POWER SYSTEM STABILIZER : ANALYSIS & SIMULATIONS Technical Report By Vihang M. Dholakiya (10MEEE05) Devendra P. Parmar (10MEEE07) Under the Guidance of Dr. S. C. Vora DEPARTMENT OF ELECTRICAL ENGINEERING INSTITUTE OF TECHNOLOGY NIRMA UNIVERSITY AHMEDABAD 382 481 MAY 2012
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POWER SYSTEM STABILIZER : ANALYSIS &
SIMULATIONS
Technical Report
By
Vihang M. Dholakiya (10MEEE05)
Devendra P. Parmar (10MEEE07)
Under the Guidance of
Dr. S. C. Vora
DEPARTMENT OF ELECTRICAL ENGINEERING
INSTITUTE OF TECHNOLOGY
NIRMA UNIVERSITY
AHMEDABAD 382 481
MAY 2012
Dedicated To
Mentor
Dr. S. C. Vora
CERTIFICATE
This is to certify that the Technical Report entitled “POWER SYSTEM STA-
BILIZER : ANALYSIS & SIMULATIONS” submitted by Mr. Vihang M.
Dholakiya (10MEEE05) and Mr. Devendra P. Parmar (10MEEE07), is the
record of work carried out by them under my supervision and guidance. The work
submitted has in my opinion reached a level required for being accepted. The results
embodied in this project work to the best of my knowledge are satisfactory.
Date:
Project Guide
Dr. S. C. Vora
Professor
Department of Electrical Engineering
Institute of Technology
Nirma University
Ahmedabad
Acknowledgements
We take this opportunity to express our sincere gratitude to our honorable guide
Dr.S.C.Vora for his invaluable guidance. It would have never been possible for
us to wok on this project without his technical support and continuous encourage-
ment. We consider ourself, extremely fortunate for having chance to work under his
guidance. In spite of his hectic schedule, he was always approachable and spent his
precious time to discuss problems. It has been a very learning and enjoyable experi-
ence to work under him.
We would like to acknowledge Mr. A. Ragaveniran et.al., authors of technical
paper titled as “MATLAB/Simulik-Based Modeling and Operation of Power System
Stabilizer” which provides us initial motivation for doing work in the area of imple-
mentation of power system stabilizer.
We would also like to thank all faculty members of Department of Electrical Engi-
neering, who have helped us during this project work. I wish to express my thanks
to other staff members of Electrical Department as well for their regular help and
co-operation during the project work. We heartily thankful staff member of library
for providing technical recourses for project work.
We would be specially thankful to our dear friend Narendra C. Mahavadia for
providing continuous help and motivational support during entire project work. We
never forget the time that we have spent with him during this tenure.
We are thankfull to our classmates for their invaluable help, suggestions and support
during the project work. We would like to thank all who have directly or indirectly
contributed to this project work.
Finally, We would like to thank The Almighty and express my deep sense of rever-
ence gratitude to our Parents and Family Members who have provided support and
blessings without which we wouldn’t have reached at this stage.
- Vihang M. Dholakiya
- Devendra P. Parmar
i
Abstract
The extensive interconnection of power networks by weak tie-lines can restrict the
steady-state power transfer limits due to low frequency electromechanical oscillations.
The low frequency oscillations may result in interruptions in energy supply due to loss
of synchronism among the system generators and affect operational system economics
and security. Further, in order to maintain steady state and transient stability of syn-
chronous generators, high performance excitation systems are essential. The static
exciters with thyristor controllers are generally used for both hydraulic and thermal
units. Such exciters are characterized by high initial response and increased reliabil-
ity due to advances in thyristor controllers and hence have become one of the major
problems in the power system stability area. As a solution to this, the generators are
equipped with Power System Stabilizers(PSSs) that provide supplementary feedback
stabilizing signals which is added to the Automatic Voltage Regulator (AVR). PSSs
augment the power system stability limit and extend the power transfer capability
by enhancing the system damping of low-frequency oscillations in the order of 0.2 to
3.0 Hz.
The report focuses on small signal performance analysis of Single Machine Infinite
Bus(SMIB) as well as of multimachine power system. The dynamic behaviour of
Haffron-Phillips model of excitation system with typical data is evaluated by devel-
oping MATLAB code for eigenvalue tracking analysis. The effect of implementation
of power system stabilizer to SMIB system has been realized by time domain sim-
ulations. In the later part optimal placement of PSS is decided, because from the
economic point of view and to avoid redundancy, it is desired, not to employ PSS
on individual generators to overcome the problem of power system oscillations. The
eigenvalue analysis of the power system for various areas is used to determine the
inter-area and local mode frequencies and participation of the generators. It is also
important to identify the generator that shall be installed with PSS. A simulation
study on well-adopted test system is carried out, with various possibilities, to deter-
mine the optimal placement of the PSS. The observations of the certain analysis are
helpful in determining the PSS placement and are presented in the report.
