MajorProject2016

COMPARATIVE ANALYSIS OF IMPROVEMENT OF
TRANSIENT STABILITY OF MULTI-MACHINE POWER
SYSTEM WITH SERIES AND SHUNT FACTS DEVICES
Submitted in partial fulﬁllment of the requirement of
BACHELOR OF TECHNOLOGY
by
PARTH MARU [12BEE032]
SHARMA TUSHARKUMAR G. [12BEE049]
GAURANG VADHIYA [12BEE057]
Under the guidance of
Ms. Meera Karamta
ELECTRICAL ENGINEERING DEPARTMENT
SCHOOL OF TECHNOLOGY
PANDIT DEENDAYAL PETROLEUM UNIVERSITY
GANDHINAGAR - 382007, GUJARAT - INDIA.
JANUARY - JUNE , 2016

APPROVAL SHEET
This report entitled Comparative analysis of improvement of transient stability of
multi-machine power system with series and shunt FACTS devices by Parth Maru,
Sharma Tusharkumar and Gaurang Vadhiya is recommended for the degree of B.Tech
( 8th semester ) Electrical Engineering.
Examiner:
Supervisor:
Chairman:
Date: May 25, 2016
Place: Gandhinagar

STUDENT DECLARATION
we hereby declare that this written submission represents our ideas in our own words,
where others idea or words have been included, we have adequately cited and refer-
enced the original sources. We also declare that we have adhered to all principles of
academic honestly and integrity and have not misrepresented or fabricated or falsi-
ﬁed any idea / data / fact / source in my submission. We understand that any viola-
tion of the above will be cause for disciplinary action by the PANDIT DEENDAYAL
PETROLEUM UNIVERSITY and can also evoke penal action from the sources which
have thus not been properly cited or from whom proper permission has not been taken
when needed.
Group Members:
1) Parth Maru [12BEE032]
2) Sharma Tusharkumar [12BEE049]
3) Gaurang Vadhiya [12BEE057]
Signature:
1)
2)
3)
Date: May 25, 2016

CERTIFICATE BY SUPERVISOR
This report entitled Comparative analysis of improvement of transient stability of
multi-machine power system with series and shunt FACTS devices by Parth Maru,
Sharma Tusharkumar and Gaurang Vadhiya is recommended for the degree of B.Tech
- 8th semester Electrical Engineering under the supervision of Ms. Meera Karamta.
Supervisor
Date: May 25, 2016
Place: Gandhinagar

PREFACE
This report is related to the analysis of transient stability of multi-machine power sys-
tem of wscc 9 bus system. The scope of report work includes the study of the transient
stability of power system and different ways to improve it.
The system level study has been conducted using MiPower and MATLAB soft-
ware. Load ﬂow analysis and transient stability analysis of wscc 9 bus system has
been done using MiPower.
i

ACKNOWLEDGEMENT
We take this opportunity to express our profound gratitude and deep regards to our
guide Ms. Meera Karamta, for his exemplary guidance, monitoring and constant en-
couragement throughout the major project. The blessing, help and guidance given by
her time to time shall carry us a long way in the journey of life. We would also like to
thank Mr. Astik Dhandhia, for providing permission for using college premises. We
would also like to thank people who have directly or indirectly supported and guided
us.
Lastly, we thank almighty, our parents and friends for their constant encouragement
without which this project would not be possible.
ii

ABSTRACT
Power systems can effectively damp power system oscillations through appropriate
management of real or reactive power. This thesis addresses some effective ways to
improve the transient stability of the power system using different series and shunt
FACTS devices.
Main objectives of the project are as follow.
• To study and understand transient stability problem.
• To carry out load ﬂow and transient stability analysis of standard WSCC system
without use of FACTS devices.
• To study and understand importance, application and operation of FACTS de-
vices.
• To perform and simulate the load ﬂow and transient stability analysis of system
with different series and shunt FACTS devices.
• To perform the comparative analysis of the effect of using different series and
shunt FACTS devices.
iii

Contents
Preface i
Acknowledgement ii
Abstract iii
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Power system stability problem . . . . . . . . . . . . . . . . 2
1.1.2 Forms of power system instability . . . . . . . . . . . . . . . 2
1.1.3 Classiﬁcation of stability . . . . . . . . . . . . . . . . . . . . 3
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Power system stability 5
2.1 Basic concepts and deﬁnitions . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Rotor Angle Stability . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Frequency stability . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Voltage stability . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Dynamics of synchronous machine . . . . . . . . . . . . . . . . . . 7
2.3 Power angle curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Transient stability 12
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Equal Area Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 12
iv

4 FACTS Controller 17
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1.1 Advantages of FACTS . . . . . . . . . . . . . . . . . . . . . 18
4.2 Types of FACTS controller . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.1 Switching Converter Type Var Generator: STATCOM . . . . 20
4.2.2 Controlled Variable impedance type Var generator: SVC . . . 24
4.2.3 Effect of shunt FACTS devices on transient stability . . . . . 26
4.2.4 Thyristor Controlled Series Capacitor ( TCSC ) . . . . . . . . 28
4.2.5 Static Synchronous Series Compensator (SSSC) . . . . . . . 30
4.2.6 Effect of series FACTS devices on transient stability . . . . . 31
5 Simulation 33
6 Future Work 34
7 Conclusion 35
Appendix A WSCC system 36
Bibliography 38

