Engineering, 2011, 3, 478-484
doi:10.4236/eng.2011.35055 Published Online May 2011 (
Copyright © 2011 SciRes. ENG
Transient Stability Analysis of Power System by Coordi-
nated PSS-AVR Design Based on PSO Technique
Ali Darvish Falehi, Mehrdad Rostami, Hassan Mehrjardi
Department of Engineering, Shahed University, Tehran, Iran
E-mail: {darvishfalehi, rostami}
Received March 8, 2011; revised April 1, 2011; accepted April 19, 2011
In this paper, Power System Stabilizer (PSS) and Automatic Voltage Regulator (AVR) are coordinated to
improve the transient stability of generator in power system. Coordinated design problem of AVR and PSS is
formulated as an optimization problem. Particle Swarm Optimization (PSO) technique is an advanced robust
search method by the swarming or cooperative behavior of biological populations mechanism. The perform-
ance of PSO has been certified in solution of highly non-linear objectives. Thus, PSO technique has been
employed to optimize the parameters of PSS and AVR in order to reduce the power system oscillations dur-
ing the load changing conditions in single-machine, infinite-bus power system. The results of nonlinear
simulation suggest that, by coordinated design of AVR and PSS based on PSO technique power system os-
cillations are exceptionally damped. Correspondingly, it’s shown that power system stability is superiorly
enhanced than the uncoordinated designed of the PSS and the AVR controllers.
Keywords: Power System Satiability, Coordinated Design, PSS, AVR, Particle Swarm Optimization
1. Introduction
In recent years, large signal stability problems have been
reported in power systems and which originated broad
studies in many literatures [1-5]. Power system is af-
fected by high electromechanical oscillations while a
disturbance occurs, which may lead to loss of synchro-
nism of generators. Thus, high performance excitation
systems are essential to maintain steady state and tran-
sient stability of generators and provide rapid control and
recover of terminal voltage [6,7]. The generator excita-
tion system using an automatic voltage regulator (AVR)
maintains the terminal voltage magnitude of a synchro-
nous generator to a defined level [8]. It also plays an
essential role to control the reactive power and improve
the stability. AVR assists improving the steady-state sta-
bility of power systems [9]. In transient state, machine is
affected by severe impacts, mostly in a short time which
causes severe drop on the terminal voltage of machine.
Generally, a controller to increase damping of elec-
tromechanical oscillations is known as power system
stabilizer (PSS), which is basically kind of classical
phase compensator [10,11]. They are used to compensate
the negative damping of AVR [12]. Also, PSS modulates
the input signal of excitation system to damp out rotor
A variety of conventional design techniques can be
used to tune controller parameters. The most common
methods are based on the pole placement method [13,14],
eigenvalues sensitivities [15,16], residue compensation
[17], and also the current control theory.
Lucklessly, the conventional methods are time con-
suming as they are repetitive and need heavy computa-
tion burden beside of slow convergence. In addition,
process is sensitive to be trapped in local minima and the
obtained response may not be optimal [18].
The progressive methods develop a technique to
search for the optimum solutions via some sort of di-
rected random search processes [19]. A suitable trait of
the evolutionary methods is to search for solutions with-
out prior problem perception.
In recent years, a number of various ingenious com-
putation techniques namely: Simulated Annealing (SA)
algorithm, Evolutionary Programming (EP), Genetic
Algorithm (GA), Differential Evolution (DE) and Parti-
cle Swarm Optimization (PSO) have been employed by
scholars to solve the different optimization problems of
electrical engineering [8,18-29]. But, the PSO technique
can produce an excellent solution within shorter calcula-
tion time and stable convergence characteristic than other
stochastic techniques [8]. In fact, PSO is a stochastic
global optimization approach based on swarm behavior
such as fish and bird schooling in nature [30]. Generally,
PSO is known as a simple concept, easy to perform, and
computationally effective. PSO has a exible and
well-balanced mechanism to enhance the global and lo-
cal exploration abilities [31].
