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---

Static VAr compensator using high
frequency pulse-width modulated AC
chopper
By
WOODHOO Satyasheel Kushal
A project submitted in the partial fulfilment of
the requirements for the award of the degree of
BEng (Hons) Electrical and Electronic
Engineering
UNIVERSITY OF MAURITIUS
Department of Electrical and Electronic
Engineering
FACULTY OF ENGINEERING

March 2015

Table of Contents
List of figures
...
vii
Acknowledgements
...
ix
Abstract
...
xi
Chapter 1: Introduction
...
1 Introduction and background
...
2 Impact of reactive power on power system
...
2
...
1
1
...
2 Transmission and load compensation
...
3 Harmonics and its effects on the power network
...
3
...
2
1
...
2 Effects of harmonics on a power network
...
3
...
4
1
...
4 Total Harmonic Distortion (THD)
...
4 Objectives
...
5 Outline of chapters
...
6
2
...
7
2
...
7
2
...
1 Transmission of power in an AC network
...
2
...
9
2
...
3 Controlling reactive power using series compensators
...
3 Examples of available resources used in VAr compensation
...
3
...
16
2
...
2 Dynamic resources to provide control over the power grid
...
26
3
...
26
3
...
27
3
...
1 Operation of the AC chopper
...
2
...
29
3
...
29
3
...
33
Chapter 4: Power system modelling and design of the proposed VAr compensator
...
1 Introduction
...
2 3-phase modelling of the power system
...
3 Equivalent single-phase model of the power system
...
4 Sizing of the capacitor and the inductor of the VAr compensator
...
5 Design of the closed loop system
...
6 Design of PI controller
...
41
5
...
41
5
...
42
5
...
42
5
...
45
5
...
48
5
...
50
5
...
53
5
...
55
Chapter 6: Conclusions and recommendations
...
1 Conclusions
...
2 Recommendations for future works
...
58
ii

Appendix A: Circuit for Power System without the compensator
...
63
Appendix C: Circuit for feedback controller
...
65
Appendix E: Closed loop power system circuit
...
Error! Bookmark not defined
...
1: Transmission line connecting two sources
...
2:Active and reactive power with respect to angle, δ
...
3: shunt compensation in two-machine power system
...
4: Phasor diagram of the circuit considering Vm as the reference phasor
...
5: uncompensated system and compensated system variation of real power and
shunt compensator reactive power variation with respect to power angle, δ
...
6: Series compensator introduced in two-machine power system
...
7: phase angle compensator in the two-machine power system
...
8: phasor diagram of the circuit showing the Veff for positive and negative α
...
15
Figure 2
...
19
Figure 2
...
19
Figure 2
...
20
Figure 2
...
21
Figure 2
...
22
Figure 2
...
24
Figure 2
...
26
Figure 3
...
27
Figure 3
...
28
Figure 3
...
29
Figure 3
...
30
Figure 3
...


...
6: Capacitor in parallel with the switched-inductor branch
...
7: Implementing the S1 and S2 using power MOSFETs
...
8: brief short circuit when S1 changes from one state to another and S2
changes its state in the opposite way
...
9: Configuration of the practical model switch S1 and S2
...
10: Gating signals for the transistors T1P, T2P, T1N, T2N
...
1: 3 phase model of power system
...
2: Single phase model of the power system
...
3: Pulse Width Modulated output
...
4: Diagram of PI controller block
...
5: The complete circuit of the proposed power system
...
1 Desired load voltage & Measured load voltage when there is no load
disturbance
...
2: Desired load voltage & Measured load voltage when load disturbance =
9ZL
...
3: Desired load voltage & Measured load voltage when load disturbance = ZL

...
4: Desired load voltage & Measured load voltage when load disturbance =
0
...
44
Figure 5
...
46
Figure 5
...
46
Figure 5
...
47
Figure 5
...
25ZL
...
9: frequency spectrum of load voltage when no load disturbance is applied
...
10: frequency spectrum of load voltage when the load disturbance = 0
...
49
Figure 5
...
50
Figure 5
...
25Z L
...
50
Figure 5
...
51
Figure 5
...
9Z L
...
51
Figure 5
...
5ZL
...
52
Figure 5
...
2ZL

...
17: Measured real and reactive power when effective load impedance is ZL
...
18: Measured real and reactive power when effective load impedance is 0
...
54
Figure 5
...
5ZL
...
54

v

Figure 5
...
2ZL
...
55
Figure 5
...
05s
...
22: inductor current from t=5s to t=5
...
56

vi

List of tables
Table 2
...
19
Table 4
...
37
Table 5
...
42
Table 5
...
45
Table 5
...
48
Table 5
...
53
Table 5
...
55

vii

Acknowledgements
First of all, I am greatly indebted to my lecturer, Dr
...