List of Figures
1.1 Classiﬁcation of power system stability . . . . . . . . . . . . . . . . 3
2.1 Flow of mechanical and electrical powers in a synchronous machine . 8
2.2 Simpliﬁed machine model . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Two bus stability study network . . . . . . . . . . . . . . . . . . . . 11
3.1 Plot of δ vs. t for stable and unstable system . . . . . . . . . . . . . 13
3.2 Rotor angle response for transient disturbance . . . . . . . . . . . . . 13
4.1 Types of controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 STATCOM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 General control scheme of Static Var Generator . . . . . . . . . . . . 22
4.4 V-I chara. of STATCOM . . . . . . . . . . . . . . . . . . . . . . . . 23
4.5 TSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.6 TCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.7 FC-TCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.8 TSC-TCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.9 General control scheme of SVG for SVC . . . . . . . . . . . . . . . . 25
4.10 V-I characteristic of SVC . . . . . . . . . . . . . . . . . . . . . . . . 26
4.11 Equal area criterion to illustrate the transient stability margin for a
simple two machine system without and with mid point compensation 27
4.12 Basic TCSC block . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.13 Impedance vs. delay angle α characteristic of TCSC . . . . . . . . . 29
4.14 Illustration of capacitor voltage reversal by TCR . . . . . . . . . . . 30
4.15 Idealized TCSC compensating voltage waveform . . . . . . . . . . . 30
vi

4.16 Machine system with a series capacitor and associated phasor diagram 31
4.17 Machine system with synchronous voltage source replacing the series
capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.18 Effect of series FACTS devices on transient stability . . . . . . . . . . 32
A.1 WSCC 3 generator, 9 bus system . . . . . . . . . . . . . . . . . . . . 36
A.2 Load ﬂow results of WSCC - 3 machine 9 bus system . . . . . . . . . 37
A.3 WSCC machine data . . . . . . . . . . . . . . . . . . . . . . . . . . 37
A.4 WSCC exiter data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
A.5 Ybus data for network shown in ﬁgure A.1 . . . . . . . . . . . . . . . 37

List of Tables
3.1 Equal area criterion of the stability for different disturbances . . . . . 15
3.2 Equal area criterion of the stability for different disturbances . . . . . 16
viii

ABBREVIATION
CMC - Current Mode Control
DC - Direct Current
DCM - Discontinuous Conduction Mode
DCR - Direct Current Resistance
ESL - Equivalent Series Inductance
ESR - Equivalent Series Resistance
MOSFET - Metal Oxide Semiconductor Field Effect Transistor
PWM - Pulse Width Modulation
SMPS - Switch Mode Power Supply
SRBC - Synchronous Rectiﬁer Buck Converter
VMC - Voltage Mode Control
ix

CHAPTER 1
INTRODUCTION
1.1 Overview
Power systems generally consist of three stages: generation, transmission, and distri-
bution. In the ﬁrst stage, generation, the electric power is generated mostly by using
synchronous generators. Then the voltage level is raised by transformers before the
power is transmitted in order to reduce the line currents which consequently reduce
the power transmission losses. After the transmission, the voltage is stepped down
using transformers in order to be distributed accordingly.
Power systems are designed to provide continuous power supply that maintains
voltage stability. However, due to undesired events, such as lightning, accidents or any
other unpredictable events, short circuits between the phase wires of the transmission
lines or between a phase wire and the ground which may occur is called a fault. Due
to occurring of a fault, one or more generators may be severely disturbed causing an
imbalance between generation and demand. If the fault persists and is not cleared in
a pre-speciﬁed time frame, it may cause severe damages to the equipments which in
turn may lead to a power loss and power outage. Therefore, protective equipments are
installed to detect faults and clear/isolate faulted parts of the power system as quickly
as possible before the fault energy is propagated to the rest of the system.
1

CHAPTER 1. Introduction 1.1. Overview
1.1.1 Power system stability problem
Transient stability analysis is one of the important part of understanding the system
behaviour during sudden disturbances (small or large). It is defined as that property of
a power system that enables it to remain in a state of operating equilibrium under nor-
mal operating conditions and to regain an acceptable state of equilibrium after being
subjected to a disturbance. Instability of power system can occur in many different
situations depending on the system configuration and operating mode. One of the sta-
bility problems is maintaining synchronous operation or synchronism especially that
power system rely on synchronous machines.
This aspect is influenced by the dynamic of generator rotor angles and power-angle
relationships. Other instability problem that may be encountered is voltage collapse
that is mostly related to load behaviour and not synchronous speed of generators. Var-
ious types of FACTS controller can be used to overcome transient stability problem.
1.1.2 Forms of power system instability
There are three different forms of power system instability: rotor angle instability,
frequency instability and voltage instability. Rotor angle stability is the ability of
interconnected synchronous machines of a power system to remain in synchronism.
Voltage stability is the ability of a power system to maintain acceptable voltages at
all buses in the system under normal operating conditions and after being subjected
to a disturbance. It refers to the ability of the power system to maintain steady fre-
quency following a severe system upset resulting in a significant imbalance between
generation and load. Long-term stability is associated with the slower and longer-
duration phenomena that accompany large-scale system upsets and on the resulting
large, and sustained mismatches between generation and consumption of active and
reactive power. In mid-term stability, the focus is on synchronizing power oscilla-
tions between machines, including the effects of some of the slower phenomena and
possibly large voltage or frequency excursions.
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CHAPTER 1. Introduction 1.1. Overview
Figure 1.1: Classification of power system stability
1.1.3 Classification of stability
Figure 1.1 provides a comprehensive categorization of power system stability. As
depicted by Figure 1.1, there are three main classes of stability: angle stability, fre-
quency stability and voltage stability. Angle stability has two main subclasses: small-
signal (steady-state) stability and transient stability. A power system is considered to
be steady-state stable if, after any small disturbance, it reaches a steady state operat-
ing condition which is identical or close to the pre-disturbance operating condition. A
power system is transient stable for a large disturbance or sequence of disturbances if,
following that disturbance(s) it reaches an acceptable steady-state operating condition.
Unlike steady-state stability which is a function only of the operating condition, tran-
sient stability is more complicated since it is a function of both operating condition
and the disturbance . Voltage stability also has two main subclasses: large disturbance
voltage stability and small-disturbance voltage stability.
For transient stability, it is usually when the power system experiences a large
disturbance caused by an imbalance between the mechanical input and the electrical
output powers. In order to study this type of stability, the focus is only on the first
swing periodic drift. Therefore, only a fraction of a second is enough to observe the
PDPU, Gandhinagar 3

