120412 thesis lydia
TRANSCRIPT
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
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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 …
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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
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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.
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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.
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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)
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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.
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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.
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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).
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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.
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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.
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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,
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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
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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
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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]
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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
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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]
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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]
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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
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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.
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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
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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.
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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
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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
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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)
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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].
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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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