International Research Journal of Computer Science and Information Systems (IRJCSIS) Vol. 1(2) pp. 12-17,
December, 2012
Available online http://www.interesjournals.org/IRJCSIS
Copyright © 2012 International Research Journals
Review
Adaptive fuzzy power system stabilizer tuned
by genetic algorithm
Tawfiq Hussein Elmenfy
Department of Electrical Engineering, University of Benghazi, Benghazi, Libya
E-mail: Tawfiq.elmenfy@benghazi.edu.ly
Accepted 23 November, 2012
The use of power system stabilizers (PSSs) to damp power system swing mode of oscillations is
practical important. An indirect adaptive fuzzy power system stabilizer (APSS) is proposed in this
paper. It consists of a fuzzy identifier and a feedback linearizing controller. The objective is to damp
local-area oscillation that occur following power system disturbance. The effectiveness of the proposed
technique is illustrated by applying the AFPSS to a single-machine infinite bus system that is typically
used in the literature to test the performance of power system stabilizers. The simulation has been
conducted in MATLAB Simulink package and single machine infinite bus was designed as generator
number (3) in Benghazi North Power Plant (BNPP). The simulations results show the effectiveness
performance of proposed AFPSS.
Keywords: Static excitation system, genetic algorithm (GA), power system stabilizer (PSS) and adaptive fuzzy
control.
INTRODUCTION
Benghazi north power plants (BNPPs) are the biggest
power plants working in General Electricity Company of
Libya (GECOL).
Excitation system (Kunder, 1994) of the generators in
BNPP was chosen for investigation because its work has
the biggest impact on dynamic stability of the GECOL. A
fast static excitation system (PID-system) UNITROL D
(IEEE Recommended Practice for Excitation System
Models for Power System Stability Studies, IEEE
Standard 421.5-2005, April 2006) produced by ABB was
installed in 1995.
Power system is steadily growing with ever larger
capacity. Formerly separated power systems are
interconnected to each other. Modern power systems
have evolved into systems of very large size. With
growing generation capacity (Klein et al., 1991), different
areas in a power system are added with even large
inertia. As a consequence in large interconnected power
systems, low frequency oscillations have an increasing
importance.
The ability of a power system to maintain stability
depends to a large of extent on the controls available on
the system to damp the electromechanical oscillations
(Klein et al., 1991). Hence the study and design of
controls are very important.
The basic function of an excitation system is to provide
direct current to the field winding of the synchronous
machine (Kunder, 1994). The protective functions ensure
that capability limits of the synchronous machine,
excitation system, and other equipment are not
exceeded.
The Power System Stabilizer (PSS) is used to improve
the damping of the power system oscillations and the
general stability of the power generation including
transmission system. By means of power system
oscillations, two modes of oscillations are to be deemed;
“Local plant oscillations“ with typical range of oscillations
from 0.8 to 2.0 Hz and “Inter-area oscillations“ with typical
range of oscillations from 0.1 to 0.7 Hz.
Whenever this state of equilibrium between the
electrical torque (Te) and the mechanical torque(Tm) is
disturbed, the load angle slips of this rest position, and
change thereby the available electrical torque Te. This
changed torque Te attempts to restore the load angle
again to a stationary position. Due to the mass inertia of
the turbine/generator rotor however, this can only take
place a periodically. It does so in the form of more or less
effectively damped oscillations (similar to the effect of
mass inertia on a torsion spring).
The main torque for damping the oscillations is
produced by the so-called damper windings of the
generator. But the dimensioning of this subject to limits
Elmenfy 13
Figure 1. Static fast exciter (IEEE Recommended Practice for
Excitation System Models for Power System Stability Studies, IEEE
Standard 421.5-2005, April 2006)
imposed by considerations of design and economy, so in
many cases further action is needed to increase the
damping effect.
An adaptive power system stabilizer using on-line self
learning fuzzy systems is proposed in (Abdelazim and
Malik, 2003) consisting of an on-line identified plant
model to obtain a dynamic equivalent model for the
synchronous machine and self-learning fuzzy logic
controller. The self learning ability of the fuzzy controller
is based on the steepest descent algorithm. An online
adaptive neuro-fuzzy power system stabilizer for
multimachine systems is derived in (Ruhua et al., 2003).
The system is divided into two subsystems, a recursive
least square identifier with a variable forgetting factor for
the generator and a fuzzy logic based adaptive controller
to damping oscillations. Adaptive neural network based
power system stabilizer design is suggested in (Liu et al.,
2003). The author presents an indirect adaptive neural
network (IDNC) design. The IDNC consists of a neurocontroller to generate a supplementary control signal to
the excitation system and a neuro-identifier which is used
to model the dynamic of the power system and to adapt
the neuro-controller parameters. An artificial intelligence
technique applied to adaptive power system stabilizer
design (Malik, 2006) gives a number of examples of
development and successful implementation of adaptive
PSSs based on AI techniques.