CHAPTER 1. Introduction 1.2. Literature review
transients and several simulation time seconds to study the system. As of the small-
signal stability, it occurs when the system lacks synchronizing torque or when an
unstable control action occurs. This type of stability requires a study of more than a
minute to several hours.
1.2 Literature review
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CHAPTER 2
POWER SYSTEM STABILITY
2.1 Basic concepts and deﬁnitions
Successful operation of power system depends largely on the ability to provide reliable
and uninterrupted service to the load. Ideally, the load must be fed at constant voltage
and frequency within certain permissble limits at all times. The stability problem
is concerned with the behaviour of the synchronous machine after they have been
perturbed. All interconnected synchronous machines should remain in synchronism if
the system is stable.
``Power system stability is the ability of an electric power system, for a given
initial operating condition, to regain a state of operating equilibrium after being sub-
jected to a physical disturbance, with most system variables bounded so that practi-
cally the entire system remains intact.´´ [2]
Figure 1.1 gives the overall picture of the power system stability problem, by iden-
tifying its categories and subcategories. [1] Discription of the corresponding forms of
stability are as follow.
2.1.1 Rotor Angle Stability
It refers to the ability of the synchronous machine of an interconnected power system
to remain in synchronous after being subjected to a disturbance. It depends on the
ability to maintain equilibrium between electromagnetic torque and mechanical torque
of each synchronous machine in the system. Instability can be explained as increasing
5

CHAPTER 2. Power system stability 2.1. Basic concepts and definitions
angular swings of some generators leading to their loss of synchronism with other
generators. Rotor angle stability can be divided into two types,
1. Small disturbance rotor angle stability : is concerned with the ability of the
power system to maintain synchronism under small disturbances.
2. Large disturbance rotor angle stability or transinet stability : is concerned
with the ability of the power system to maintain synchronism under severe dis-
turbances such as short circuit on a transmission line. The time frame of interest
of the transient stability studies is usually 3 to 5 seconds following the distur-
bances. It may extend to 10 - 20 seconds for very large systems with dominent
inter-area swings.
2.1.2 Frequency stability
It refers to the ability of the power system to maintain steady frequency following a
severe system upset resulting in a significant imbalance between generation and load.
Severe system upsets generally result in large excursion of frequency, power flows,
voltages and other system variables. Frequency stability can be explained based on
the short-term and long-term phenomenon.
A short term frequency instability is the formation of the under generated island
with insufficient under frequency load shedding such that frequency decays rapidly
causing blackout of the island within a few seconds. Long term frequency instability
is caused by steam turbine over speed controls or boiler protection with the time frame
ranging from tens of seconds to several minutes.
2.1.3 Voltage stability
It refers to the ability of the power system to maintain steady voltages at all buses
in the system after being subjected to a disturbance from a given initial operating
condition. A possible outcome of the voltage instability is loss of load in an area,
or tripping of the transmission lines and other elements by their protective systems
PDPU, Gandhinagar 6

