

3.2 Switching function Concept

3.3 Control strategy

3.4 Modeling program

3.4.1 MATLAB Simulink

3.4.2 Building and Interconnecting subsystems

CHAPTER IV STATCOM Model

4.1 Introduction

4.2 Block diagram of model

4.3 Model Parameter

4.4 SPWM technique

4.5 Voltage and current …

3

4.5.1 ? Voltage

4.5.2 ? Voltage

4.5.3 ? Voltage

4.5.4 ? Current

CHAPTER V RESULTS AND ANALYSIS

5.1 Introduction

5.2 Modelling Categories

5.2.1 Low Switching Frequency

5.2.2 Medium Switching Frequency

5.2.3 High Switching Frequency

5.3 Simulation results

5.3.1 Effect of varying switching frequency on harmonics generated

5.3.2 Effect of varying switching frequency on THD

5.3.3 Effect of varying switching frequency on ?

CHAPTER V I

6.1 Conclusion

6.2 Recommendation

4

ABSTRACT

Recently, electrical utilities and heavy industries face a number of challenges related

to reactive power. Heavy industrial application can cause phenomena like voltage unbalance,

distortion or flicker on the electric grid. Developments in power electronics and

semiconductor technology have lead improvements in power electronic systems. Hence, the

most advanced solution to compensate reactive power is the use of a voltage source inverter

incorporated as a variable source of reactive power. STATCOM is defined as a self-

commutated switching power converter/inverter supplied from an appropriate electric energy

source and operated to produce a set of adjustable multiphase voltage. This thesis will focus

on designing the STATCOM based on switching function concept. The modelling of these

devices is based on graphic models using the electromagnetic transient simulation program

MATLAB Simulink. The functional simulation models of three-phase VSI using switching

function concept have been modelled. SPWM technique is used in this project as a control

strategy. In the SPWM switching method, the widths of the voltage pulses are varied to

control the ac output voltage. The SPWM is a kind of multi-pulse trigger mode in which in

one period, the inverter switches are turned on and off several times. The SPWM signal is

used to control ON/OFF switching state of the IGBTs will functions in driver model that

created to control the switching scheme. Then, the simulation is made from the inverter

model in Simulink. At the end of this project, by varying several frequencies, result taken

from simulation will be compared with the percentage total harmonic disorder.

5

CHAPTER 1

INTRODUCTION

1.1 Background

This project is mainly about to model and simulate Static Synchronous Compensator

(STATCOM) using switching function method. In this project, the simulation of three-

phase VSI with the Sinusoidal Pulse Width Modulation (SPWM) control algorithm using

switching function is developed. Then the model will implemented by using the

functional block to evaluate the model performance and also analyse effect of total

harmonic distortion presence to the model.

The model is implemented using MATLAB Simulink software with the SimPower

System Block. The simulations play an important role in design, analysis and evaluate the

power electronic converter. MATLAB is an effective tool to analyse a SPWM inverter

because it have the following advantages such as faster response, the various simulation

tools and function blocks and lack of convergence problem.

Three phase voltage source inverter are recently showing growing popularity

for heavy industrial applications. The main reasons for this popularity are easy

sharing of large voltage between the series devices and the improvement of the

harmonic quality at the output.

Static VAR Compensator (STATCOM) is defined as a self-commutated

switching power converter supplied from an appropriate electric energy source and

operated to produce a set of adjustable multiphase voltage, which may be coupled to

an AC power system for the purpose of exchanging independently controllable real

and reactive power [1]. The controlled reactive compensation in electric power system

is usually achieved with the variant STATCOM configuration.

6

Figure 1.1: Block diagram of the static power conversion system [2]

Referring to figure 1, the dc and ac variables can be input and output according

to the operation mode. Then, the transfer function is obtained to describe the task to

be performed by the circuits. In particular, the transfer function can be used to

compute a dependent variable in terms of its respective independent circuit variable.

For example, in Pulse Width Modulation (PWM), the waveform to be modulated is

considered as the independent variable and the resulting modulated waveform is the

dependent variable. Using switching function theory, the detailed relationship

between the input and output variables can be obtained [2].

1.2 Project Objective

The aim of this project:

i. To understand the functionality of STATCOM simulation model in power system.

ii. To develop an inverter model by using MATLAB Simulink based on switching

function concept.

iii. To understand and implement SPWM method for the STATCOM system.

iv. To analyse the simulation results in terms of harmonics components and also the

total harmonic disorder (THD)

7

1.3 Thesis Outline

This thesis is prepared to ensure clarity and make it easier to read and it contains of

five chapters. Chapter 1 explain the introduction of STATCOM and its advantages

against the power system. The overview of project objectives and project scopes also

discuss in this chapter.

Chapter 2 to emphasize on literature review about the introduction of distortion in

power system network, a details explanation about the harmonics. The principle of the

STATCOM and switching function concept are the method that had been used in this

project. This chapter also presents how the model developed using MATLAB Simulink

and also the function of FFT and THD.