Thus, PSO technique has been selected to coordinate
the operation of both the PSS and AVR controllers in
order to improve the transient stability and diminish the
power system oscillations.
To appraise the coordinated design problem of these
devices, a severe disturbance condition is considered in
the transmission line of single-machine, infinite-bus
power system. Furthermore, effect of coordinated design
of these devices is assessed in spite of changes in the
loading of the generator.
2. Power System Structure and Modeling
The model of electrical power system is exhibited in Fig-
ure 1, which is comprised of a generating unit connected
to electrical network through a transformator. It is almost
similar to the power system used in [23]. The generator
is equipped with hydraulic turbine and governor (HTG).
Also, excitation system furnished with an automatic
voltage regulator (AVR) and a power system stabilizer
(PSS) to maintain the terminal voltage and to damp os-
cillations. Speed deviation of generator is chosen as the
input signal of the PSS. The single-machine, infinite-bus
power system has been simulated using MAT-
LAB/SIMULINK environment. All of the other relevant
parameters are given in Appendix.
2.1. Automatic Voltage Regulator Model
A first order AVR model is used in this paper which is
almost derived from ref [5,32]. The block diagram of the
model is shown in Figure 2.
The parameters to be adjusted, on the model of AVR
presented in Figure 2, are: the gain Ka and the time con-
stant Ta. The values of the parameters: Kf, Tf and Tr are
considered 0.001, 0.1 and 0.02 respectively [33].
2.2. Power System Stab ilizer Mode l
PSS includes a transfer function comprise of an amplifi-
cation block, a wash out block and lead-lag block and
sensor time constant [12,19]. The PSS input signal can
be either the speed deviation or active power. The struc-
ture of the PSS controller is presented in Figure 3. The
value of TWS and sensor delay time are considered 3 and
15 ms respectively. Parameters of the power system sta-
bilizer, including: gain (KP) and the time constants (T1P
and T2P) shall be determined.
2.3. Coordinated Design of AVR and PSS
In this study, the PSS and AVR controller are designed
and optimized by minimizing objective function in order
to enhance the system response in terms of the settling
time, overshoots and undershoot. There are many differ-
ent methods to appraise the response performance of a
control system, for example: integral of time weighted
absolute value of error (ITAE), integrated absolute er-
ror(IAE), integral of squared error (ISE), and integral of
time weighted squared error (ITSE) [34]. In this paper,
the integral time absolute error (ITAE) of the speed signal
deviation is considered as the fitness function J [18]. This
fitness function is determined as:
is the speed deviation in and sin is the time
range of the simulation. The time-domain simulation of
the nonlinear system model was performed for the simu-
lation period. It is aimed to minimize this fitness function
in order to improve the system response in terms of the
settling time and overshoots. The problem constraints are
the PSS and AVR parameter bounds. Therefore, the design
Figure 1. Single-machine, infinite-bus power sys tem.
Copyright © 2011 SciRes. ENG
Copyright © 2011 SciRes. ENG
Figure 2. AVR first order model with feedback.
Figure 3. Structure of the power system stabilizer.
problem can be formulated as the following optimization
inimize J (2)
Subject to:
min max
min max
min max
KKK (3)
min max
min max
PSO technique is applied to solve the coordinated de-
sign problem and optimal set of PSS and AVR parame-
3. Description of the Implemented Particle
Swarm Optimization Technique
PSO is a stochastic global optimization method, which
has been motivated by the behavior of organisms, such as
fish schooling and bird flocking. Simplicity and fast con-
vergence rate is the important characteristic of this tech-
nique [35]. PSO has the exibility than other heuristic
algorithms to control the balance between the global and
local configuration of the search space. This unique fea-
ture of PSO vanquishes the premature convergence prob-
lem and enhances the search capability. Also unlike the
traditional methods, the solution quality of this technique
does not depend on the initial population. Starting any-
where in the search space, PSO algorithm ensures the
convergence of the optimal solution. The following is a
brief introduction to PSO [36]. In the current research, the
process of PSO technique can be summarized as follows
Initial positions of pbest(personal best of agent i)
and gbest are (group best) varied. However, using the
different direction of pbest and gbest, all agents
piecemeal receive near-by the global optimum.