Special acknowledgements are due to my family, who has constantly supported me in
my endeavour
...
My respect and gratitude is extended to my
mother for her love and understanding, her moral and emotional support which at every
step helped me to complete this work
...
I am also grateful to my
friends who never refused to lend me a help when in need
...
Unlike the typical thyristorbased Static VAr Compensator (SVC) which controls the impedance of the inductor by
adjustment of the firing angle, the AC chopper-based SVC can change the impedance of
the inductor by varying the duty cycle of the switches of the AC chopper
...
Consequently, the filter required to remove the
harmonics is relatively smaller for the AC chopper based SVC than the thyristor-based
SVC
...
A power system consisting of the proposed SVC used for maintaining the voltage
profile across a load is modelled and implemented on the SIMLINK platform
...
A disturbance is applied to the load to verify whether the SVC is able to
realise voltage regulation after the voltage profile is disturbed
...
The most important of all the analysis is the frequency spectrum of
the load voltage which shows that the harmonics are moved to higher orders
...


ix

List of acronyms
SVC:

Static Var Compensator

PWM:

Pulse-Width Modulation

MOSFET:

Metal Oxide Semiconductor Field Effect Transistor

RMS:

Root Mean Square

THDi:

Total Harmonic Distortion in current

THDv:

Total Harmonic Distortion in voltage

PF:

Power Factor

FACTS:

Flexible AC Transmission Systems

VAr:

Voltage-Ampere reactive

x

Chapter 1: Introduction
1
...
Nowadays, the modern grid is loaded so that the available
transmission facilities are utilized to the maximum
...
These harmonics cause inductive losses associated with dramatic drop in
transmission line voltages leading to poor power quality and consequently, instability in
the power system
...

Thus, it is desired that the power system can be controlled and operated within safety
margins
...


1
...
2
...
Reactive power plays a
major part in the voltage regulation of a network as it aids the system to withstand and
prevent voltage collapse
...
” However, reactive power can prove to have harmful effects on the electrical
infrastructure and its interconnected equipments too
...
This
degrades the efficiency and reliability of the power system and becomes costlier as
customers are penalized for drawing excessive power from the ac network
...

1
...
2 Transmission and load compensation
Transmission compensation is used for voltage regulation, that is, maintain the voltage
desired at terminals at sources/buses by supply of leading or lagging reactive power to
the transmission lines
...

Consequently, situations like over-voltage and under-voltage are prevented making the
overall system more stable
...
As a result, the load, combined with the compensator, appears as
unity power factor load from the source and the desired voltage across the load is
maintained [4]
...
3 Harmonics and its effects on the power network
1
...
1 Harmonic
A harmonic is a component that can take the form of a voltage or current level, the
frequency of which is an integral multiple of the transmission line’s fundamental
frequency
...

Harmonics are generated as a consequence of non-linear elements/loads in an ac
network because the non-linear elements draw current from the supply that is dissimilar
in shape to the applied voltage waveform
...

1
...
2 Effects of harmonics on a power network
Harmonics cause problems in generators, transformers and induction motors by
increasing iron losses and copper losses which are both frequency dependent
...
Hysteresis losses,
proportional to the frequency and square of magnetic flux, are increased at harmonic
frequencies which are higher than fundamental frequency and cause more rapid
reversals in the generator’s core magnetic field each time the current changes polarity
...


Relationship between Eddy current losses and frequency:

--------- (1
...


--------- (1
...
3)

Where,

= copper losses
= winding resistance
= combined RMS value of the fundamental current and harmonic

currents
= magnitude of nth harmonic
Furthermore, harmonics are undesired when it is required that generators and motors
work smoothly (reduced noise and oscillations)
...
Positive sequence harmonics, for
example, 7th harmonic rotates in the same direction as the fundamental frequency and
induces a positively rotating 6th harmonic in the rotor
...
These harmonic pairs(positively and
negatively rotating 6th harmonic), for the 5th and 7th harmonic, create torque pulsations
at six times the fundamental frequency resulting in undesired mechanical oscillations on
the generator or the motor shaft
...


Voltage is also affected by harmonics as harmonic currents produce additional and
undesired voltage drops across impedances located in the system leading to voltage
distortion [6]
...
3
...
The displacement
power factor is a result of the energy stored in inductive and capacitive
elements [16]
...
4)
where,

= phase angle between input voltage waveform and fundamental

component of total current
...


--------- (1
...
6)
From equation 1
...
Thus, it is necessary to mitigate harmonics so that there is
minimum loss of true power
...
3
...

Total harmonic distortion in current and voltage can be expressed using equations 1
...
8 respectively:

--------- (1
...
8)
where,

and
and

are the fundamental current and voltage components respectively,
are the harmonic components of current and voltage respectively
...
4 Objectives
The purpose of this research is to design a static VAR compensator (SVC) which is
capable of providing both VAR and harmonic compensation and the proposed controller
is based on load compensation that was highlighted in section 1
...
2
...
This is achieved by using a control method called Pulse Width
Modulation (PWM) AC chopper control
...
Consequently, the low-pass filter
required to remove the harmonics and to obtain the fundamental component from the
voltage and current waveform becomes smaller and thus, less costly as compared to the
Thyristor-based SVC
...


1
...

Chapter 1 introduces the need for reactive power compensation to make a power system
become more reliable and ‘healthy’
...

Chapter 2 involves the different methods of reactive power compensation and gives an
idea of how existing static and dynamic are used in power systems
...

Design of a power system incorporating the proposed SVC based on high frequency
pulse-width modulation which is used to compensate or rather regulate the voltage
across a load is carried out in chapter 4
...