Chapter 3 describes about the methodology of this project. This chapter also discuss

about the circuit construction using MATLAB Simulink and the system works.

Chapter 4 shows

Chapter 5 illustrates the simulated results obtained and the analysis of the project.

Comparisons are made by varying several switching frequency also the percentage of

total harmonic disorder using simulation software.

Finally, chapter 6 is the conclusion part where contributions of the study are

discussed. This final chapter also presents some recommendation about the future

development of the project.

8

CHAPTER 2

THEORY OF STATCOM HARMONIC STUDIES

2.1 Distortion in Power Network

Network distortion and power quality are issues of increasing importance, as the

share of sensitive electronic circuits is increasing steadily in modern power systems.

Network distortion can be classified into transient events such as voltage sags, swells

and spikes. Other events of longer duration are for example mains failures, harmonic

voltage distortion and steady-state over-voltages and under-voltages [3]. As the

causes of network distortion are based on the fundamental laws of electricity and

physics, they have to be considered to be normal phenomena in any electrical

network.

In some cases, these disturbances can lead to a complete shutdown of an entire

production line, in particular at high-tech industries like semiconductor plants, with

severe economic consequence to the affected industries [4]. If voltage sag exceeds

even a few cycles, motors, servo drives, robot and machine tools cannot maintain

control of the processes and it may cause a large amount of damage.

A power quality disturbance is an occurrence manifested in a nonstandard voltage,

current or frequency deviation that results in a failure or a disoperation of end-use

equipment [5]. Table 2.1 presents a most common power quality problem, their

effects and the causes.

9

TABLE 2.1 Most common power quality problem in power network [6]

1.

Voltage Sag (or dip)

Description: A decrease of the normal voltage level between 10 and 90% of the nominal rms voltage at the power frequency, for duration of 0.5 cycle to 1minute.

Causes: Faults on the transmission or distribution network (most of the times on parallel feeders). Faults in consumer’s installation. Connection of heavy loads and start-up of large motors.

2.

Very Short Interruption

Description: Total interruption of electrical supply for duration from few milliseconds to one or two seconds.

Causes: Mainly due to the opening and automatic reclosure of protection devices to decommission a faulty section of the network.

3.

Long Interruption Description: Total interruption of electrical supply for duration greater than 1 to 2 seconds.

Causes: Equipment failure in the power system network, storms and objects (tree, cars, etc.) striking lines or poles, fire, human error, bad coordination or failure of protection devices.

4.

Voltage Spike Description: Very fast variation of the voltage value for durations from a several microseconds to few milliseconds. These variation may reach thousands of volts, even in low voltage.

Causes: Lightning, switching of lines or power factor correction capacitors, disconnection of heavy loads.

5.

Voltage Swell Description: Momentary increase of the voltage, at the power frequency, outside the normal tolerances, with duration of more than one cycle and typically less than a few seconds.

Causes: Start/stop of heavy loads, badly dimensioned power sources, badly regulated transformers (mainly during off-peak hours).

6.

Harmonic Distortion

Description: Voltage or current waveform assume non-sinusoidal shape. The waveform corresponds to the sum of different sine-waves with different magnitude and phase, having frequencies that are multiples of power system frequency,

Causes: Electric machines working above the knee of the magnetization curve (magnetic saturation). All non-linear loads, switched mode power supplies, data processing equipment, high efficiency lighting.

7.

Voltage Fluctuation

Description: Oscillation of voltage value, amplitude modulated by a signal with frequency of 30Hz.

Causes: Arc furnaces, frequent start/stop of electric motors (for instance elevators), oscillating loads.

8.

Noise Description: Superimposing of high frequency signals on the waveform of the power system frequency.

Causes: Electromagnetic interferences provoked by Hertzian waves such as microwaves, television diffusion and radiation due to arc furnaces and electronic equipment. Improper grounding may also be cause,

9.

Voltage Unbalance

Description: A voltage variation in a three-phase system in which the three voltage magnitudes or the phase-angle differences between them are not equal.

Causes: Large single-phase loads (induction furnaces, traction loads), incorrect distribution of all single-phase loads by the three phases of the system (this may be due to a fault).

10

The increased concern for power quality has resulted in measuring power quality

variations, studying the characteristics of power disturbances and providing solutions to

the power quality problems [5]. Some of the concerned issues related to the effects of

power disturbances are:

i. The utility power supply can have a detrimental effect on the performance of

industrial equipment.

ii. Harmonics produced by industrial equipment such as rectifiers and adjustable

speed drives can have detrimental effects on the reliability of the plant’s

electrical system as well as on the utility system.

There are several strategies to reduce the occurrence and the impact of such

disturbances, such as [3]:

i. Careful design of power systems and installations in order to reduce the risk of

short-circuits.

ii. Optimisation of the protection systems for fast and selective fault clearing.

iii. Installation of special back-up systems such as diesel generators or UPS

systems.

iv. Reduction of human error.

v. Redundancy of equipment and energy sources.

vi. Assurance of a certain immunity of user is equipment against disturbances.