Adjustment of the agent position is perceived by the
position and velocity information. However, the me-
thod can be used to the separate problem applying
grids for XY position and its velocity.
Didn’t have any incompatibilities in searching proce-
dures even if continuous and discrete state variables
are utilized with continuous axes and grids for XY po-
sitions and velocities. Namely, the method can be ap-
plied to mixed integer non-linear optimization prob-
lems with continuous and district state variables easily
and naturally.
The above statement is based on using only XY axis
(two dimensional spaces). Thus, this method can be
easily employed for n-dimensional problem.
The modied velocity and position of each particle can
be calculated using the current velocity and the distances
from the pbestj,g to gbestg as presented in the following
equations [38]:
(1) ()()
22 ,
gjg jg
crgbest x
 
 
(1) (1)
1,2, and 1,2,.
jgjg jg
with jngm
where n is the number of particles in the swarm; m is the
number of components for the vectors
, t is the
number of generation (iteration); ()
is the gth compo-
nent of the velocity of particle j at iteration t
min( )max
 (6)
where c1 and c2 are two positive constants, called cogni-
tive and social parameters respectively. r1 and r2, are ran-
dom numbers, uniformly distributed in (0, 1). ()
is the
component of the position of particle at iteration t;
pbestj is the pbest of particle j; pbest is the pbest of the
gth j
w is the inertia weight, which produces a balance be-
tween global and local explorations requiring less itera-
tion on average to nd a suitably optimal solution. It is
determined by the following equation:
max min
w witer
 
where max is the initial weight, min is the nal weight,
iter is the current iteration number, is the maxi-
mum iteration number.
w w
it max
The particle in the swarm is represented by a
d-dimensional vector ,1 ,2,d
and its
rate of velocity is symbolized by another d-dimensional
,1 ,2
. The best previous posi-
tion of the jth particle is represented by
,1 j,2,
pbestpbest pbestpbest
. The index of
best particle among all of the particles in the population is
represented by the gbestg. In PSO, each particle moves in
the search space for seeking the best global minimum (or
maximum). The velocity update in a PSO comprises of
three parts; namely cognitive, momentum and social parts.
The performance of PSO algorithm depends upon the
balance among these parts. The parameters c1 and c2 de-
termine the relative pull of pbest and and the
parameters r1 and r2 help in stochastically varying these
Ultimately the flowchart of proposed optimization al-
gorithm is shown in Figure 4.
4. Simulation Results
To assess the coordinated control AVR and PSS, three
different operating positions with different Fault Clear-
ing Time (FCT) are considered, which are exhibited in
Table 1.
4.1. Nominal Loading
A 3-phase fault located at sending bus and triggered at t =
1 sec, then be cleared after 0.262 sec (FCT = 1.262 sec).
PSO technique is employed to coordinate among AVR
and PSS controllers, and also to optimal tune the parame-
ters of these devices. Optimal parameters of AVR and
PSS are presented in Table 2.
The system responses under this severe disturbance are
presented in Figures 5-7. These figures approve the co-
ordination between AVR and PSS controllers in order to
improve the power system stability. Also, power system
oscillations have been improved significantly as com-
pared to non-coordination of these devices.
Figure 4. Flowchart of the PSO technique.
Table 1. Loading positions considered.
Loading conditions Pe (pu) δ0 (deg) FCT (sec)
Small 0.35 19.6 0.454
Nominal 0.7 42.2 0.262
Heavy 0.95 58 0. 133
Table 2. Optimal parameter settings of the AVR and PSS.
Ka T
a K
1P T2P
292.8481 0.0031 4.9759 0.1493 1.1971
Figure 5. Active power generation response for 3-ph fault in
trans m ission line with no minal loading.