Conclusions drawn from the proposed concept are presented in Chapter 6 as well as
future works are also discussed
...
1 Introduction
Generally, a complex power system is composed of numerous sources and loads
whereby the flow of reactive and active power is determined by voltages and
impedances and particular points in the network
...
Thus, there is a
need to exercise control over parameters such as impedances, voltages, currents ad
phase angles to improve the controllability and reliability of the ac network
...


2
...
2
...
The sending end voltage is denoted by Vs
and the receiving end voltage by Vr
...
Vs is considered as the reference phasor so
that it leads Vr by an angle of δ [7]
...
1)

The two machine system is as shown in figure 2
...


Figure 2
...

Let Sij and Sji be the line powers that flow from source i to source j and source j to
source i respectively
...
2)
Using equation 2
...
3)

--------(2
...
Therefore, the new line powers are given by:
δ

δ

δ

δ

δ

δ
δ

δ --------- (2
...
6)

The line powers, Sij and Sji are composed of real and reactive powers that are related by
the equations 2
...
8 as follows:
--------- (2
...
8) is the active power flow from source i to source j and

where,

δ --------- (2
...


--------- (2
...
11) is the active power flow from source j to source i

where,
and
Qij =

δ --------- (2
...
12) is the reactive power flow from source j to

source i
...
2 show the plots for the active power and reactive power flow against the
power angle, δ
...
2:Active and reactive power with respect to angle, δ
...
2 and the equations 2
...
11,
1
...

2
...

3
...

2
...
2 Controlling reactive power using shunt compensators
The principle of shunt compensation is to inject a leading or lagging current into the
system at the point where the shunt controller is connected to maintain the desired
voltage at a particular node
...
The
compensator is connected at the midpoint of the transmission line of figure 2
...
It is desired to connect the compensator
at the midpoint because it allows for maximum mitigation of voltage sag which is

greatest at the midpoint and also, maximum VAr compensation is achievable by
locating the controller at the middle of the transmission line
...
The configuration for the system
incorporating the compensator is shown in figure 2
...


Figure 2
...

The midpoint voltage, Vm is treated as the reference phasor and the phasor diagram for
the circuit is shown in figure 2
...


Figure 2
...

From the phasor diagram, the magnitudes of the voltages and currents are obtained as:

δ

--------- (2
...
14)
δ

δ

δ

δ

δ

where,

--------- (2
...

Therefore, the real power, Pt transmitted from the sending to the receiving end for the
lossless transmission line is given by:
δ

δ

δ

δ

-------(2
...

Therefore, the sending and receiving end reactive powers can be expressed as:
δ

δ

δ

δ

δ

----------

-------------------------------------------------------------------------------------------------- (2
...
18)

The graphs for the variation of the real power, Pt with and without the compensator and
reactive power, Qc on the shunt compensator against the power angle, δ is shown in
figure 2
...


Figure 2
...

From equations 2
...
18 and figure 2
...
However, it also causes the reactive
power required by the compensator to be increased
...
2
...
There are two
cases for series compensation:
1
...
This is technique is
discussed in section 2
...
3
...

2
...

This technique is referred to as phase-angle compensation which is elaborated in
section 2
...
3
...
2
...
1 Series compensation when line current is leading or lagging the introduced
compensator voltage, Vc by 900
...
6 shows the arrangement of the series compensator in the power system [8]
...
6: Series compensator introduced in two-machine power system
...
Thus, the compensator can be viewed as an
inductive impedance if the I lags Vc by 900 or a capacitive impedance if I leads Vc by
900 [8]
...
19)
where, Xc=the equivalent series compensator reactance which is negative when it
capacitive and positive when it is inductive and

=the compensation factor and

0≤|s|≤1
...
20)
δ

--------- (2
...
19 and 2
...
22)

δ

--------- (2
...
22, it can be concluded that the transmittable real power can be
increased by placing a compensator the reactance of which is capacitive
...
From equation 2
...
Series compensation is used
mostly in long transmission lines having large reactive impedances
...
8, power is inversely proportional to reactance
...
2
...
2 Series phase-angle compensation when line current is not in phase
quadrature with the introduced compensator voltage, Vc
...
7 below [8]
...
7: phase angle compensator in the two-machine power system
...
24)
--------- (2
...
7 is shown in figure 2
...
8: phasor diagram of the circuit showing the Veff for positive and negative α
...
26)
δ

α

--------- (2
...
26 and 2
...


2
...
Static resources are used to ensure the required power flow
throughout the power system in the steady-state
...
However, these devices
prove to be less reliable when they are required to operate with a fast response time, that
is, they take a long time period to move the system’s operating point to a new one
...
For example, if the fundamental frequency
is 50Hz (time period = 0
...
02s, that is, the device should have sub-cycle response time
...


2
...
1 Static resources to provide control over the power grid
Static solutions to power grid control involve the use of devices that work under steadystate conditions
...
2
...
Voltage control can be achieved by a direct and an indirect method
...
However, other parts of the transmission system that are not adjacent to
the generators use the indirect method where voltage control is brought about by
controlling the reactive power through compensators like series and shunt controllers
[10]
...