CHAPTER 2. Power system stability 2.2. Dynamics of synchronous machine
leading to cascading outages. Voltage stability problem can be classified based on the
severity of the disturbance.
• Small disturbance voltage stability : Refers to the system’s ability to main-
tain steady voltages when subjected to small perturbations such as incremental
changes in system load. This stability is influenced by the characteristics of load
, continuous controls and discrete control at a given instant of time.
• Large disturbance voltage stability : refers to the system’s ability to maintain
steady voltages when subjected to large disturbances such as system faults, loss
of generations or circuit contingencies. Determination of large disturbance volt-
age stability requires the examinations of the nonlinear response of the power
system over a period of time sufficient to capture the performance and interac-
tions of such devices as motors, under-load transformer tap changers and gen-
erator field current limiters. The study period of the interest varies from a few
seconds to tens of minutes.
2.2 Dynamics of synchronous machine
The kinetic energy of the rotor at synchronous machine is,
KE =
1
2
J ω2
sm ×10−6
MJ (2.1)
J = rotor moment of inertia in kg.m2 , ωsm = synchronous speed in rad (mech)/s
But,ωs = rotor speed in rad (elect)/s, P = No. of machine poles
ωs = (
P
2
)ωsm (2.2)
From equation 2.1 and 2.2, KE = 1
2 M ωs
Where,M = moment of inertia in MJ-s / elect rad
M = J (
2
P
)2
ωs ×10−6
(2.3)
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Now, deﬁning inertia constant H such that,
GH = KE =
1
2
M ωs MJ
Where, G = Machine rating (base) in MVA (three phase)
H = Inertia constant in MJ/MVA or MW.s/MVA
so, It follows that,
M =
2GH
ωs
=
GH
π f
[MJ.s/rad(elect)] =
GH
180f
[MJ.s/degree(elect)] (2.4)
M is also called as inertia constant.
Taking G as base, the inertia constant in pu is,
M(pu) =
H
π f
[s2
/rad(elect)] =
H
180f
[s2
/degree(elect)] (2.5)
The inertia constant H has the range of the values for each class of machine. i.e.
The values of H is considerably higher for steam turbogenerators than for water wheel
generators. 30-60 % of the total inertia of a steam turbogenerator unit is that of the
primemover, whereas only 4-15% of the inertia of a hydroelectric generating unit is
that of the waterwheel including water.
The swing equation Figure 2.1 shows the torque, speed and ﬂow of mechanical
and electrical powers in a synchronous machine. [1] It is assumed that the windage,
friciton and iron loss torque is negligible.
Figure 2.1: Flow of mechanical and electrical powers in a synchronous machine
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The differential equation governing the rotor dynamics can be written as,
J
d2θm
dt2
= Tm −Te [Nm] (2.6)
Where, θm = angle in rad (mech),
Tm = turbine torque in Nm; it acquires a negative value for a motoring machine
Te = electromagnetic torque developed in Nm; negative value for a motoring machine
While the rotor undergoes dynamics as per eq. 2.6, the rotor speed changes by
insigniﬁcant magnitude for the time period of interest. Equation 2.6 can therefore be
converted into its more convenient power form by assuming the rotor speed to remain
constant at the synchronous speed (ωsm). Multiplying bith the sides of eq. 2.6 by ωsm,
J ωsm
d2θm
dt2
×10−6
= Pm −Pe [MW] (2.7)
Where, Pm = mechanical power input in MW
Pe = electrical power input in MW; stator copper loss is assumed negligible
Rewriting eq. 2.7,
(J (
2
P
)2 ωs ×10−6)d2θe
dt2 = Pm −Pe [MW]
Where, θe = angle in rad (elect)
M
d2θe
dt2
= Pm −Pe[MW] (2.8)
It is more convenient to measure the angular position of the rotor with respect to a
synchronously rotating frame of reference. Let,
δ = θe −ωst (2.9)
Rotor angular displacement from synchronously rotating reference frame called torque
angle / power angle. From eq. 2.9, d2θe
dt2 = d2δ
dt2
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Hence, eq. 2.8 can be written in terms of δ as,
M
d2δ
dt2
= Pm −Pe[MW] (2.10)
With M as deﬁned in eq. 2.10, we can write
GH
π f
d2δ
dt2
= Pm −Pe[MW] (2.11)
Dividing throughout by G, the MVA rating of the machine,
M(pu)
d2δ
dt2
= Pm −Pe[MW]
where, M(pu) =
H
π f
,
or,
H
π f
d2δ
dt2
= Pm −Pe[MW] (2.12)
Equation 2.12 is called as swing equation and it describes the rotor dynamics for
synchronous machines. It is second order differential equation where the damping
term (proportional to dδ
dt ) is absent because of the assumption of a lossless machine
and a fact that the torque of damper winding has been ignored. This assumption leads
to pessimistic results in transient stability analysis - damping helps to stabilise the
system.
For multi machine system Machine inertia constant in system base is given by,
Hsystem = Hmachine
Gmachine
Gsystem
(2.13)
Where, Gmachine = machine rating (base), Gsystem = system base.
If machine swinging coherently Two machine swinging coherently are thus reduced
to a single machine. so, equivalent inertia can be written as,
Hequivalent = (H1machine
G1machine
Gsystem
)+(H2machine
G2machine
Gsystem
) (2.14)
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CHAPTER 2. Power system stability 2.3. Power angle curve
The above results are easily extandable to any number of machine swinging coher-
ently. For the solution of swing equation, certain simplifying assumptions are made.
These are:
• Mecanical power input to the machine remains constant during the transient
stability analysis period. It means that the effect of the turbine governing loop
is ignored.
• Rotor speed changes are insignificant.
• Effect of the voltage regulating loop during the transient is ignored as a conse-
quence the generated machine emf remains constant.
2.3 Power angle curve
For the purpose of the stability studies, transient emf of generator / motor remains
constant or it is an independent variable determine by voltage controlling loop but the
generator terminal voltage is dependent variable. Therefore, the buses of the stability
study network, pertain to the emf terminal in the machine model shown in figure, while
the machine reactance is absorbed in the system. Further the loads will be replaced
by equivalent static admittances. This is because load voltage varies during stability
studies.
Figure 2.2: Simplified machine
model
Figure 2.3: Two bus stability
study network
For a two bus system of figure ??

CHAPTER 3
TRANSIENT STABILITY
3.1 Introduction
The swing equation describes the rotational dynamics of a synchronous machine and
is used in stability analysis to characterize that dynamic. During normal operation, the
relative position of the rotor axis and the resultant axis is ﬁxed. During disturbance to
the machine, the rotor either accelerates or decelerates with respect to the synchronous
rotating air gap MMF. The swing equation describes this relation as follow.
M
d2δ
dt2
= Pm −Pe = Pm −Pmax sinδ [MW] (3.1)
No generalized criteria are available for determining system stability with large dis-
turbances (called transient stability). But, stability with large disturbance can be un-
derstood using equal area criterion.
3.2 Equal Area Criterion
In a system where one machine is swinging with respect to an inﬁnite bus, it is possible
to study transient stability by means of a simple criterion, without resorting to the
numerical solution of a swing equation.
Consider the swing equation,
d2δ
dt2
=
1
M
(Pm −Pe) =
Pa
M
; Pa = accelerating power (3.2)
12

CHAPTER 3. Transient stability 3.2. Equal Area Criterion
Where, M = H
π f in pu system
lf the system is unstable δ continues to increase indefinitely with time and the ma-
chine loses synchronism. on the other hand, if the system is stable, δ(t) performs
oscillations (nonsinusoidal) whose amplitude decreases in actual practice because of
damping terms (not included in the swing equation). These two situations are shown
in figure 3.1. [1]
Response δ(t) in a power system generally falls in two categories as shown in
figure. It can be visualized now that for a stable system, indication of stability is given
by the observation of the first swing where δ will go to a maximum and will start to
reduce. This fact can be stated as a stability criterion, that, (for a sufficiently long
time.)
the system is stable if at some time,
dδ
dt = 0
and is unstable if,
dδ
dt > 0
Figure 3.1: Plot of δ vs. t for stable and
unstable system
Figure 3.2: Rotor angle response for tran-
sient disturbance
Figure 3.2 illustrates the behaviour of a synchronous machine for stable and un-
stable situations. In Case 1, the rotor angle increases to a maximum, then decreases
and oscillates with decreasing amplitude until it reaches a steady state. This case is
considered transient stable. In Case 2, the rotor angle continues to increase steadily
until synchronism is lost. This type on transient instability is referred to as first swing
instability. In Case 3, the system is stable in the first swing but becomes unstable as a