B.1 Machine Data of Two Area Test System . . . . . . . . . . . . . . . . 50B.2 Line Data of Two Area Test System . . . . . . . . . . . . . . . . . . . 51B.3 Load Data of Two Area Test System . . . . . . . . . . . . . . . . . . 51B.4 Exciter & PSS Data of Two Area Test System . . . . . . . . . . . . . 51
• S-domain analysis of Kundur’s Two Area System using Power System Analysis
Toolbox(PSAT).
• Primary screening of generators for placement of PSS through participation
factors.
• Time domain simulations of developed Kundur’s Two Area System.
1.4 Scope of Work
The scope of the project work can be broadly outlined as below:
• Realization of Haffron-Philips Model of Excitation System.
• Effect of PSS implementation on behavior of SMIB.
• Eigenvalue analysis of Kundur’s Two Area System in various PSS arrangement.
• Participation factor analysis.
• Response analysis in time domain for Kundur’s Two Area System with typical
different cases.
• Choice of optimal location of PSS based on observations of S-domain analysis
and time-domain simulations.
CHAPTER 1. INTRODUCTION 3
1.5 Outline of Thesis
• Chapter 1 introduces the main problem associated with the low frequency
oscillation damping by optimally placed PSS and the same is considered as the
objective of this work. The project planning and scope of work is also included.
• Chapter 2 gives general background of power system stability. The detail
description of eigenvalue analysis method used for evaluating small signal per-
formance of power system is focused and the other methods are discussed briefly.
• Chapter 3 includes the dynamic analysis of Hafron-Phillips model of excitation
system through eigenvalue tracking method. The effect of implementation of
PSS in SMIB has also been analyzed by performing time domain simulations.
• Chapter 4 discusses about optimal placement of PSS in multimachine power
system. The eigenvalue analysis of for Kundur’s two area system is used to de-
termine the mode of oscillation and participation of the generators. A simulation
study on considered test system is carried out, with various PSS arrangement,
the optimal placement of the PSS is decided.
• Chapter 5 comprises of conclusion and future work.
Chapter 2
Power System Stability
2.1 Background
Modern power system can be characterized by widespread system interconnections.
The interconnected power system is comprised of multiple machines connected by the
transmission network. The supply of reliable and economic electric energy is a major
determinant of industrial progress and consequent rise in the standard of living. In
practical terms this means that both voltage and frequency must be held within allow-
able tolerances so that the consumer’s equipment can operate satisfactorily. Further,
with deregulation of power supply utilities, the power network has become a highway
for transmitting electric power from wherever it is available to places where required,
depending on the pricing that varies with time of the day. In such scenario, the anal-
ysis of dynamic performance and stability of power system has great importance.
The stability problem is concerned with the behavior of the synchronous machines
under perturbed conditions. If the perturbation does not involve any net change in
power, the machines should return to their original state and if an unbalance between
the supply and demand is created by perturbation, a new operating state should be
achieved. When the system changes its operating point from one stable point to the
other,it is mandatory that all interconnected synchronous machines should remain in
synchronism. i.e., they should all remain operating in parallel and at the same speed.
4
CHAPTER 2. POWER SYSTEM STABILITY 5
Thus, Power System Stability may be broadly defined as that property of power
system that enables it to remain in a state of operating equilibrium under normal
operating condition and to regain an acceptable state of equilibrium after being sub-
jected to disturbance[1].
Although, stability of a system is an integral property of the system, for purposes of
the system analysis, it is mainly divided into following categories:
• Steady State Stability relates to ability of synchronous machine to maintain
synchronism followed by small disturbances. e.g. gradually changing load.
• Dynamic or Small Signal Stability concerns with the response of syn-
chronous machine to small perturbations that are oscillating in nature. If these
oscillations are of small amplitude, the system may be considered as small signal
stable, but if the amplitude of oscillations is of growing nature, with the passage
of time the system may lose its stability. Usually, heavy power flow in trans-
mission line or interaction of controller with system frequency is responsible for
small signal instabilities. The phenomenon is concerning with few seconds to
10s of seconds of time period.
• Transient Stability involves response of synchronous machine to large dis-
turbances such as application and clearing of faults, sudden load changes and
inadvertent tripping of transmission lines or generators. Such large disturbances
can create large changes in rotor speeds, power angles and power transfer. The
phenomenon is concerns with time period of 1 second or less.
The detailed classification of power system stability is depicted in the following Fig.2.1
[1].The report focuses on the Small Signal Stability of power system.