Examples of static devices are:
2
...
1
...
This is achieved by
connecting the switched shunt capacitor and reactor banks in and out of the system
through mechanical switches or circuit breakers
...
The reactive power output from the capacitor and
reactor banks is proportional to the square of the voltage; thus, when the power system
suffers from low-voltage conditions, the reactive power also decreases causing the
voltage to be lowered further [9]
...
Thus, mechanically switched
capacitor and reactor banks are found to have a better impact on systems where VAr
control is required in the steady-state
...
3
...
2 Phase-shifting transformers (PSTs)
The PST, also called as the phase-angle regulator is based on phase-angle compensation
technique to control the flow of real and reactive power over the transmission line
which is achieved by adjusting the phase-angle difference between the sending and
receiving end of the system
...
The
principle of operation of the PST is to inject a voltage such that it is maintained fixed at
±900 with respect to the line voltage
...
PSTs are used especially in the
control of real power flow along parallel paths which is dependent on system’s
transmission line impedance
...
The
disadvantage of PST is that they have a slow response time because these devices make
use of mechanical taps to inject the required voltage and thus they are preferred to be
operated under steady-state system conditions
...

2
...
1
...
This can be achieved by equipping the power transformer
with tap changers which can control the amount and direction of flow of reactive power
through the transformer depending on the settings of the tap
...
The tap changers, located on the primary or secondary side of the
transformer windings, control the voltage by forcing voltage on one side of the
transformer to go up which in turn, results in the lowering of the voltage on the other
side [12]
...
Off-load tap changers are used to do adjustments when
the transformer is de-energised and are preferred to be located on the low voltage side
of the transformer and OLTCs on the contrary are usually located on the high voltage of
the transformer because of their current-commutation capacity and are operated under
load
...
The mechanical tap changer consists of insulators and contacts which when
subjected to high currents, degrade over time and thus require regular maintenance
...
Also, these
semiconductors are quite expensive and their configuration is quite complex when
control strategies are analysed [9]
...

2
...
2 Dynamic resources to provide control over the power grid
Dynamic resources are those solutions used to exercise control over power grid when
the system suffers a sudden and unpredicted disturbance, that is, the system is brought
about to its new operating by the dynamic device in a relatively lesser time than a static
device
...
Dynamic devices also participate in
exploiting the maximum transmittable power through the transmission line, allowing the
transmission facilities to be fully utilized and in damping oscillations in the power grid
...

FACTS devices are based on high-speed semiconductor power electronics controllers
which can not only provide dynamic control over the flow of real and reactive power
but also, increase the transmittable power capability in ac systems [8]
...
Table 2
...

Mode of

FACTS

Volta

Transien

Damping

Reactive

Power

Sub-

connection

ge

t

of power

power

flow

Synchronous

of the

contr

stability

oscillation

compensatio

contro

Resonance(SSR

controller

ol

s

n

l

)

SeriesShunt







X

















SVC









X

X

STATCOM

Shunt

TCSC
SSSC

Series









X

X

UPFC













Table 2
...
3
...
1 The Thyristor-Controlled Series Capacitor (TCSC)
The TCSC is composed of a series capacitor, C in parallel with a thryristor-controlled
reactor (TCR), L as shown below in figure 2
...


Figure 2
...

By varying the firing angle, α of the thyristors (T1 and T2), the shunted thyristorcontrolled reactor can be modelled as a variable inductive impedance, X L (α) as shown
in the figure 2
...


Figure 2
...

The equivalent inductive impedance is give by the equation:
--------- (2
...

Thus, it can be deduced that the inductive impedance can be varied from its maximum
( ) to its minimum (XL)
...
29)

Where, XC is the reactance of the capacitor
...
Also, transient response of the power system is rather slow because the
thyristors can be triggered only once in each half-cycle
...

2
...
2
...
This is achieved by
the SSSC injecting a voltage containing an appropriate phase angle with respect to the
line current
...
The SSSC is composed of a voltage source converter (VSC) and a DC
energy storage as shown in Figure 2
...


Figure 2
...

The DC energy storage used, that is, the capacitor provides the basic DC to AC
conversion as well as it aids in the reduction of ripples in the DC voltage that is fed into
the VSC
...
30)
Where, V is the magnitude of the voltage at the sending and receiving ends of the
transmission line, δ is the angular difference across the line, X is the reactance of the
line and Vc is the injected voltage by the compensator
...
31)

The compensator voltage can be adjusted by varying the angular difference across the
line to make it
a) Lead the line current by 900 to provide additional inductive reactance in the line;
in this case the SSSC aids in the damping of power oscillations
...

The main disadvantage of the SSSC is that it is costly
...
Also the SSSC is able to inject voltage in
the system independent of the line current
...
3
...
3 The Static VAr compensator (SVC)
The SVC is one of the most commercially used FACTS devices because of its relatively
low cost compared to other FACTS controllers
...
12 below:

Figure 2
...

a) The TCR

The source voltage is expressed as:
--------- (2
...

The TCR current can be expressed as:
α

α

--------- (2
...
33, the controllable range of the firing angle of the TCR is from 90 0 to
1800
...
13 below:

Figure 2
...

By performing Fourier analysis, the fundamental component of the TCR current, ITCR1
(α) is obtained as:
α

α
α

Since,
α

α --------- (2
...
35),

α

α --------- (2
...

Thus, it can be deduced that the reactor can be modelled as a variable susceptance
...