result of growing oscillations as the end state is approached. This form of instability
occurs when the post fault steady state condition is itself is small signal unstable.
Stability criterion for single machine inﬁnite bus system Multiplying both sides
of swing equation 3.1 by (2 dδ
dt ) and integrating, we have
dδ
dt
= (
2
M
δ
δ0
Pa dδ)
1
2 (3.3)
where δ0 is the initial rotor angle before it begins to swing due to disturbance. So,
from stability condition and eq. 3.3, the condition for the stability can be written as,
δ
δ0
Pa dδ = 0 (3.4)
The condition for the stability can be stated as: The system is stable if the area
under Pa (accelerating power) - δ curve reduces to zero at some value of δ. In other
world, the positive (accelerating) area under Pa −δ curve must equal the negative (de-
celerating) area and hence the name equal area criterion of the stability.
In transient stability studies, the study period of interest is usually limited to 3 to
5 seconds following the disturbance, although it may extend to about 10 seconds for
very large systems with dominant inter area modes of oscillation. To illustrate the
equal area criterion of the stability, we now consider several types of disturbance that
may occur in a single machine inﬁnite bus bar system.

TypeofdisturbanceExplanation
•Increaseinmechanicalpowerinput
•A1=δ1
δ0
(Pm1−Pe)dδ;•A2=δ2
δ1
(Pe−Pm1)dδ
•Forstablesystem,A1=A2.
•δ2=δmax=π−δ1=π−sin−1
(
Pm1
Pmax
)
•Effectofclearingtimeonstability
•A1=Pm(δcr−δ0)
•A2=Pmax(cosδcr−cosδmax)−Pm(δmax−δcr)
•Forstablesystem,A1=A2.
•cosδcr=
Pm
Pmax
(δmax−δ0)+cosδcr
•tcr=
2H(δcr−δ0)
πfPm
Table3.1:Equalareacriterionofthestabilityfordifferentdisturbances

TypeofdisturbanceExplanation
•Suddenlossofoneoftheparallelline
Poweranglecurve,
•Beforeswitchingoff,
Pe1=(
|E||V|
Xd+X1||X2
sinδ)=Pmax1sinδ
•Afterswitchingofftransmissionline2,
Pe2=(
|E||V|
Xd+X1
sinδ)=Pmax2sinδ
•Forstability,δmax=δ1=π−δc
Table3.2:Equalareacriterionofthestabilityfordifferentdisturbances

CHAPTER 4
FACTS CONTROLLER
FACTS: Altemating current transmission systerns incorporating power electronic based
and other static controllers to enhance controllability and increase power transfer ca-
pability.
4.1 Introduction
Transmission inter-connections enables taking advantage of diversity of loads, avail-
ability of sources, and fuel price in order to supply electricity to the loads at minimum
cost with a required reliability. Problems associated with power transfer are -
• The power systems of today, large and complex, are mechanically controlled.
when operating signals are sent to the power circuits, where the ﬁnal power
control action is taken, the switching devices are mechanical so control speed is
less.
• In mechanical devices, control cannot be initiated frequently, because these me-
chanical devices tend to wear out very quickly compared to static devices.
In effect, from the point of view of dynamic and steady-state operation, the system is
really uncontrolled. Increased demands on transmission lines in absence of long-term
planning and the need to provide open access to generating companies and customers,
all together have created tendencies toward less security and reduced quality of supply.
The FACTS technology is essential to alleviate some of these difﬁculties by enabling
17

CHAPTER 4. FACTS Controller 4.1. Introduction
utilities to get the most service from their transmission facilities and enhance grid
reliability.
FACTS controller can be used to control the interrelated parameters that govern
the operation of transmission systems including series impedance, shunt impedance,
current, voltage, phase angle, and the damping of oscillations at various frequencies
below the rated frequency.
The FACTS technology is not a single high-power Controller, but rather a collec-
tion of Controllers, which can be applied individually or in coordination with others
to control one or more of the interrelated system parameters.
Transmission capability of line is limited by different stability mimits like Tran-
sient stability, Dynamic stability, Steady-state stability, Frequency collapse, Voltage
collapse, Sub-synchronous resonance. The FACTS technology can certainly be used
to overcome any of the stability limits, in which case the ultimate limits would be
thermal and dielectric.
4.1.1 Advantages of FACTS
• Controlled power flow in transmission lines.
• Increased loading capability of lines to their thermal capability limits.
• Increase the system security through raising the transient stability limit
• Provide secure tie line connections to neighbouring utilities and regions thereby
decreasing overall generation reserve requirements on both sides.
• Provide greater flexibility in sitting new generation.
• Upgrade of lines.
• Reduce reactive power flows, thus allowing the lines to carry more active power.
• Reduce loop flows.
• Increase utilization of lowest cost generation.