2.2.1 Harmonic generation

Under some operating conditions, power system devices exhibit non-linear

characteristics such as magnetic saturation, resulting in distorted voltage and

current waveforms that can interfere with other devices on the power system.

The type of load also affects the power quality of the system. This is due to the

current draw of each type of load [20]. Linear loads draw current that is sinusoidal

in nature so they generally do not distort the waveform (Figure 2.11). Most

household appliances are categorized as linear loads. Non-linear loads, however,

can draw current that is not perfectly sinusoidal (Figure 2.12). Since the current

waveform deviates from a sine wave, voltage waveform distortions are created.

11

Figure 2.11 : Ideal Sine Wave [20]

Figure 2.12: Distorted Waveform [20]

As can be observed from the waveform in Figure 2.12, waveform distortions can

drastically alter the shape of the sinusoid. However, no matter the level of complexity of

the fundamental wave, it is actually just a composite of multiple waveforms called

harmonics. Harmonics have frequencies that are integer multiples of the waveform’s

fundamental frequency. For example, given a 60Hz fundamental waveform, the 2nd, 3rd,

4th and 5th harmonic components will be at 120Hz, 180Hz, 240Hz and 300Hz

respectively. Thus, harmonic distortion is the degree to which a waveform deviates from

its pure sinusoidal values as a result of the summation of all these harmonic elements

[21]. The ideal sine wave has zero harmonic components. In that case, there is nothing to

distort this perfect wave.

12

In general industry and consumers both are responsible for the

increasing deterioration of the power system voltage and current

waveforms. Figure 2.2 presents a power system with sinusoidal source

voltage (Vs) operating with linear and nonlinear loads. The non-linear load

current (iL1) contains harmonics and is non-sinusoidal. The resulting

harmonics in the source-current (is) produces a non-linear voltage drop (∆v)

in the line impedance, which distorts the load voltage (VL). Since load

voltage is distorted, even the current at the linear load (iL2) becomes non

sinusoidal [11].

The presence of harmonics in power lines result in low power factor,

low efficiency, increased power losses in the distribution system and

interference problems in communication systems [10], [12]. Sometimes this

leads to the failures of electronic equipments, which are very sensitive to

voltage and current distortions [11].

Figure 2.2 : Power System with Linear and Non-linear Load [11]

2.2.2 Sources of Harmonics

The use of these nonlinear loads is rapidly increasing in industry and also by

consumers. These equipments draw non-linear currents from the AC mains as compare to

traditional loads such as motors and resistive heating elements. This leads to the distortion

of power system voltage and other problems [10]. Nonlinear loads are classified broadly

into three types, namely

Power-electronic interface/device - rectifiers, inverters, UPS, switch-mode power

supply, lighting controls, adjustable speed drive etc [14].

arc-type,

13

magnetic saturation - type nonlinearities.

Among the modern nonlinear loads, three-phase power electronic

devices have a significant contribution in generating harmonics during their

switching processes [7].

2.3 Power Electronic interface/device

Among today’s power electronic applications are rectifiers, inverters, variable

speed drives, UPS systems and in many types of industrial applications. Due to the

advanced technologies in power electronics development over the past decade, the

application of power electronics has been widely spread to all types of industries [7].

They offer a number of advantages in controlling power flow and in efficiency, but

they perform this by chopping, flatting, or shaping sinusoidal voltages and currents.

Harmonics are produced in the process.

Other power electronic devices which may generate harmonics in the power

system include static phase shifters, isolation switches, load transfer switches, and

energy storage and instantaneous backup power systems as well as those devices

covered under the subjects of Flexible AC Transmission System (FACTS) and

Custom Power Systems [8]. The family of custom power devices mainly includes

distribution static compensator (D-STATCOM), dynamic voltage restorer (DVR) and

solid state breakers applied in solid state transfer switch (SSTS) and solid state fault

current limiter (SSFCL) [9] .

Converter-based FACTS equipment will act as a source of harmonic current

injection to the system and it will interact with harmonic distortions already present

within the system. In order to prevent harmonic instability of the system and to

appropriately rate the components of the VSC, an improved understanding of these

harmonic interactions must be developed.

Three-phase static power topologies can be classified as voltage-source rectifiers

(VSR) and inverters (VSIs) and current source rectifiers and inverters as shown in Figure--.

The advent of switching devices with turn-off capabilities e.g., insulated gate bipolar

14

transistors (IGBTs), gate-turn-off thyristors (GTOs) has made the voltage source rectifier

widely used for ac-to-dc conversion, in applications such as motor drives, power supplies,

uninterruptible power supplies (UPSs), and static power compensators (STATCOMs).

Voltage source inverter have become standard in most dc-to-ac applications, such as

induction and synchronous motor drives, UPS systems, and, in general, ac power supplies.