The TCR generates harmonics because as the firing angle is increased above 900, the
TCR current becomes discontinuous [4]
...
The TSC is switched in and out
of the system unlike the TCR which is controlled by variation of the firing angle of the
thyristors
...
37)

Where, V is the peak ac source voltage, α is the firing angle of the thyristors, w is the
angular frequency of the system, VCO is the initial capacitor voltage, wn is the natural
frequency of the inductor-capacitor combination and is given by:
--------- (2
...
39) where, Xc is

the reactance of the capacitor and XL is the reactance of the inductor, Ls
...
However the two other terms involving wn,
cause oscillatory transients
and are thus avoided by forcing:
i)

α to 0 or

α to ±1

ii)
After eliminating the transient switching, the TSC current is given by:
α -------- (2
...
40, it can be deduced that the TSC current is sinusoidal and thus free
from harmonics
...

Thus, SVC can provide both leading and lagging VAr at fast response time to achieve
voltage regulation at the point of connection
...
SVCs
also have the disadvantage of limited control over different voltage conditions that the
power system may suffer from [4], [5]
...
3
...
4 The Static Synchronous Compensator (STATCOM)
The STATCOM is typically a voltage-source converter (VSC) which has the ability to
control the flow of real and reactive independently throughout the ac system
...
STATCOMS are well known for
their ability to maintain a constant voltage across the transmission line by supplying the
appropriate amount of reactive power to the power system to which it is connected
...
14:

Figure 2
...

If the converter’s output voltage is increased above the source voltage, then the flow of
current is from the converter to the ac system through the reactance so that the

STATCOM generates capacitive reactive power fed into the grid
...
If the converter’s output voltage is the same as
that of the source voltage, then no reactive power exchanger occurs [4]
...
The converter’s output voltage is thus made to lead or lag the source
voltage so as to decide whether the converter is to supply active power or absorb active
power that will be stored in the DC energy storage element [4]
...
Their main
advantage is that they can control the flow of real and reactive power between the VSC
and the AC system independently of each other
...
They also have a wide range of
control as they can control their output current from their rated maximum capacitive to
inductive range without being affected by the line current of the ac system [4], [5]
...
3
...
5 The Unified Power Flow Control (UPFC)
The UPFC is the most desired of all the existing FACTS devices in the dynamic
compensation of the ac system because of its ability to realise any desired function
...
Thus, the
UPFC consists of 2 voltage-source converters, one connected in parallel with the
transmission line while the other one in series with the line and both converters are fed
by a common DC source
...
15:

Figure 2
...

The UPFC allows for independently and very rapidly controlled power flow in the
transmission line
...
Thus, both the active and reactive power flow can controlled
...
This is achieved by the VSC1 drawing or
generating the active power from the transmission line itself
...
Reactive power compensation is achieved
by both of the VSC by operating them as STATCOM or SSSC independently [4], [15]
...


Chapter 3: Concept of the Static VAr compensator based on
high swtiching frequency Pulse-Width Modulated AC
chopper
...
1 Introduction
In chapter 2, section 2
...
2, existing FACTS devices that are proved to exercise control
over the voltage at every node in the system as well as on the flow of both reactive and

active power were presented
...
However, the TCR branch of the SVC causes undesired
harmonics to be generated due to the switching of the thyristors and as a result, the load
current and voltage are distorted
...
To make this achievable, the proposed SVC
operates on the concept of the AC chopper and how it can realise load compensation in
a power system to maintain the voltage across the load constant by using high switching
power electronic devices like MOSFETs, IGBTs and BJTs
...
2 Concept of PWM AC chopper controllers
In this scheme, the input supply voltage is chopped into portions by employing pulsewidth modulation technique, whereby the output voltage level is decided by controlling
the duty cycle of the chopper switching function [8]
...
2
...
1
...
1: Basic PWM AC chopper circuit [20]
...

When SB is switched ON, SA turns OFF so that the voltage, Vo is 0 and the current, io
freewheels across the switch SB
...
Figure 3
...


where w is the angular frequency of

Figure 3
...
2, the dashed red line is the fundamental component
of the load current, io
...
The input
voltage, Vi is chopped by the switch SA to give the load voltage, Vo
...

D is the switching duty cycle of the switch which will decide the ON duration time of
SA which is given by DTs and by adjusting D, it is possible to control the magnitude of
the fundamental component of the load voltage, Vo
...
1), where w is the angular frequency
...
2
...
2)
Where, D is the switching duty cycle, fs is the switching frequency, M is an integer
value from 1 to infinity and f1 is the fundamental frequency
...

The second term,

gives all the harmonic

components from M=1 up to infinity
...


The frequency spectrum of the load voltage is shown in figure 3
...


Figure 3
...

As it can be observed from figure 3
...
Thus, the main advantage of using an AC chopper is that by applying a high
switching frequency to its switch, the harmonics can be pushed to higher frequencies
and as a result, the low-pass filter that is required to extract the fundamental component
from the load voltage is of a small size
...
3 The proposed SVC
An attempt is made to construct a SVC, based on the principle of operation of AC
choppers that provides the same function as the thryristor-controlled reactor based
compensator
...
Figure 3
...


Figure 3
...

Switch S1 is used to modulate the voltage, Vin(t) that is applied to the inductor while
switch S2 is used to freewheel the inductor current, IL(t) when S1 is open
...
Pulse-Width Modulation technique is employed
to modulate the switches with the desired duty cycle, D (duty cycle of S1) and 1-D
(duty cycle of S2)
...
The expected waveforms for the F(t), IL(t) and Iin(t) are
presented in figure 3
...