CHAPTER 4. FACTS Controller 4.2. Types of FACTS controller
4.2 Types of FACTS controller
Figure 4.1(a) shows the general symbol for a FACTS Controller : a thyristor ar-
row inside a box. FACTS controller can be classified into four different types as per
its connections with the power system networks. Figure 4.1(b) indicates the series
controllers while figure 4.1(c) gives idea about shunt controller connections. Combi-
nation of series - series and series - shunt FACTS devices could be used.
Figure 4.1: Types of controller
Shunt FACTS devices
The shunt controller may be variable impedance, variable source or a combination of
these. In principle, all shunt controller inject current into the system at the point of
connections. Even a variable shunt impedance connected to line voltage causes a vari-
able current flow and hence represents injection of the current into the line. As long
as the injected current is in phase quadrature with the line voltage, shunt controller
only supplies or consumes variable reactive power. Any other phase relationship will
involve handling of real power as well.
Objective of shunt compensation
It has long been recognized that the steady-state transmittable power can be increased
and the voltage profile along the line controlled by appropriate reactive shunt compen-

sation. The purpose of, this reactive compensation is to change the natural electrical
characteristics of the transmission line to make it more compatible with the prevailing
load demand. Thus, shunt connected switched reactors are applied to minimize line
over voltage under light load conditions, and shunt connected switched capacitors are
applied to maintain voltage levels under heavy load conditions.
The ultimate objective of applying reactive shunt compensation in a transmission
system is to increase the transmittable power. This may be required to improve the
steady-state transmission characteristics as well as the stability of the system. Var
compensation is thus used for voltage regulation at the midpoint to segment the trans-
mission line and at the end of the line to prevent voltage instability, as well as for
dynamic voltage control to increase transient stability and damp power oscillations.
4.2.1 Switching Converter Type Var Generator: STATCOM
Static Var generators generate or absorb controllable reactive power by synchronously
switching capacitor and reactor banks ‘in’and ‘out ’of the network. The aim of this
approach is to produce a variable reactive shunt impedance that can be adjusted to
meet the compensation requirements of the transmission network.
The possibility of generating controllable reactive power directly, without the use
of ac capacitors or reactors, by various switching power converters was invented.
These (dc to ac or ac to ac) converters are operated as voltage and current sources
and they produce reactive power essentially without reactive energy storage compo-
nents by circulating alternating current among the phases of the ac system. Function-
ally, from the standpoint of reactive power generation, their operation is similar to
that of an ideal synchronous machine whose reactive power output is varied by exci-
tation control. Like the mechanically powered machine, they can also exchange real
power with the ac system if supplied from an appropriate, usually dc energy source.
Because of these similarities with a rotating synchronous generator, they are termed
Static Synchronous Generators. When an SSG is operated without an energy source,
and with appropriate controls to function as a shunt-connected reactive compensator, it

is termed, analogously to the rotating synchronous compensator, a Static Synchronous
Compensator or STATCOM.
Basic operating principle of STATCOM
Figure 4.2: STATCOM.
The basic principle of reactive power generation
by a voltage-sourced converter can be understood
by ﬁgure 4.2. The reactive current I drawn by
the synchronous compensator is determined by
the magnitude of the system voltageV, converter
output voltage V0, and the total circuit reactance
X. Therefore,
I =
V −E
X
(4.1)
And the corresponding reactive power Q ex-
changed can be expressed as follows,
Q =
1−
E
V
X
∗V2
(4.2)
The three-phase output voltage is generated by a voltage-sourced dc to ac converter
operated from an energy storage capacitor. From a dc input voltage source, provided
by the charged capacitor C5, the converter produces a set of controllable three-phase
output voltages with the frequency of the ac power system. Each output voltage is in
phase with, and coupled to the corresponding ac system voltage via a relatively small
(0.1-0.15 p.u.) tie reactance.
By varying the amplitude of the output voltages produced, the reactive power ex-
change between the converter and the ac system can be controlled in a manner similar
to that of the rotating synchronous machine. That is, if the amplitude of the out-
put voltage is increased above that of the ac system voltage, then the current ﬂows
through the tie reactance from the converter to the ac system, and the converter gen-
erates reactive (capacitive) power for the ac system. If the amplitude of the output

voltage is decreased below that of the ac system, then the reactive current flows from
the ac system to the converter, and the converter absorbs reactive (inductive) power.
If the amplitude of the output voltage is equal to that of the ac system voltage, the
reactive power exchange is zero.
General control scheme
Static Synchronous Compensator (STATCOM) are Static Var Generators, whose out-
put is varied so as to maintain or control specific parameters of the electric power
system. There is basic external control structure that defines the functional opera-
tion of the compensator, and to this end derives the necessary reference inputs for
the Var generator, is substantially the same, independent of the type of Var generator
used. A general control scheme, converting a static Var generator (either a controlled
impedance type or a converter based type) into a transmission line compensator, is
shown in Figure 4.3.
Figure 4.3: General control scheme of Static Var Generator
The power system, at the terminal of the compensator, is represented by a gener-
ator with a generally varying rotor angle, internal voltage u, and source impedance Z
that is a function of the angular frequency or and time t. The terminal voltage Vt of

the power system can be characterized by a generally varying amplitude and angular
frequency ω.
The output of the static Var generator is controlled so that the amplitude I, of the
reactive current, drawn from the power system follows the current reference IQref .
With the basic static compensator control, the amplitude Vt of the terminal voltage
is measured and compared with the voltage reference VRef ; the error δVt is processed
and amplified by a PI (proportional integral) controller to provide the current reference
IQref for the Var generator. In other words, I0 is closed-loop controlled via IQref so
that Vt is maintained precisely at the level of the reference voltage VRef in face of
power system and load changes.
If the proper compensation of the ac power system requires some specific variation
in the amplitude of the terminal voltage with time or some other variable, then an
appropriate correcting signal VRc derived from the auxiliary inputs, is summed to the
fixed reference V∗
Ref in order to obtain the desired effective reference signal V∗
Ref that
closed-loop controls the terminal voltage.
V-I characteristic of STATCOM
Figure 4.4: V-I chara. of STATCOM
A typical terminal voltage versus output
current characteristic of a static compen-
sator with a specific slope is shown in
Figure ??, together with particular load
lines of the ac system. Load line 1 inter-
sects the compensator V-I characteristic
at the nominal voltage, thus the output
current of the compensator is zero. Load
line 2 is below load line 1 due to a de-
crease in the power system voltage. Its intersection with the compensator V-l charac-
teristic calls for the capacitive compensating current lc. Load line 3 is above load line
1 due to an increase in the power system voltage. Its intersection with the compensator