2.3.1 Line Commutated Converters

The introduction of economic and reliable line commutated converters has caused a

significant increase in harmonic-generating loads, and they have dispersed over the entire

power system. In most cases, line commutated converters are the cause of harmonic

problems in power distribution systems. These devices are work horse circuits for ac/dc

power conversion. The common application of static power converters is in adjustable speed

drives for motor control. Another application is in HVDC terminals. The device can be

operated as a six pulse converter, as shown in Figure --, or configured in parallel

arrangements for higher pulse operation.

Theoretically, a static power converter load draws currents from the source system

that consists of positive and negative currents which are equally separated. The pulse number

refers to the number of “humps” on the dc output voltage that are produced during every ac

cycle [8].

Figure 2.1 : Six-Pulse Line Commutated Converter [8]

In Figure 2.1, each pair of thyristors is triggered (firing angle) and conduct until they

are reverse-biased. If a thyristor is triggered at zero firing angle, it acts exactly like a diode.

The term line commutated converter refers to the fact that the load actually turns thyristors

off, rather than them being turned off by external control circuits. The ideal ac current

15

waveform for a six-pulse converter is on for 120 degrees and off for another 60 degrees.

During the on period, the dc load current is assumed constant in the ideal case due to the

assumed existence of a large series dc inductor [8]. Assuming no commutation overlap and

balanced three-phase operation, it can be shown that the phase a current is

ia ( t )=∑h

I ₁h

sin(hω₁ t+δh) (2.1)

where h = 1, 5, 7, 11, 13, ... .

We see that the ac harmonic currents generated by a six-pulse converter include all odd

harmonics except triplens. Harmonics generated by converters of any pulse number can be

expressed by

h=pn±1 ,

where n is any integer and p is the pulse number of the converter [8].

2.3.2 Pulse-Width Modulated Converters

The sinusoidal pulse width modulation (SPWM) strategy is widely used in power

applications such as dc to ac inverters, switch mode power supply, and industrial machine

drive controls [15], since it provides an efficient means of power transfer. The reference

signal is compared against a high frequency triangular carrier signal resulting in a

pulsewidth modulated 2-level output. Figure 2.3 gives the basic circuitry of SPWM using

an analog comparator. The output of the comparator at node A is shown in Figure 2.4

[16]. The low voltage swing at A is then up converted to a higher voltage through the

output configuration.

Figure 2.3: Basic SPWM Topology [16]

16

Figure 2.4: Sine- Triangle PWM at A [16]

PWM converters use power electronic devices that can be turned off and turned on.

Therefore, voltage and current waveforms can be shaped more desirably. The switching

components can be thyristors that are forced off by external control circuits, or they can be

GTOs or power transistors. The latter devices are usually used because of their fast switching

characteristics are needed for effective PWM. In a PWM converter, the switching devices are

controlled to switch on and off to produce a series of pulses. These pulses are to be varied in

width to produce a pulsed three-phase voltage wave for the load. Due to their low

efficiencies, PWM converters are limited to low power applications in the several hundred

kW or horse power (hp) ranges [8].

2.4 Harmonic mitigation in PWM technique

The frequency spectrum of the pulse width modulated signal contains one component

at the reference signal frequency, and others are shifted to the carrier frequency, which is

much higher than the sinusoidal frequency. These high frequency components are

eliminated by the low pass L-C filter and the resultant filter output is the reference signal

with higher amplitude determined by the power supply voltage.

The use of pulse width-modulated (PWM) gating patterns to control the power valves

in such topologies is the base to achieve faster dynamic responses and nearly sinusoidal

ac waveforms. Several PWM techniques have been reported in the literature, which can

be classified as online e.g., sinusoidal PWM and space vector or offline, e.g.: selective

harmonic elimination and fundamental magnitude control [19].

2.4.1 Delayed triangular carrier in SPWM

For examining harmonic cancellation of unwanted bands, the configuration of Figure

2.5 is proposed that employs N paths where each triangular carrier is delayed from

17

previous one by t= Tc/ N or phase angle ϕ = 2π/ N radians, where Tc is time period of

triangular wave [16].

Figure 2.5: Harmonic Cancellation [16]

If Vc(t) denotes the carrier of the first path, the n-path carrier is given by

VCN (t) = VC [t – (n-1) Tc / N], n= 1, 2,….. N (2.2)

Figure 2.6 shows the reference sinusoid and a pair of shifted carrier waves, and the

corresponding encoded PWM signals y1(t) and y2(t).

Figure 2.6: PWM Coding with Shifted Carriers [16]

18

Assuming the signals to be synchronized, it is seen that each signal y (t) and y2(t) are

periodic with period T where T is 1/fo. fo is the frequency of the reference sinusoid. Their

Fourier coefficients can be evaluated [17], and the magnitude spectrum of the carrier-

shifted PWM signals closely match at low frequencies as shown in Figure 2.7 and 2.8.