Figure 3
...

The switching function, F(t) is expressed as:
-------- (3
...

Since

-------- (3
...
5)
Let

and

, where ws is the angular switching frequency and x is an

integer value between 1 to infinity
...
6)

-------- (3
...

The inductor current is chopped by the switch S1 so that the input current, Iin(t) is given
by:
-------- (3
...
Thus, the fundamental input current, Iin1(t),
free from harmonics, is given by:
-------- (3
...
9), the fundamental impedance, Zin1 as seen from the input side is
given by:
-------- (3
...
10), it can be concluded that impedance of the switched-inductor
branch can be varied by changing the switching duty cycle, D
...
7)
Thus, reactive power control can be achieved by adjusting the duty cycle
...

This is achieved by placing a capacitor in parallel with the switched-inductor branch as
shown in figure 3
...


Figure 3
...

Given that the reactance of the capacitor is Xc, the leading reactive power, Qc that is
supplied by the capacitor is given by:
-------- (3
...
4 Operation of the AC-chopper based SVC
For the design of the proposed SVC, MOSFETs are used to model the switches as
shown in figure 3
...


Figure 3
...
This
can create a brief short-circuit at the change-over instant as shown in figure 3
...


Figure 3
...

The solution to this problem is to use two back-to-back connected MOSFETs to model
the switches as shown in figure 3
...
In this way, the current is controlled independently
in each direction [22]
...
9: Configuration of the practical model switch S1 and S2
...
During the positive half-cycle, when S1 is closed and S2 is open,
transistor T1P conducts and when S1 is open and S2 closed, transistor T2P conducts as
it provides the freewheeling path for the inductor current
...

During the negative half-cycle, when S1 is closed and S2 is open, transistor T1N
conducts and when S1 is open and S2 closed, transistor T2N conducts as it provides the

freewheeling path for the inductor current
...

The driving signals (G1P, G1N, G2P, G2N) for the transistors are shown in figure 3
...

From figure 3
...


Figure 3
...


Chapter 4: Power system modelling and design of the
proposed VAr compensator
...
1 Introduction
The modelling of the power system incorporating the SVC is presented in this chapter
...
The parameters were designed appropriately so as to ensure the optimal
performance of the VAr compensator
...


4
...
The
power system is designed with a lagging load that needs compensation
...
1
shows the layout of the system whereby Wye-connection of the generator with the load
is considered and table 4
...


Figure 4
...
8kV

Line apparent power, SL

36MVA

Generator power factor, P
...
85 lagging

Frequency, f

50Hz

Total rated real power of load, Pload

30
...
85 lagging

Phase angle of infinite bus with respect to generator, δ

-300

Length of transmission line

20km

Transmission line impedance/km, XL

0
...
1: System parameters for 3-phase circuit
...
3 Equivalent single-phase model of the power system
The 3-phase model of the system is converted into its equivalent single phase circuit
using the following equations:
Phase voltage,

-------- (4
...
2)
Since, line apparent power,

-------- (4
...
3), the line and phase current is calculated as:
-------- (4
...
5) where,

is the power factor,

P
...

Line reactive power,

-------- (4
...
3), (4
...
6), the single phase apparent, real and reactive
powers are given by:
Apparent power,
Real power,
Reactive power,

-------- (4
...
8)
-------- (4
...
10)

Reactive power demand of load,

---- (4
...
12)
Ω
Impedance of the transmission line,

-------- (4
...
14)

From equation (4
...
15)

Figure 4
...


Figure 4
...
4 Sizing of the capacitor and the inductor of the VAr compensator
The capacitor was chosen so that it is able to supply reactive power rated at 90MVAr
and the inductor was chosen so that it can absorb 100MVAr reactive power
...
5 Design of the closed loop system
The block diagram for the proposed closed loop system is shown in figure 4
...
This is achieved by measuring the root-mean-square (RMS) value of the load

voltage and is compared to another RMS value which is called the reference RMS
value
...
001 to reduce the high level of
voltage (in the range of kV) and then is fed into a feedback controller, that is, the
Proportional-Integral controller (PI-controller) which attempts to minimise the error
signal to its smallest possible value
...
This is done by comparing
the output of the PI controller with the saw-tooth waveform using a comparator such
that when the output signal of the PI controller is less than or equal to the signal of the
saw-tooth, the output of the comparator is 1
...
The frequency of the saw-tooth signal is the
switching frequency, Fs of the switch itself
...
Thus, the time period of the saw-tooth waveform is calculated as:

...
3
...
3: Pulse Width Modulated output

4
...

The block diagram of the PI-controller is as shown in figure 4
...
4: Diagram of PI controller block
...
16)
Procedure for deciding the appropriate value of Kp & Ki,
1) Kp was first set to 0
...

2) Kp was increased in steps of 0
...
The value at which this
occurred was Kp=0
...


3) Ki was then set to 0
...
01 until the steady state
error was minimised in output of the load voltage
...
However, Ki was improved to a higher value of 5 so that the rise
time of the load voltage to its corresponding reference value would be
decreased
...
16)
A schematic of the closed loop power system is shown below in figure 4
...


