International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
Design of Robust Power System Stabilizer
using Neuro-Fuzzy controller
M.D.Udayakumar#1, M.Bhavani#2
#1
#2
PG student, Dept. of Electrical and Electronics Engg., Anna University, Regional Centre Madurai, Tamilnadu, India
Assistant Professor, Dept. of Electrical and Electronics Engg., Anna University, Regional Centre Madurai, Tamilnadu, India
Abstract— A power system stabilizer (PSS) installed in the
excitation system of the synchronous generator improves
the small-signal power system stability by damping out low
frequency oscillations in the power system. This paper
introduces a neural network to tune the fuzzy-logic power
system stabilizer (FPSS) which has been designed to
provide a supplementary signal to the excitation system of
the synchronous generator. This mechanism of tuning the
FPSS by the neural network makes the FPSS adaptive to
changes in the operating conditions. The performance of
neuro-fuzzy power system stabilizer (NFPSS) is
investigated by applying to a single machine infinite bus
(SMIB) system. The simulations have been tested under
different fault conditions and the obtained results show
that the proposed controller for stabilizing power system
can provide very good damping characteristic, comparing
with the conventional PSS and FPSS, through wide range
of operating condition for power system and improves
dynamic stability of the power system substantially.
Index Terms— Power System Stabilizer, Stability, Single
Machine System, Fuzzy Logic, Fuzzy Set Theory, Machine
Dynamic, Simulink.
I. INTRODUCTION
The electrical power system is a dynamic system. If the
interconnecting ties between neighboring power systems are
relatively weak, It easily leads to low frequency inter
oscillation. Low frequency Oscillations often persist for long
periods of time and in some cases can hinder power transfer
capability. Power system stabilizers were developed to aid in
damping these oscillations via modulation of the generator
excitation.
In power systems, generally many generators are designed
with high gain, fast acting AVRs to enhance large scale
stability to hold the generator in synchronism with the power
system during large transient fault conditions. But with the
high gain of excitation systems, it can decrease the damping
torque of generator. A supplementary excitation controller
referred to as PSS have been added to synchronous generators
to counteract the effect of high gain AVRs and other sources
of negative damping [10]. To provide damping, the stabilizers
must produce a component of electrical torque on the rotor
which is in phase with speed variations [4]. The PSS is used to
generate a supplementary stabilizing signal, which is fed to the
excitation system of the generating unit to produce a positive
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damping. The conventional PSS uses lead-lag compensation,
where the gain settings are determined for specific operating
conditions, gives poor performance under different loading
conditions [9].The changing nature of power system which
will make the design of CPSS a difficult task.
To overcome this problem, numerous techniques have been
proposed for their design, such as using intelligence
optimization methods (simulated annealing, genetic algorithm,
Tabu search, fuzzy, neural networks) and many other
nonlinear techniques [5]-[9]. Here Fuzzy logic based
technique has been suggested as a possible solution where the
complex mathematical model can be avoided. Recent research
indicates that more emphasis has been placed on the combined
usage of fuzzy logic systems and other technologies such as
neural networks to add adaptability to the design [1] & [2].
In this paper a rule-based FPSS is designed. Its parameters
are tuned with a neural network, making it adaptable to
changes in operating conditions. It is then applied to a
mathematical model of a synchronous machine. Responses of
the machine subjected to a fault in the transmission line are
obtained by nonlinear simulations. System responses with the
neural network- tuned fuzzy power system stabilizer (NFPSS)
for three different operating conditions are then compared
with a fixed-parameters FPSS and a conventional power
system stabilizer (CPSS).
II. RULED BASED FUZZY-LOGIC PSS
In the design of fuzzy-logic controllers, unlike most
conventional methods, a mathematic model is not required to
describe the system under study. It is based on the
implementation of fuzzy logic technique to PSS to improve
system damping. In contrast to a conventional PSS, which is
designed in the frequency domain, a fuzzy logic PSS is being
designed in the time domain. A fuzzy logic controller
determines the operating condition from the measured values
and selects the appropriate control actions using the rule base
created from the expert knowledge. Depending on the system
state, the controller operates in the range between no control
action and full control action in a non-linear manner. The
fuzzy controller in itself has no dynamic component, i.e. it can
immediately perform the desired control action. In rule-based
fuzzy control, the human knowledge is approached by means
of linguistic fuzzy rules in the form if-then, which describes
the control action in a special condition of the system. Due to
the nonlinear behavior exhibited by the machine, designing a
linear control is not successful.
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By knowing the advantages of the fuzzy control, described
before, a nonlinear fuzzy control might be desirable as a
power system stabilizer, instead of PSS, by providing a
supplementary signal to the excitation system of the
synchronous generator.
In designing a fuzzy controller, the first step is to decide
which state variables represent of system dynamic
performance must be taken as the input signal to the
controller. Next, choosing the proper linguistic variables
formulating the fuzzy control rules are very important factors
in the performance of the fuzzy control system. System state
variables, which are usually used as the fuzzy derivative, state
error integral or etc., generally generator speed deviation (dω)
and acceleration (da) are chosen to be the input signals of
fuzzy PSS.
The output of fuzzy PSS is given to the excitation system as
input which would be the control variable. Generally shaft
speed deviation is readily available in practice. Hence, the
acceleration signal can be derived from speed signals
measured at two sampling instant by the following
expression
( kTs ) 
( kTs )  (( k  1)Ts )
→
Ts
(1)
where Ts is the sampling time.