However, the phase of the spectrum at fc and its harmonics is shifted by 2π/N [16]. The

overall output of the summing circuit is then:

y (t )= ∑m=−∞

∞

¿¿1m + h2m + ……..)e jmωot∑n=1

N

e− jmωo(n−1) Tc

N (2.3 )where o= 2πfo, and h lm, h2m ... are Fourier coefficients of the PWM signal of each consecutive paths. The second sum in (2.3) is a geometric series and the sum is zero for all values of m = K except m = KN, where K = kmf, k is an integer, and mf (modulation ratio) = fc/fo (an integer multiple). This is the basic idea in harmonic cancellation, and the output harmonic components corresponding to m ≠ KN are eliminated. When m = KN, the sum equals N and the harmonic phasor are oriented in the same direction [18]. Although this method eliminates the harmonic components, the sidebands around each component may remain intact.

Figure 2.7: Amplitude Spectrum: Y₁ (t) (fO= 1 KHz, fc= 4 KHz) [16]

19

Figure 2.8 : Amplitude Spectrum: Y₂(t) (fO= 1 KHz, fc = 4 KHz) [16]

2.4.2 Selective Harmonic Elimination

The elimination of low-order harmonics is an important issue in many

applications where low-switching-frequency PWM patterns are required. As

an alternative, selective harmonic elimination (SHE) techniques were

introduced to provide low-order harmonic elimination in VSR/Is .

Figure 2.9: Three-phase power converter topologies of voltage

source inverter [19].

The chopping angles for three-phase VSIs as shown in Figure 2.9 are

specified between 0– π/2 to eliminate an even number of low-frequency

harmonics (e.g., 5th and 7th) and between 0– π/3 to eliminate an odd

number of low-frequency harmonics (e.g., 5th, 7th, and 11th), which

20

allow maximum dc voltage utilization. For instance, to eliminate the 5th

and 7th harmonics and perform fundamental magnitude control, the

Fourier coefficients of this switching function given is used:

an= 4nπ [−1−2∑

k=1

N

(−1 )ᵏ cos (nαk )] (2.4)

bn = 0 (2.5)where three angles (N= 3) are required. Thus N-1 = 2, and the equations to be solved are:

cos (1α¿₁)−cos (1α ₂)+cos (1α ₃)=(2+mπ)/4 ¿ (2.6)cos (5α¿₁)−cos (5α ₂)+cos (5 α ₃)=1 /2¿ (2.7)cos (7α ¿₁)−cos (7α ₂)+cos (7α ₃)=1/2¿ (2.8)

where the angles , , and are defined as shown in₁ ₂ ₃ Figure 2.10 and m is the modulation index (amplitude of the fundamental phase voltage component for a 1-pu dc-link voltage). The angles , , and are plotted for₁ ₂ ₃ different values of the line voltage fundamental amplitude component m√3] assuming 1–pu dc-link voltage. The general expressions to eliminate N-1(N-1=2,4,6…. even) harmonics were derived and are given by the following equations [19]: −∑

k=1

N

(1 ) ᵏ cos (nk )=2+mπ4

(2.9 )

−∑k=1

N

(1 ) ᵏ cos (nk )=12, for n=5,7… .. ,3N−2 ( 2.10)

Where ₁, ₂….,N should satisfy ₁< < …. < ₂ N < π/2.

21

Figure 2.10: Selective harmonic elimination in voltage-source

inverters for 5th and 7th harmonic elimination (N-1 = 2), m = 0:8/

√3. (a) Gating pattern S₁ . (b) Normalized ac voltage Vab. (c) AC

voltage spectrum.

2.5 Harmonics

The purpose of harmonic studies is to quantify the distortion in voltage and/or current

waveforms at various locations in a power system. The need for a harmonic study may be

indicated by excessive measured distortion in existing systems or by installation of

harmonic producing equipment. These harmonics can cause problems ranging from

telephone transmission interference to degradation of conductors and insulating material

in motors and transformers. One important step in harmonic studies is to characterize

harmonic-generating sources.

2.5.1 Displays of individual harmonics

2.5.2 Displays of groups of harmonics

2.5.3 THD

22

Power sources act as non-linear loads, drawing a distorted waveform that contains

harmonics. The first step in controlling the distortions is measuring them accurately.

Therefore it is important to gauge the total effect of these harmonics. The summation of

all harmonics in a system is known as total harmonic distortion (THD) [20].

Total harmonic distortion, or THD, is the summation of all harmonic components of

the voltage or current waveform compared against the fundamental component of the

voltage or current wave:

THD=√¿¿¿¿ (2.11)

The formula above shows the calculation for THD on a voltage signal. The end result

is a percentage comparing the harmonic components to the fundamental component of a

signal. The higher the percentage, the more distortion that is present on the mains signal.

23

CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

In the project, the simulation of three-phase VSI with the Sinusoidal Pulse Width

Modulation (SPWM) control algorithm using switching functions is implemented from the

functional blocks of MATLAB Simulink.