Figure 4
...
1 Introduction
This chapter contains the results of the simulation of the modelled power system
incorporating the proposed SVC
...
Then, also very important was the analysis of the frequency spectrum
of the load voltage which will show how the low order harmonic harmonics that would
be generated by the TCR is shifted to a higher order
...


5
...
The purpose of the application of the load
disturbance to the load is to study its effect on the voltage across the load
...
The effect of the load disturbance
was observed for a duration of 2s as the load disturbance was switched into the system
at time t=1s and removed at t=3s over a simulation period of 6s
...
The impedance load disturbance was scaled by a factor of k of the load impedance
as shown in table 5
...
2+j6
...
8+j56
...
9ZL=9
...
688

ZL

1

ZL=10
...
32

0
...
1+j3
...
25

0
...
55+j1
...
2ZL=2
...
264

Table 5
...

All the following analysis carried out will be based on using the listed parameters in
table 5
...


5
...
1 will be observed by carrying out the simulation without the
compensator
...

Figure 5
...
The
measured RMS value of the load voltage is 11080V
...
1 Desired load voltage & Measured load voltage when there is no load
disturbance
Figure 5
...
The measured RMS value of the load voltage is
11020V during the disturbance
...


Figure 5
...


Figure 5
...
The
measured RMS value of the load voltage during the disturbance is 10570V
...


Figure 5
...
4 shows the load voltage variation when the load disturbance is 0
...
The
measured RMS value of the load voltage is during the disturbance is 9131V
...


Figure 5
...
25ZL
...
2 summarises the uncompensated power system load voltage variation as they
are affected by a disturbance
...
9ZL

11020

980

ZL

0
...
25ZL

0
...
2: Uncompensated system load variation with the specified disturbances
...
4 Analysis of the load voltage with the SVC
In this case, the transmission line is connected to the compensator and the power system
is simulated
...
1 itself
...
5 shows the load voltage variation of the measured and reference load voltage
for the compensated power system
...
It is seen that the measured load voltage
approaches very near to the reference voltage so that the voltage regulation is ±5%
...


Figure 5
...

Figure 5
...
9Z L
...


Figure 5
...

Figure 5
...
5ZL
...
11s
...
11s
...
7: Desired load voltage and Reference voltage for the compensated
transmission line when load disturbance = ZL
...
8 shows the load voltage variation when the effective load impedance is 0
...

It can be observed that at the time the disturbance connects to the load (t=1s), a drop in
the voltage of about 2536V occurs which is brought back to reference load voltage in
about 0
...
Similarly, when the disturbance is disturbance is disconnected, an
overshoot in voltage of about 3980V occurs that is stabilised back to the desired load
voltage in around 0
...


Figure 5
...
25ZL
...
3 summarises the load variations for the compensated power system as they are
affected by the disturbance
...
9ZL

11950

50

ZL

0
...
25ZL

0
...
3: Compensated system load variation with the specified disturbances
...
5 Analysis of the frequency spectrum of the load voltage for the
compensated transmission line
The aim to do the frequency analysis of the load voltage is to show that using the SVC
based on high frequency PWM AC choppers helps to push the high amount of low order
harmonics to higher orders so that they can easily be filtered out
...
The analysis is again carried out by varying the

effective impedance of the load given in table 2
...


Figure 5
...


Figure 5
...

Figure 5
...
9ZL
...
10: frequency spectrum of load voltage when the load disturbance = 0
...

Figure 5
...
5ZL
...
11: frequency spectrum of load voltage when the load disturbance = ZL
...
12 shows the frequency spectrum of the load voltage for the effective load
impedance, 0
...


Figure 5
...
25ZL
...


5
...
1)
Where S is the apparent power, P is the real power demand, Q is the reactive power
demand of the load, Z is the impedance of the load, R is the resistance of the load and X
is the reactance of the load
...
1
...
13 shows the variation of real and reactive power when
effective load impedance is ZL
...
13: Measured real and reactive power when effective load impedance is ZL
...
14 shows the variation of real and reactive power when effective load
impedance is 0
...


Figure 5
...
9ZL
...
15 shows the variation of real and reactive power when effective load
impedance is 0
...


Figure 5
...
5ZL
...
16 shows the variation of real and reactive power when effective load
impedance is 0
...


Figure 5
...
2ZL

Table 5
...

Load

Effective

Calculated

Calculated

Measured

Measured

disturbance,

total

Real Power

Reactive

Real Power

Reactive

ZLD=k(ZL)

impedance

demand,

power

demand,

power

Ω

of load,

P/MW

demand, Q/

P/MW

demand,

Zt Ω

MVAr

Q/ MVAr

0

ZL

10
...
32

8
...
829

9ZL

0
...
3

7
...
56

5
...
5ZL

20
...
62

15
...
795

0
...
2ZL

51
...
6

Table 5
...


5
...
Figure 5
...


Figure 5
...

Figure 5
...
9ZL
...
18: Measured real and reactive power when effective load impedance is 0
...
19 shows the variation of real and reactive power when effective load
impedance is 0
...


Figure 5
...
5ZL
...
20 shows the variation of real and reactive power when effective load
impedance is 0
...