V-I characteristic defines the inductive compensating current IL.
4.2.2 Controlled Variable impedance type Var generator: SVC
All of the different semiconductor power circuits, with their internal control enabling
them to produce Var output proportional to an input reference, are collectively termed
as static Var generators (SVC). Thus, a static Var compensator (SVC) is, a static Var
generator whose output is varied so as to maintain or control specific parameters of
the electric power system. The static Var generator is a self-sufficiently functioning
device that draws controllable reactive current from an alternating power source.
The control input to the Var generator can be an arbitrary reactive current, impedance,
or power reference signal that the SVG is to establish at its output. Thus, the static Var
generator can be viewed as a power amplifier that faithfully reproduces the reference
signal at the desired power level. Consequently, a static Var generator becomes a static
Var compensator when it is equipped with special external controls which derive the
necessary reference for its input, from the operating requirements and prevailing vari-
ables of the power system, to execute the desired compensation of the transmission
line.
Examples of variable impedance type static Var generator
Figure 4.5: TSC
Figure 4.6: TCR

Figure 4.7: FC-TCR Figure 4.8: TSC-TCR
Basic operating principle and control scheme
Static Var generator of a controlled reactive impedance type, employing thyristor-
controlled and switched reactors and capacitors. Although the operating principles of
these different Var generators are disparate and their V-I and loss versus Var output
characteristics, as well as their speed of response and attainable frequency bandwidth,
are quite different, they all can provide the controllable reactive shunt compensation,
exhibiting similar overall functional capabilities within their linear operating range.
This means that the basic external control structure that deﬁnes the functional opera-
tion of the compensator, and to this end derives the necessary reference inputs for the
Var generator, is substantially the same independent of the type of Var generator used.
Figure 4.9: General control scheme of SVG for SVC

V-I characteristic of SVC:
Figure 4.10: V-I characteristic of SVC
The V-I characteristic of SVC is pretty much similar to STATCOM but the main
difference is that outside of the linear operating range the STATCOM and SVC act
differently. The dynamic performance of two types of compensator is also different.
4.2.3 Effect of shunt FACTS devices on transient stability
Reactive shunt compensation can significantly increase the maximum transmittable
power. So with suitable and fast controls, shunt compensation will be able to change
the power flow in the system during and following dynamic disturbances so as to
increase the transient stability limit and provide effective power oscillation damping.
Here are the real and reactive power flow equations for the case of ideal midpoint
shunt compensation. It can be observed that it can significantly increase the trans-
mittable power at the expense of rapidly increasing reactive power demand on the
midpoint compensator.
P = 2×
V2
X
×sin
δ
2
(4.3)
Q = V ×I ×sin
δ
4
=
4V2
X
(1−cos
δ
2
) (4.4)
To understand the concept of stability margin the equal area criterion of compensated

and uncompensated system is applied here and for the analysis both system are sub-
jected to same fault for the same amount of time and dynamic behaviour of system is
illustrated in figure 4.11.
Figure 4.11: Equal area criterion to illustrate the transient stability margin for a simple
two machine system without and with mid point compensation
By seeing this we can say that The areas between the P versus δ curve and the
constant Pm line over the intervals defined by angles 3 and δcrit, and p3 and pcrit re-
spectively, determine the margin of transient stability, that is, the `ùnused´ánd still
available decelerating energy, represented by areas Amargin and Apmargin.
Comparison of Figures 4.11 clearly shows a substantial increase in the transient
stability margin the ideal midpoint compensation with unconstrained Var output can
provide by the effective segmentation of the transmission line. Alternatively, if the
uncompensated system has a sufficient transient stability margin, shunt compensation
can considerably increase the transmittable power without decreasing this margin.
Series FACTS devices
Actual power transmission depends on series line impedance and angle between two
end transmission line voltages. so, power transmitted in long lines is limited by series
reactive impedance. To improve power transfer capability of transmission line variable
line impedance is needed and that can be achieved using series FACTS devices. Series
FACTS devices are used to control power flow, to minimize the receiving end voltage

variation and to stabilize the system.
Concept of series capacitive compensation
The basic idea behind series capacitive compensation is to decrease the overall effec-
tive series transmission impedance from the sending end to the receiving end. The ef-
fective transmission impedance Xef f with the series capacitive compensation is given
by:
Xef f = X −Xc = (1−K)X (4.5)
K is degree of series compensation. K =
Xc
X
; 0 ≤ K ≤ 1. Four types of series com-
pensation are af follow. 1. GTO Thyristor Controller Series Capacitor ( GCSC ), 2.
Thyristor Switched Series Capacitor ( TSSC ), 3. Thyristor Controlled Series Capaci-
tor ( TCSC ), 4. Static Synchronous Series Compensator ( SSSC ).
4.2.4 Thyristor Controlled Series Capacitor ( TCSC )
This method is also known as ‘rapid adjustment of network impedance’. The basic
unit of TSCS consists of the series compensating capacitor shunted by a Thyristor-
controlled Reactor. In a practical TCSC implementation, several such basic compen-
sators may be connected in series to obtain the desired voltage rating and operating
characteristics. The steady state impedance of the TSCS is that of a parallel LC circuit,
Figure 4.12: Basic TCSC block
XTCSC(α) =
XCXL(α)
XL(α)−XC
(4.6)
Where, XL = ωL and α is the delay
angle measured from the crest of the ca-
pacitor voltage. So,
XL(α) = XL
π
π −2α −sinα
;XL ≤ XL(α) ≤ ∞ (4.7)
The TCSC thus presents a tunable parallel LC circuit to the line current that is sub-

stantially a constant alternating current source. As the impedance of the controlled
reactor,XL(α) is varied from its maximum (infinity) toward its minimum (ωL), the
TCSC increases its minimum capacitive impedance,XTCSCmin = XC = 1
ωC , (and there by
the degree of series capacitive compensation) until parallel resonance at XC: XL(α)is
established and theoretically XTCSCmax becomes infinite. Decreasing XL(α)further, the
impedance of the TCSC, XTCSC(α) becomes inductive, reaching its minimum value
of XLXC
(XL−Xc) at α = 0, where the capacitor is in effect bypassed by the TCR.
Figure 4.13: Impedance vs. delay angle α characteristic of TCSC
Actual operation of TCSC
For deeper insight into TCSC, lets assume thyristor valve sw is initially opened line
current I producing voltageVco across the capacitor, as shown in figure 4.14(a). Suppose
that the TCR is to be turned on at α, measured from the negative peak of the capacitor
voltage. At that instant, capacitor voltage is negative and line current is positive, thus