3.2 Switching Function Concept

The switching function concept has shown to be a powerful tool in understanding and

optimizing the performance of the power electronic circuits. Advantages of switching

function concept can be listed as follows [27]:

Powerful tool in understanding and optimizing the performance of the static

power converter/inverter.

Power conversion circuits are modeled according to their functions, rather than

circuit’s topologies.

Achieves simplification of the overall power conversion functions.

Allows for the development of analytical concepts that are applicable to families of

converters.

The concept allows the designer to decompose the synthesis of a power converter system

into three major steps:

1. The derivation of the converter transfer function from the task to be

performed by the converter.

2. The synthesis of topologies to realize the required transfer function.

3. The determination of the gating strategy required to produce the transfer

function with the topology derived in 2.

More specially, a converter transfer function can be used to compute a

dependent variable in terms of its respective independent converter variable. For

24

example, the input current of a voltage source inverter (dependent input) depends

on the converter transfer function and the converter output phase currents

(independent output) [27].

Figure 2.16: Variable classification for power converters [27]

A summary of converter independent and dependent variables is

presented in Figure 2.16. This table conveniently considers the port connected to

the source of power (e.g., utility, batteries) as the input converter port, and the port

connected to the load as output port. Consequently, with the definition of

dependent variables the transfer function of a switch mode converter is defined as

Transfer Function= Dependent VariableIndependent Variable

=UnmodulatedWaveformModulatedWaveform

(2.23)

3.3 Control strategy

Practical realization of a switch mode converter transfer function is

accomplished using control strategy, for example pulse width modulation

(PWM). With the applied control strategy, each transfer function consists of

the various particular switching functions, such as:

TF= [SF1, SF2, SF3, …….] (2.17)

Where:

TF – Transfer function

SF – Switching function

25

Using switching function, detailed relationship between the input and output

variables can be obtained [27]. Proper switching function is important to

describe the role of the static power converter/inverter.

(a) (b)

Figure 2.15: (a) Circuit configuration of VSI and (b) Input and output variables of

VSI [27]

Referring to Figure 2.15, based on transfer function theory, in the voltage source

inverter (VSI), the dependent variables are input current (Iin) and output voltages (Vab, Vbc,

Vca). Input voltage (Vd) and output current (Ia, Ib, Ic) are the independent variables. The

relationship between the input and output variables can be expressed as [27]:

[Vab ,Vbc ,Vca]=TF .Vd ( 2.18) Iin=TF . [Ia , Ib , Ic ]ᵀ ( 2.19)

Where TF is the transfer function of VSI. Generally, the transfer function consists of

the several switching function as

TF=[SF₁ , SF₂ , SF₃….] (2.20)

26

A control strategy to be applied should be selected in order to define the switching

functions. For this project, the sinusoidal pulse width modulation (SPWM) is used as a

control strategy. The switching function SF express the V₁ ao, Vbo and Vco and it is used to calculate the inverter line-to-line voltages (Vab, Vbc, Vca) and phase

voltage (Van, Vbn, Vcn). Switching function SF₂ designates the voltage across the switch and

load currents (Ia,Ib,Ic) are derived as ratios of voltage and respective impedances using the

switching function SF₂. Mathematical representations SF₁ and SF₂ are given by:

SF₁=∑n=1

∞

An sin (n t ) (2.21)

S F2=Bo+∑n=1

∞

Bn sin (n t ) (2.22)

3.4 Modeling program

MATLAB is a high-level language of technical computing and has several of

roles for algorithm development, data visualization, data analysis, and calculation

of the figures. MATLAB function to solve technical computing problems faster

than with traditional programming languages such as C and so on. In addition,

MATLAB also provides a variety of applications, including signal and image

processing, communications, control design, test and measurement, financial

modelling and analysis, and biological computation. Add-on toolboxes

(collections of special-purpose MATLAB functions, available separately) extend

the MATLAB environment to solve problems in the areas of application specific

classes.

3.4.1 MATLAB Simulink

Inside MATLAB software, the SIMULINK is the best tool to do simulation

and model-based design. SIMULINK is an environment for multi-domain

simulation and model-based design for dynamic and embedded systems. It

provides an interactive graphical environment and a customizable set of block

libraries that can design, simulate, implement, and test a variety of time-varying

systems, including power systems, communications, controls, signal processing,

27

video processing, and image processing. By using SIMULINK, user can quickly

create, model and maintain a detailed block diagram of system.

SIMULINK includes an extensive library of functions commonly used in

modelling a system such as continuous and discrete dynamic block (integration),

algorithmic blocks (sum, product, etc) and structural blocks (MUX, switch and

bus selector). After building the model, SIMULINK user can simulate its

dynamic behaviour and view the result live. SIMULINK also has debugger which

is an interactive tool for examining simulation results and locating unexpected

behaviour in a SIMULINK model.

3.4.2 Building and Interconnecting subsystems

MORE EXPLANATION.