CHAPTER 2. POWER SYSTEM STABILITY 6
Figure 2.1: Classification of Power System Stability
CHAPTER 2. POWER SYSTEM STABILITY 7
2.2 Small Signal Stability
Small Signal Stability is the ability of the power system to maintain synchronism
when subjected to small disturbances. A power system at a particular operating
state may be large disturbance unstable and still such a system may be operated with
insecurity with proper control and protective actions. But, if the system is small-signal
unstable at a given operating condition, it cannot be operated at all, because small
signal instability may result in steady increase in generator rotor angle due to lack of
synchronizing torque or in rotor oscillations of increasing amplitude due to insufficient
damping torque. Thus, small-signal stability is a fundamental requirement for the
satisfactory operation of power systems.The reasons for the system can become small
signal unstable are enlisted hereunder[3]:
• Use of high gain fast acting exciters
• Heavy power transfer over long transmission lines from remote generating plants
• Power transfer over weak ties between systems which may result due to line
outages.
• Inadequate tuning of controls of equipment such as generator excitation systems,
HVDC-converters and static var compensators.
• Adverse interaction of electrical and mechanical systems causing instabilities of
torsional mode oscillations.
The issue of small signal instability in current scenario is generally because of insuffi-
cient damping of oscillations. In practical power system, the main types of oscillations
associated with small signal stability are as follows:
1) Swing Mode
2) Control Mode
3) Torsional Mode
CHAPTER 2. POWER SYSTEM STABILITY 8
• Swing Mode of Oscillation
This mode is also referred to as electromechanical oscillations. For an n gen-
erator system, there are (n-1) swing (oscillatory) modes associated with the
generator rotors.The location of generators in the system determines the type
of swing mode.Hence, the swing mode of oscillation can be further sub classified
as shown in following Table 2.1 [3].
Table 2.1: Types of Swing Mode of Oscillations
Local Mode Inter-Unit(Intra-plant) Mode Inter-AreaThese oscillations generally These oscillations These oscillations usuallyinvolve one or more typically involve two or involve combinations of manysynchronous machines at a more synchronous synchronous machines onpower station swinging machines at a power one part of a power systemtogether against a plant swing against each swinging against machinescomparatively large power other. on another part of the system.system or load center.Freqency Range: 0.7 to 2 Hz Freqency Range: 1.5 to 3 Hz Freqency Range: 0.1 to 0.5 Hz
• Control Modes of Oscillations
Control modes are associated with generating units and other controls. Poorly
tuned exciters, speed governors, HVDC converters and static var compensators
are the usual causes of instability of these modes.
• Torsional Mode of Oscillations
These oscillations involve relative angular motion between the rotating elements
(synchronous machine rotor, turbine, and exciter) of a unit, with frequencies
ranging from 4Hz and above. Instability of torsional mode may be caused
by interaction with excitation controls, speed governors and series capacitor
compensated transmission lines.
Of these oscillations, local mode, intra-plant mode, control mode and torsional mode
are generally categorized as local problems as it involves a small part of the system.
Further, inter-area mode oscillations are categorized as global problems and have
widespread effects.
CHAPTER 2. POWER SYSTEM STABILITY 9
2.3 Small Signal Stability Analysis
There are mainly four techniques which are used to analyze the small signal stability
of power system:
a. Eigenvalue Analysis
b. Synchronizing and Damping Torque Analysis
c. Frequency Response and Residue Based Analysis
d. Time domain Simulations
2.3.1 Eigenvalue Analysis
In this report ,of the above methods, Eigenvalue Analysis is used to study oscillatory
behavior of power systems and hence has been described in detail. The system is
linearized about an operating point and typically involves computation of eigenvalues,
eigenvectors, participation factors and system modes from state-space representation
of power system model. This can also be termed as “Small Signal Stability Analysis”
or “Modal Analysis”. Technique employed in this report for studying oscillatory
modes is also based on eigenvalue analysis. Initially, eigenvalues and eigenvectors
are derived. From this, modes of oscillations and participation factor of particular
generator are found out. It gives preliminary idea about possible location of PSS. The
derivation of eigenvalues and participation factor can be found in [1] and can be briefly
explained as follows: Linear approximation of power systems can be characterized by
the following state-space equations:
∆x = A∆x+B∆u (2.1)
∆y = C∆x+D∆u (2.2)
Where,
∆ x is the state vector of length equal to the number of states n
CHAPTER 2. POWER SYSTEM STABILITY 10
∆ y is the output vector of length m
∆ u is the input vector of length r
A is the (n × n) state matrix
B is the input matrix of (n × r)
C is the output matrix of (m × n)
D is the feed forward matrix of (m × r)