Figure 4.14: Illustration of capacitor voltage reversal by TCR
capacitor will get charged in positive direction and thyristor valve can be seen as an
ideal switch, closing at α, in series with diode, as shown in ﬁgure 4.14(b).
Figure 4.15: Idealized TCSC compensat-
ing voltage waveform
At closing, charge of capacitor will
be reversed during half-cycle of LC cir-
cuit formed and this resonant charge
reversal produces a dc offset for next
positive half cycle as shown in ﬁgure
4.14(c).
So, the reversal of capacitor volt-
age is key to control of the TCSC.
Thus, steady-state compensating voltage
across series capacitor comprises an un-
controlled and a controlled component.
The uncontrolled component VCO, a sine
wave whose amplitude proportional to line current, and the controlled component is
VCTCR.
4.2.5 Static Synchronous Series Compensator (SSSC)
The basic operating principles of the SSSC can be explained with reference to the
conventional series capacitive compensation. Here, at given line current, the voltage
across the series capacitors forces the opposite polarity voltage across the series line
reactance to increase by the magnitude of the capacitor voltage.

Figure 4.16: Machine system with a series capacitor and associated phasor diagram
Thus, the series capacitive compensation works by increasing the voltage across
the impedance of the line, which lead to increase in line current and transmitted power.
Figure 4.17: Machine system with synchronous voltage source replacing the series
capacitor
So, it follows that the same steady-state power transmission can be established if
the series compensation is provided by synchronous ac voltage source, whose output
precisely matches the voltage of the series capacitor.
Here, Vq = Vc = −j(XcI) = −j(K X I) , where Vc is injected voltage, I is the line
current, Xc is the reactance of the series capacitor, X is line reactance, K is the degree
of compensation.
4.2.6 Effect of series FACTS devices on transient stability
Considering two identical systems, with and without series capacitive compensation,
transmits the same powerPm as shown in ﬁgure 4.18. Both are subjected to same
fault for same time duration. The sending end generator accelerates from steady state
anglesδ1 and δs1 to angles δ2 and δs2 respectively.
After fault clearing, the transmitted electric power exceeds the mechanical input
and therefore sending end machine decelerates and areas are shown in ﬁgure 4.18.

Figure 4.18: Effect of series FACTS devices on transient stability
Time interval deﬁned by angles δ3 , δcrit , δs3 and δscrit , respectively , determines the
margin of transient stability.
It clearly shows an increase in the transient stability margin by partial cancellation
of the series impedance of line. So, the increase of transient stability is proportional
to the degree of series compensation.

CHAPTER 6
FUTURE WORK
Following are the areas of future work.
• Hardware implementation of the Buck converter circuit.
• To study and implementation of voltage control mode of converter.
• Optimization of whole model of converter.
• Testing and calibration of complete hardware of buck converter to conﬁrm the
actual response with theoretical answers.
34

CHAPTER 7
CONCLUSION
Designing a voltage-mode controlled buck converter is very challenging. So far the
most difﬁcult part was to determine the simulation for the feedback loop network. The
PWM is a relatively simple concept, but a real world design of this block would be
troublesome. Design and simulation of the circuit is done using PID controller through
MATLAB. Unfortunately auto tuning of PID controller in MATLAB Simulink was not
possible because of some errors. Current values are selected by trial and error method.
Improvement in the response of the converters through the use of a feedback path with
proper controller gain has been achieved by doing the same. Voltage mode control
of buck converter is simulated using powersim and buck converter circuit hardware
implemented. While doing hardware implementation of open loop buck converter,
results are not as per expectation due to failure in gate triggering of MOSFET.
35

Appendix A
WSCC SYSTEM
We have considered western system coordinating council (WSCC) 3 machine, 9 bus
system shown in figure A.1. The base MVA is 100MVA and frequency is 60 HZ. The
Figure A.1: WSCC 3 generator, 9 bus system
machine data and exciter data is given in figure A.3 and figure A.4. The exciter is
assumed to be identical for all machines and is of the IEEE-Type I. Define 2Hi
Ws
∼= Mi.
Assume that D1
M1
= 0.1, D2
M2
= 0.2, and D3
M3
= 0.3 (All in pu).
36

Appendix A. WSCC system
Figure A.2: Load ﬂow results of WSCC - 3 machine 9 bus system
Figure A.3: WSCC machine data Figure A.4: WSCC exiter data
Figure A.5: Ybus data for network shown in ﬁgure A.1

Bibliography
[1] D P Kothari, I J Nagrath. Modern power system analysis. Fourth edition, Tata
McGraw Hill Education pvt. Ltd., New delhi. ISBN : 987-0-07-107775-0, 2012.
[2] P. Kundur Power system stability and control. Tata McGraw Hill Education Pvt.
Ltd. New Delhi - India. 987-0-07-063515-9, 2012.
[3] Hingorani, Narain G. Understanding FACTS : Concepts and Technology of ﬂexible
AC transmission systems. IEEE Inc. New York. ISBN 978-81-265-3040-3. 2015.
38

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