The model of this project using subsystem to combined all circuit together. To

build the subsystem there are a few step need to follow:

Suppose we want to model the SPWM as shown in Figure 2.17

Figure 2.17: SPWM block using MATLAB Simulink

Then group the block into subsystem as follows:

a) From the menu, select [Edit][Select All].

b) From the menu again, select [Edit][Create Subsystem].

28

c) Rename the subsystem to be : SPWM block

d) Resize the subsystem and move the inports and outports so they match

Figure 2.18

Figure: 2.18: Subsystem for SPWM block

The subsystem can be “open” by double-clicking the subsystem block. So can

continue to edit the circuit when the subsystem open at the separate window.

29

4.0 STATCOM Model based on SF concept

4.1 Introduction

The Static Synchronous Compensator (STATCOM) is a shunt device of the

Flexible AC Transmission Systems (FACTS) family. It is based on power electronics

devices to control voltage and improve transient stability.

Figure 2.13: Basic scheme of STATCOM connected to a bus at the

transmission system [25].

The STATCOM basically consists of a step-down transformer with a leakage

reactance, a three-phase GTO or IGBT, voltage source converter/inverter (VSC/VSI)

and a DC capacitor. The STATCOM regulates the voltage magnitude at its terminals

by controlling the amount of reactive power injected into or absorbed from the power

system. When power system voltage is low, the STATCOM generates reactive power

(STATCOM capacitive); when system is high, it absorbs reactive power (STATCOM

inductive) [26].

Figure 2.13 shows the basic operation of STATCOM in power transmission

system. In steady state operation, the voltage V2 generated by the VSC is in phase

with V1 (δ=0), so that only reactive power is flowing (P=0). If V2 is lower than V1, Q

is flowing from V1 to V2 (STATCOM is absorbing reactive power). On the reverse, if

V2 is higher than V1, Q is flowing from V2 to V1 (STATCOM is generating reactive

power). A capacitor connected on the DC side of the VSC acts as a DC voltage

30

source. In steady state the voltage V2 has to be phase shifted slightly behind V1 in

order to compensate for transformer and VSC losses and to keep the capacitor

charged [25]. If V2 is equal to V1 the reactive power exchange is zero. The amount

of reactive power is given by

Q=V 1(V 1−V 2)

X(2.15)

The majority of converters are not run off a constant DC voltage source, but

are instead designed using a dc side capacitor. The average steady state dc voltage

level is then a function of the modulation index and delay angle of the sinusoidal

pulse width modulation (SPWM) signal. Furthermore, harmonics will now appear on

the dc capacitor voltage, thus it is no longer permissible to assume is constant over the

entire period [26].

4.2 Model Parameter

In MATLAB, the proper state equations should be obtained in order to describe the

power conversion circuit. With the state equations, the circuit can easily be modelled by

using the functional block, which are supported in MATLAB Simulink. In particular, in

MATLAB, the various kinds of control algorithms can be easily implemented without

using actual analog components. However, obtaining the state equation according to the

circuit configuration is a cumbersome and time-consuming job. Whenever there is a

minor change in the circuit configuration, new state equations should be obtained for

describing the new circuit.

Therefore, a simple method to model the power conversion circuits is highly

desirable, which is not based on the state equations. Using the switching function

concept, the power conversion circuit can be modelled according to their functions,

rather than circuit topologies [27]. Based on the switching functions concept, a

functional model for the VSI is built by using MATLAB Simulink.

The functional model built consists of five functional blocks, called as sub

models: SPWM generator, switching function block, inverter block, load current block,

and pure switch and diode current generating block.

31

Parameter that has been used for each block model simulation in listed in Table ?:

Parameter of Vd (constant) = 300?.

Table 3.1: SPWM block

Parameter Value

SPWM block Carrier Frequency (Fc) 1000Hz

Reference Frequency (Fref)

50Hz

Amplitude 1

Gain 3.5

Load current block

Inductance (L) 20mH

Resistor 5 Ω

4.3 SPWM Control subsystem

Figure 3.2 illustrates the sinusoidal PWM (SPWM) control strategy. In the

SPWM method, the widths of the voltage pulses are varied to control the ac output

voltage. This is achieved by comparing the carrier signal is with three different

control signals. Its outputs became the inputs to the switching function block to

generate the two sets of switching function signals (SF1 and SF2).

The SPWM is a kind of multi-pulse trigger mode in which in one period, the

inverter switches are turned on and off several times. Thus, SPWM requires higher

switching rate for multi-pulse per cycle of the line frequency. The advantage of using

SPWM switching method is that it can control two parameters independently. These

are the magnitude and the phase of the inverter voltage [3].

32

Figure 3.2: SPWM generator using Matlab Simulink

4.4 STATCOM outputs subsystems?

4.4.1V?