In this paper, an indirect adaptive fuzzy power system
stabilizer is developed and applied to single machine
infinite bus designed as BNPP generator (Klein et al.,
1991). It uses the actual speed and the actual speed
deviation as inputs to the fuzzy identifier (obtained online
and assumed to be measured from the output of the
plant). The output of the fuzzy identifier is the estimates
of the unknown nonlinearities of the model. These are
used in a feedback linearization algorithm to provide the
necessary damping in the power system. The paper
organized as follow. Section 2 explains the ST1A
excitation system mode. Section 3 introduces the
basically PSS theory. Sections 4 introduce the basic
Concepts and Identification of AFPSSand 5 gives the
overview of GA and section 6 and 7gives the single
machine infinite bus system which used as the system
description and simulations study. The conclusion of our
work is depicted in Section 8.
In this paper, Genetic Algorithm technique (GA)
(Whitley, 1993) is used to search for the gains value of
the proposed adaptive power system stabilizer.
ST1 A Excitation System Mode
The computer model of the fast static exciter potentialsource controlled-rectifier excitation system shown in
Figure 1. Is intended to represent systems in which
excitation power is supplied through a transformer from
the generator terminals (or the unit’s auxiliary bus) and is
regulated by a controlled rectifier (Klein et al., 1991). The
maximum exciter voltage available from such systems is
directly related to the generator terminal voltage.
In this type of system, the inherent exciter time
constants are very small, and exciter stabilization not
required.
Basical PSS theory
A synchronous generator working on the network is
principally an oscillating structure. In order to produce a
torque the rotating magnetic fields of the rotor and the
stator must form a certain angle (the so called load angle
δ). The electrical torque Te increases, as the angle δ
increases, just similar to a torsion spring. Because during
steady-state operation the electrical torque Te of the
generator and the mechanical driving torque Tm from the
turbine are in equilibrium, the load angle δ remains in a
given position.
The dynamic of the mechanical power Tm, electrical
power Te, and rotor angular speed ω of the synchronous
machine is an origin for theoretical consideration and
justifications of the PSS processing signal. The
relationship between the above physical magnitudes is
shown in the motion equation of the synchronous
machine (1a and 1b).
(1)
(2)
Where:
14 Int. Res. J. Comput. Sci. Inform. Syst.
estimate of
x and estimate
give measurements of
f
θf.
We use the series-parallel identification model in [9].
For the generator running at rated speed (ω = 1p.u) it is
allowed to re-write equations (1) and (2) as:
The aim of the PSS (which output acts to the Generator
Voltage Regulator) is to supply an additional electric
torque component (by influencing the Field Voltage)
phase-synchronous with the rotor angular speed.
However the influence signal of the PSS must lead the
rotor angular speed ω with a certain angle to compensate
the time constants lag (mainly the field time constant Td')
between the influence signal and the electric torque Te.
Basic concepts and identification algorithm
y r = f ( x ) + g ( x )u
(3)
Where f
and g are unknown nonlinear function,
and suppose that, g ( x ) ≠ 0
for all value of x and
must be bounded in the compact set. We need to
develop an adaptive law to adjust the free parameters of
the fuzzy identifier for the purpose of making the output
value y follow the desired output y m .
From the nonlinear system (3), the control law can be
selected as
[
]
g
g
gˆ ( x θ g ) to be fuzzy system
characterized by singleton fuzzifier, the center average
defuzzification, the product in faience and Gaussian
membership function. From (Wang, 1995) we have:
T
f
p( x)
(6)
T
gˆ ( x θ g ) = θ g p ( x ) (7)
Where
n
∏µ
p k ( x) =
m1
i =1
mn
Fi ji
( xi )
∑ L∑ ∏ µ
j1
(8) and it is called
n
jn =1 i =1
FI
JI
( xi )
Fuzzy Basis Function (FBF).
µ F ji ( xi ) is the membership function assigned to the
th
linguistic variable in the i
th
rule.
p (x ) , θ if and θ ig into
are stable,
θ f and
are replaced by fˆ ( x θ f )
f
θ if and vector θ ig and with the same order of
p (x ) .
θg
and
gˆ ( x θ g ) and the adaptation law to updating parameters
θ and θ . The notation fˆ ( x θ ) means the
f
fˆ ( x θ f ) and
Choose
vector
= ym − y
are free parameters to be adjusted by the fuzzy identifier.
The goal of this paper is to design an indirect adaptive
power system stabilizer based on the actual speed and
the deviation of the actual speed measurement such that
all variable in the closed loop system are bounded and
the output y follow the desired output y m .
The control law (4) is feedback linearization controller.
First we need to develop an identification model where
and
model must be bounded. The error between the actual
output and it is estimation must be as small as possible.