Eigenvalues of the system state matrix is available from the characteristic equation
of the state matrix A. It can be expressed as
det(A− λI) = 0 (2.3)
For each of the eigenvalues, there are two sets of orthogonal eigenvectors, namely the
left and right eigenvectors, satisfying the following equations:
AΦi = λiΦi (2.4)
ΨiA = λiΨi (2.5)
Where,
λi, is the ith eigenvalue Φi is the right eigenvector corresponding to λi Ψi is the left
eigenvector corresponding to λi
Eigenvalue & Stability of Power System
The time-dependent characteristic of a mode corresponding to an eigenvalue λi is
given by eλit. Therefore, the stability of the system is determined by the eigenvalues
analysis. Real eigenvalues are associated with non-oscillatory modes, whereas the
complex ones, appearing in conjugate pairs, correspond to oscillatory modes - one
mode for each pair. If the eigenvalue of an oscillatory mode is expressed as,
λi = σ ± jω (2.6)
CHAPTER 2. POWER SYSTEM STABILITY 11
The damping coefficient which gives the rate of decay of amplitude of the oscillation
is given by,
ζ =−σ√σ2 + ω2
(2.7)
and the frequency of oscillation in Hz is determined by,
f =ω
2π(2.8)
A negative real part of the eigenvalue represents positive damping coefficient that
is, decaying oscillation, and the positive real part indicates negative damping, i.e.,
increasing oscillation. The right eigenvector of a mode gives an idea about how this
mode is distributed among different states of the system and hence known as Mode
Shape. Based on this idea, if a mode is found to be distributed among specific state
variable of generating units in different areas, then that mode can be identified as a
local mode or inter-area mode. Typically, rotor speed is used as the test state variable
for mode shape analysis in inter-area oscillation study[1] , [4].
Participation Factor is a measurement of relative participation of any state variable
in any specific mode. It is mathematically expressed as the multiplication of left and
right eigenvectors. For example, participation factor pki of any kth state variable in
any ith mode can be measured as[1],
pki = Φki ×Ψik (2.9)
Where,
Φki is the kth entry of the right eigenvector of ith mode
Ψik is the kth entry of the left eigenvector of ith mode
Thus, participation factors are the sensitivities of the eigenvalues to changes in the
diagonal elements of the state matrix. They indicate possible locations where a
stabilizer may effectively control the mode of concern[8]. Eigenvalue or modal analysis
describes the small-signal behavior of the system about an operating point, and does
not take into account the nonlinear behavior of components such as controller’s limits
at large system perturbations. Further, design and analysis carried out using various
CHAPTER 2. POWER SYSTEM STABILITY 12
indices such as participation factors, may lead to many alternate options. These
options need to be verified by time-domain simulations.
Advantages of Eigenvalue Analysis
i) Separate identification of modes of oscillations
ii) Root loci plotted with variations in system parameters or operating conditions
provide valuable insight into the dynamic characteristics of the system.
iii) Using eigenvectors coherent groups of generators which participate in a given
swing mode can be identified.
2.3.2 Synchronizing and Damping Torque Analysis
The synchronous operation of generators is generally dealing with balance between the
input mechanical torque and output electrical torque of each machine. The change in
electrical torque of alternator following small perturbation can be illustrated through
following equation:
∆Te = Ts∆δ + TD∆ω (2.10)
Where,
• Ts∆δ is the component of torque change in phase with the rotor angle pertur-
bation and is referred to as the synchronizing torque component.
• Ts is the synchronizing torque coefficient.
• TD∆ω is the component of torque in phase with the speed deviation and is
referred to as the damping torque component.
• TD is the damping torque coefficient.
The nature of system oscillations to small perturbation depends on both the com-
ponents of electrical torque. The response of generator without automatic voltage
regulator (constant field) can result into instability due to lack of sufficient synchro-
nizing torque. Such instability is known as non-oscillatory instability. Further, the
CHAPTER 2. POWER SYSTEM STABILITY 13
presence of automatic voltage regulator can also result in instability with oscillations
having nature of continuously growing amplitude. Such instability is known as oscilla-
tory instability. Both types of instabilities are illustrated in following Fig.3.1 [1]. This
analysis assumes that the rotor angle and the speed deviations oscillate sinusoidally.
Hence this can be represented by phasors as depicted in Fig.2.2
Figure 2.2: Phasor Representation of Electrical Torque
From the above figure the damping torque component can be written as
∆TeD = ∆Te cosφ (2.11)
And synchronizing torque component can be written as
∆TeS = ∆Te sinφ (2.12)
If either or both damping and synchronizing torques are negative, i.e., if ∆TeD <
0 and/or ∆TeS < 0, then the system is unstable. A negative damping torque im-
plies that the response will be in the form of growing oscillations, and a negative