Figure 6. Power angle response for 3-ph fault in transmis-
sion line with nominal loading.
Figure 7. Speed deviation response for 3-ph fault in trans-
mission line with nominal loading.
Copyright © 2011 SciRes. ENG
4.2. Heavy Loading
In this state, to appraise the coordinated design problem,
it is considered that the generator loading experiencing
heavy step change as shown in Table 1. The 3-phase
fault occurs at t = 1 sec, then it is cleared after 0.133 sec.
System responses under such 3-phase fault are displayed
in Figures 8-10. Obviously by optimal coordination of
AVR and PSS, power system stability is superiorly en-
4.3. Small Loading
The robustness of coordination among the AVR and PSS
is also veried when generator loading is altered to small
Figure 8. Active power generation response for 3-ph fault in
transmission line with heavy loading.
Figure 9. Power angle response for 3-ph fault in transmis-
sion line with heavy loading.
Figure 10. Speed deviation response for 3-ph fault in trans-
mission line with heavy loading.
loading. 3-phase fault happened at t = 1 sec, subsequently
fault is cleared after 0.454 secat t = 1.454 sec. System
responses under such 3-phase fault are displayed in Fig-
ures 11-13. As it has been expected like to two before
cases, the power system stability is significantly improved
by coordinated control between AVR and PSS rather than
despite the non-coordination of these devices.
5. Conclusions
This paper presents the particle swarm optimization al-
gorithm for the simultaneous coordinated design of the
AVR and PSS in order to enhance the power system sta-
bility. Time domain simulations are performed to dem-
onstrate the efficiency of proposed optimization method.
Figure 11. Active power generation response for 3-ph fault
in transmission line with small loading.
Figure 12. Power angle response for 3-ph fault in transmis-
sion line with small loading.
Figure 13. Speed deviation response for 3-ph fault in trans-
mission line with small loading.
Copyright © 2011 SciRes. ENG
Coordination among these devices based on PSO tech-
nique has been deeply investigated under severe distur-
bance for single-machine, infinite-bus power system. To
confirm the robustness of coordinated design of these
controllers, power system stability has been assessed in
spite of load changes of generator. Also, the particular
features of PSO algorithm namely its superior computa-
tion efficiency and high accuracy solutions have been
approved. Finally, the results of non-linear simulation
have shown that by using PSO technique, power system
transient stability dramatically improves as compared to
non-optimized parameters of PSS and AVR.
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Appendix Transmission line: 3-Ph, 60 Hz, Length = 300 km each,
R1 = 0.02546 /km, R0 = 0.3864 /km, L1 = 0.9337e
3 H/km, L0 = 4.1264e 3 H/km, C1 = 12.74e 9 F/km,
C0 = 7.751e 9 F/km.
Single-machine infinite-bus power system
Hydraulic turbine and governor: Ka= 3.33, Ta= 0.07,
Gmin= 0.01, Gmax= 0.97518, Vgmin= –0.1 p.u./s, Vgmax= 0.1
SB = 2100 MVA, H = 3.7 s, VB = 13.8 kV, f = 60 Hz,
RS = 2.8544e 3, d=1.305 p.u., Xd
= 0.296 p.u.,
 =0.252 p.u., q
= 0.474 p.u., q
= 0.243 p.u.,
 = 0.18 p.u., = 1.01 s, = 0.053 s,
= 0.1 s. Rp = 0.05, Kp = 1.163, Ki = 0.105, Kd = 0, Td = 0.01 s,
β= 0, Tw = 2.67 s.
Load at Bus-2: 250 MW.
PSSs: sensor time constant = 0.015 s, VS
max = 0.15 p.u.,
min = 0.15 p.u.
Transformer: 2100 MVA, 13.8/500 kV, 60 Hz, R1 = R2
= 0.002 p.u., L1= 0, L2= 0.12 p.u., D1/Yg connection, Rm
= 500 p.u., Lm = 500 p.u.