Figure 5
...
2ZL
...
5 shows the calculated and measured power demands of the loads with the
compensator
...
2

6
...
19

6
...
9ZL

11
...
02

11
...
963

ZL

0
...
4

12
...
36

12
...
25ZL

0
...
0

31
...
9

31
...
5: Power absorbed by load with the compensator
...
7 Test for AC-chopper voltage and current waveform
A test was carried out to confirm whether the inductor voltage and current were as
expected as in theory
...
25ZL
...
21 and 5
...


Figure 5
...
05s

Figure 5
...
05s

Chapter 6: Conclusions and recommendations

6
...
The proposed SVC consisted of a
switched inductor which was connected in parallel with a capacitor
...
By employing a
proper automatic control method, the duty cycle was varied in such a way that the
appropriate switching pulses for the operation of switches were generated
...

Automatic voltage compensation was carried out by using a PI-controller which
minimised the difference between the measured load voltage and the desired load
voltage
...
The simulation results were deemed satisfactory, especially when
the main objective to show that the harmonics produced were pushed to higher
frequencies was expected
...
The THD

in the load voltage decreased when the load disturbance became smaller
...
This enabled the compensator to provide the load with the power that it demands
...
Hence, it can be concluded that the AC chopper-based
SVC operation was satisfactory
...
2 Recommendations for future works
Improvements for the proposed SVC:
1) Comparing it to the thyristor-based SVC so that their respective frequency
spectrum could be analysed and hence, the THD could be compared
...

2) The hardware implementation of the system could be carried out later to test the
efficacy of the compensator
...
One example of
the difference that it will make is that the transmission will also contain resistive
and capacitive elements that will affect the flow of power differently
...

4) The test was only made on a load having a lagging power factor
...

5) The PI-controller was tuned manually so that the proportional constant and the
integrator constant were only a guess
...


References:

[1] Task Force on Terms and Definitions System Dynamic Performance Subcomitter,
“Proposed Terms and Definitions for power system stability,” IEEE Transactions
...
1894-1898
...
D
...
W
...
A
...
493-500
...
, “Concepts of reactive power
control and voltage stability methods in power system network,” in IOSR Journal of
Computer Engineering (IoSR-JCE), Vol 11, June 2013, pp15-25
...
Mohun
...
K
...
USA: John Wiley & Sons, 2002, pp
...

[5]E
...
G
...
Anaya-Lara, T
...
E
...
Great Britain: MPG Books Ltd, Bodmin, Cornwall, 2002, pp
...

[6] American Bureau of Shipping, “Guidance Notes for Control of Harmonics in
Electrical

Power

Systems,”

USA

ABS,

May

2006,

[Online]
...
eagle
...
I
...
India: Tata
McGraw-Hill, 1971, pp
...

[8] Muhammad
...
Rashid, Power Electronics: Circuits, Devices and Applications
...
500-513, 522-526, 534-535, 570597
...
Sastry, Direct AC control of grid assets, PhD [Dissertation] Georgia Institute
of Technology, Georgia, 2011, pp
...

[10] Tore
...

Available:
http://www
...
ufmg
...
pdf

[11] “Phase-Shifting Transformers,” [Online]
...
electricalknowhow
...
html
...
Verboomen, D
...
Hertem, P
...
Schavemaker, W
...
Kling, R
...
1-6
...
C
...
XLIV, January 1925, pp
...

[14] G
...
Pillar, Arindam
...
Joshi, “Torsional Interaction Studies on a
Power System Compensated by SSSC and fixed capacitor,” in IEEE transactions on
power delivery, Vol
...
988-993
...
Kanch, Vijay
...
Garg, “Unified Power Flow Controller (FACTS
device): A review,” in International Jounal if Engineering Research and Applications
(IJERA), Vol
...
1430-1435
...
Wildi, Electrical Machines, Drives and Power systems
...
Ltd, 2002, pp
...
(2013, October 8)
...

Available: http://wiki
...
org/wiki/Classification_of_Powerlines
[18] Nicholas
...
Seeley, Cameron
...
Rainey, “Advances in generator control
and automatic synchronisation – Eliminating the need for standalone synchronisation
system,” in Petroleum and Chemical Industry Technical Conference (PCIC), 2012
Record of Conference Papers Industry Applications Society 59th Annual IEEE, 24-26
September 2012, pp
...

[19] P
...
Sen, Principles of electric machines and power electronic
...
Ltd, 2011, pp
...

[20] I
...
Class Lecture, Topic:“AC voltage controllers,” Faculty of
engineering, University of Mauritius, Reduit, Mauritius, 20th October 2014
...
Jin, G
...
Lopes, “An Efiient Switched-Reactor/Capacitor-Based Static
VAR Compensator,” in Industry Applications Society Annual Meeting, 1992,
Conference Record of the 1992 IEEE, Vol
...
822-828
...
Marouchos, “A New Switched Inductor VAR compensator,” in Power
Electronics and Applications, 2009
...
13th European Conference, 8-10
September 2009, pp
...

[23] Christos
...
London, United Kingdom: The Institution of Engineering and Technology,
2006, pp
...


Appendix A: Circuit for Power System without the
compensator

Appendix B: Circuit of proposed SVC

Appendix C: Circuit for feedback controller

Appendix D: Control signal for switches T1P, T2P, T1N and
T2N

Appendix E: Closed loop power system circuit



---