33

Figure 3.3 : Switching function block using Matlab Simulink

The signals applied to the control input port are two-level. Referring to Figure

3.3, a two-level SF ( s 2 ) is used to generate the ac output leg voltage in a

VSI. By using the concept of switching functions, and with the assumptions of no

losses and no parasitic reactive elements in the converter, the V ?? is given by [27]:

Vao=Vd2∙ S F ₁¿a=

Vd2∙∑n=1

∞

An sin (nωt) (3.1)

Vbo=Vd2∙ S F₁¿ b=

Vd2∙∑n=1

∞

An sinn (ωt−120 °) (3.2)

Vco=Vd2∙ S F ₁¿c=

Vd2∙∑n=1

∞

Ansinn (ωt+120 ° ) (3.3)

The Vao,Vbo ,Vco are used to calculate the inverter line-to-line voltages

(Vab,Vbc ,Vca) and phase voltages (Van,Vbn ,Vcn). On the other hand, the switching

function designates the voltage across the switch and the load currents (Ia, Ib, Ic) are

derived as ratios of voltages and respective impedances using the switching function

SF2.

4.4.2 Line-to-line voltage

34

Figure 3.4: Inverter line-to-line and phase voltage generating block using Matlab Simulink

Considering the circuit of an inverter as shown in the Figure 3.4, an equivalent

circuit with a switch in each leg can be simplified as in Figure 3.5.Then, the

inverter line-to-line voltage ( Vab, Vbc, Vca) can be derived as [27]:

Vab=Vao−Vbo=√3

2Vd∑

n=1

∞

An sinn(ωt+30° ) (3.4)

Vbc=Vbo−Vco=√32Vd∑

n=1

∞

Ansinn(ωt−90 ° ) (3.5)

Vca=Vco−Vao=√32Vd∑

n=1

∞

An sinn(ωt+150 ° ) (3.6)

Figure 3.5: Part of circuit

configuration of VSI

4.4.3 ? Phase Voltage

In order to calculate the inverter phase voltage ( Van, Vbn, Vcn), Vno is calculated as:

Vno=13(Vao+Vbo+Vco) (3.7)

The phase voltages are obtained as:

Van=Vao−Vno (3.8)

Vbn=Vbo−Vno (3.9)

Vcn=Vco−Vno (3.10)

4.4.4 Load Current

35

Figure 3.6: Load current calculating block using the phase voltage

Referring to Figure 3.6, load current block is used to obtain the load current (Ia,Ib,Ic).

Assuming the load consists of R-L load and a balanced one, the load currents are

derived as ratios of the phase voltage and respective impedance as [27]:

Ia=VanZa

= VanR+ jωL

(3.11)

Ib=VbnZb

= VbnR+ jωL

=Ia (ωt−120 ° ) (3.12)

Ic=VcnZc

= VcnR+ jωL

=Ia(ωt+120 ° ) (3.13)

4.4.5 Switch and Diode Currents

36

Figure 3.7: Pure switch and diode currents and inverter input current (Iin) generating block using Matlab Simulink.

Referring to Figure 15, the switch currents (Is1,Is3,Is5) are calculated by the product of

the load currents with the corresponding switching function SF2_a,b,c , that is [27],

Is₁=Ia ∙ SF₂a (3.14)

Is₃=Ib ∙ SF₂b (3.15)

Is₅=Ic ∙ SF ₂c (3.16)

In order to calculate the current rating of power semiconductor switch, one needs the

information for the pure switch current and pure diode current. Actually, the switch

current (IS1) can be divided into :

Is₁=Is₁¿s−Is ₁D (3.17)

37

Where IS1_S is the pure switch current and is the pure diode current of the switch S1.

Equations (3.11)–(3.17) are implemented in the load current block and the pure current

generator block as shown in Figure 3.1 and the actual implementations are designated as

shown in Figure 6 and 7. Also, from the switch currents, the inverter input current (Iin)

can be obtained by:

Iin=Is₁+ Is ₃+ Is₅=Ia ∙ SF₂¿+ Ib ∙ SF ₂¿

+ Ic ∙ SF₂c¿¿ (3.18)

4.5 Overall STATCOM functional model

Figure 3.1 shows the proposed overall functional model for calculating the design

parameters of the VSI or called as Parent Model. Its consists of five functional blocks,

called as sub models: SPWM generator, switching function block, inverter block, load

current block, and pure switch and diode current generating block.

dfgfhdfhdhdh

Figure 3.1: Overall block diagram of the proposed simulation model for VSI using

switching function concept (Parent Model)

38

CHAPTER 5

RESULTS AND ANALYSIS

5.1 Introduction

5.2 Modeling Categories

5.2.1 Low Switching Frequency

5.2.2 Medium Switching Frequency

5.2.3 High Switching Frequency

5.3 Simulation results

5.2.1 Effect of varying switching frequency on harmonics generated

5.2.2 Effect of varying switching frequency on THD

5.2.3 Effect of varying switching frequency on ?

39

CHAPTER 6

conclusion & recommendation

conclusion

recommendation

40

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