Collect the p k (x ) into vector
T
the f
basis function (FBF) and the adaptive law for the
parameters θ f and θ g . The signals in the identification
j
(4)
and k = [k r , K , k1 ] is such that roots of
s r + k1 s r −1 + L + k r = 0
fˆ ( x θ f ) and gˆ ( x θ g ) using the fuzzy
Identify the
i
Where
( r −1)
e1 = [e1 , e&1 ,K, e1 ]T
(5)
where α is a positive scalar that determine the error
between the actual and it is estimation value and it is
designer selected. The goals of identification are
following:
fˆ ( x θ f ) = θ
Consider the nonlinear system
1
r
u=
− fˆ (x θ f ) + ymr + k e1
gˆ(x θ g )
x&ˆ = −αxˆ +α x + fˆ(x θ f ) + gˆ(x θ g ) u
The error e 2 = x − xˆ . According to (Wang, 1995) the
unknown parameters can update by
θ& f = Γ f e 2 T p ( x)
θ& g = Γg e 2 p( x)u
(9)
(10)
Where Γ f and Γg are diagonal matrices.
Overview of genetic algorithm
Genetic algorithms are stochastic global search method
that mimics the process of natural evolution. The genetic
algorithm starts with no knowledge of the correct solution
and depends entirely on responses from its environment
Elmenfy 15
Create Population
Measure Fitness
Select Fittest
.
Mutation
Crossover/ Reproduction
\
Optimum Solution
Non Optimum
Solution
Figure 2. The Genetic Algorithm Outlines
Gen.
Trans.
Load 1
Load 2
Figure 3. Single machine infinite bus power system
and evolution operators (i.e reproduction, crossover and
mutation) to arrive at the best solution.
A genetic algorithm is typically initialized with a random
population consists of between 20-100 individuals. this
population is usually represented by a real-valued
number or a binary string called chromosome (figure 2).
The steps involved in creating and implementing a
genetic algorithm are as follows:
•
Generate an initial random population of
individuals for a fixed size.
•
Evaluate their fitness.
•
Select the fittest members of the population.
•
Reproduce using a probabilistic method.
•
Implement
crossover
operation
on
the
reproduced chromosome.
•
Execute mutation operation with low probability.
•
Repeat step 2 until a predefined convergence
criterion is met.
System description
A three-phase generator rated 210 MVA, 15.75 kV, 3000
rpm is connected to a 230 kV, 10,000 MVA network
through a Delta-star 210 MVA transformer.
At t = 0.1 s, a three-phase to ground fault occurs on the
230 kV bus. The fault is cleared after 6 cycles (t = 0.2 s).
During this system, we will initialize the system in order to
start in steady-state with the generator supplying active
power and observe the dynamic response of the machine
speed deviation and of its active power (figure 3).
Simulation study
The adaptive fuzzy power system stabilizer (AFPSS) in
Benghazi North Power Plant (BNPP) is implemented as
shown in Figure 4. Its gains are tuned off-lines using the
16 Int. Res. J. Comput. Sci. Inform. Syst.
ω ref
Governor
∆ω
Generator
T.L
G
Turbine
Δω
x
Exciter
AVR
AFPSS
Vref
U pss
Figure 4. Power system model used in study
-3
6
x 10
4
s p e e d d e v ia t io n p u
2
0
-2
-4
-6
0
1
2
3
4
5
t(sec)
6
7
8
9
10
Figure 5. Speed deviation for operating condition 1
genetic algorithm (GA).
The performance of the AFPSS in BNPP is evaluated
by applying a large disturbance in the form of a threephase fault of the transmission line. The fault occurs at
0.1 sec. and cleared at 0.2 sec. Two different operating
points are shown here to measure the performance of the
power system stabilizer (AFPSS) in Unitrol D.
Operating point 2
Operating Point 1
CONCLUSION
P = 0.75 pu
As power systems have evolved through continuing
, Q = 0.0123 pu
P = 0.95 pu
, Q = 0.025 pu
As shown in the two figures (figure 5 and figure 6) for
two operating points the one noted that, the damping
stability is greatly improvement when AFPSS is used as
power system stabilizer.
Elmenfy 17
-3
8
x 10
6
4
speed deviation pu
2
0
-2
-4
-6
-8
-10
0
1
2
3
4
5
t(sec)
6
7
8
9
10
Figure 6. Speed deviation for operating condition 2
growth in interconnections, use of new technologies and
controls, and the increased operation in highly stressed
conditions, different forms of system instability have
emerged. Many major trips caused by power system
instability due to power system stabilizer which need
retune to adapt to new interconnected power system. So
our purpose is proposed new adaptive fuzzy power
system stabilizer and its gains are tuned by genetic
algorithm. The proposed AFPSS uses the actual speed
and the actual speed deviation as inputs to the fuzzy
identifier (obtained online and assumed to be measured
from the output of the plant). The output of the fuzzy
identifier is the estimates of the unknown nonlinearities of
the model. These are used in a feedback linearization
algorithm to provide the necessary damping in the power
system.
The retuned power system stabilizer (PSS1A) can cope
with large disturbance at different operating points and
has enhanced power system stability.
The simulation has been conducted in MATLAB
Simulink package and single machine infinite bus was
designed as generator number (3) in Benghazi North
Power Plant (BNPP). The simulations results show the
effectiveness performance of proposed AFPSS.
ACKNOWLEDGMENT
The author thanks the National Academy for Scientific
Research (NASR) in Libya for financial support of this
study.
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2006.
Liu W, enayagamoorthy GKL, Donald C (2003). "Adaptive Neural
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