After selecting proper variables as input and output of fuzzy
PSS, it is required to decide the linguistic variables. Usually,
these variables transform the numerical values of the input of
the fuzzy controller to fuzzy values. The number of these
linguistic variables decides the quality of the control which
can be achieved by using the fuzzy controller. If the number of
the linguistic variables increases, the computation time and
required memory will get increased. Therefore, a compromise
between the quality of control and computational time is
needed to choose the number of linguistic variables.
For the power system under study, five linguistic variables
for each of the input and output variables are used to describe
them, as in the following table 1. The two inputs; speed
deviation and acceleration, result in 25 rules for each machine.
Decision table in 2 shows the result of 25 rules, where a
positive control signal is for the deceleration control and a
negative signal is for acceleration control.
Table 1: Input and output linguistic variables
acceleration
(da)
NS
ZE
PS
PB
NB
NB
NB
NS
ZE
NB
NS
NS
ZE
PS
NB
NS
ZE
PS
PB
NS
ZE
PS
PS
PB
ZE
PS
PB
PB
PB
deviation(dω)
NB
NS
ZE
PS
PB
Table 2: Decision table for PSS output
The stabilizer output is obtained by applying a particular
rule expressed in the form of membership function. There are
different methods for finding the output in which Minimum
Maximum and Maximum Product Method are among the most
important ones. Here the Minimum- Maximum method is
used. Finally, the output membership function of the rule is
calculated. This procedure is carried out for all of the rules and
every rule an output membership function is obtained.
Since a non-fuzzy signal is needed for the excitation system
by knowing the membership function of the fuzzy controller
its numerical value should be determined. This is done by the
so called defuzzification process. There are different
techniques for defuzzification of fuzzy quantities such as
Maximum Method, Height Method, and Centroid Method. In
this method the Centroid Method is used.
Figure 1: Membership function of inputs
The example of first rule is;
Rule 1:
“If speed deviation is NS (negative small)
AND acceleration is NB (negative big)
THEN PSS output of fuzzy is NB (negative big)”.
Figure 2: Membership function of output
NB
NS
ZE
PS
PB
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NB
speed
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NEGATIVE BIG
NEGATIVE SMALL
ZERO
POSITIVE SMALL
POSITIVE BIG
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The interval of the each membership functions should be
determined by trial and error procedure, using the simulation
of system to achieve optimum performances.
Five fuzzy subsets have been used and for each of these
fuzzy sets, Triangular membership function (MF) has been
used. These membership functions are shown in Figures 1& 2.
Totally 25 fuzzy subsets result through these fuzzy sub-sets
for computing the output is shown in table 2.
III. FEED FORWARD NEURAL NETWORK
The basic processing element of a neural network is often
called a neuron, by analogy with neurophysiology. Neurons
perform as summing and nonlinear mapping junctions. In
some cases they can be considered as threshold units that fire
when their total input exceeds certain bias levels. Neurons
usually operate in parallel and are often organized in layers.
Each connection strength is expressed by a numerical value
called a weight.
Figure 4: Neural network configuration for calculating optimum scaling
factors
computing optimum
K p and K d , exploiting a neural network
as shown in Fig. 4. The neural network is composed of three
layers, i.e., an input layer, a hidden layer, and an output layer.
The generated active power P and reactive power Q are
selected for input signals to represent the operating condition
of the synchronous machine. X e , the total reactance of the
transmission line, is also selected as an input to represent the
external information. The activation functions for the hidden
layer are sigmoid functions, i.e. f x 
1  e x
and the output
1  e x
characteristics are linear functions. To reduce the required
computation time in the learning process a bias signal is put in
the neural network. For various sets of input data to the neural
network, the optimum values of K p and K d are searched
Figure 3: Single layer feed forward neural network
An elementary feed forward neural network (FNN)
architecture of ‘m’ neurons receiving ‘n’ inputs is shown in
Fig. 3. This type of network can be connected in cascade to
create a multi-layer FNN. In such a network, the output of a
layer is the input to the following layer. Even though the FNN
has no explicit feedback connection, the output values are
often compared with the desired output values, provided by a
“supervisor”. The error between the outputs of the neural
network and the desired values can be employed for adapting
the network’s weights. The error is used to modify weights so
that the error decreases. This type of learning is called
supervisory learning. A set of input and output patterns called
a training set is required for this learning mode.
IV. TUNING THE FPSS
In order to tune the FPSS, speed deviation is scaled
according to the relation  *  K p . and accelerating
power is scaled according to the relation P*  Kd .P . Also,
the output of the FPSS is scaled according to a similar
relation. In the aforementioned relations,
K p and K d are the
speed and acceleration scaling factors, respectively. The
scaling factor for the output U is fixed to a suitable number,
i.e. 0.5 for the system under study. The FPSS is tuned by
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sequentially using nonlinear simulations.
The evaluation of the optimality is checked by the discrete
time performance index J p as shown in equation 2,
n
J p    (k ) .tk
→
(2)
k 0
where  (k ) = speed deviation at the kth sample
tk =
k T = kth sampling time after fault occurrence
n = total number of data acquisition.
A set of learning data is composed for training the neural
network. An optimization technique called LevenbergMarquardt method is used to train the neural network. This
method is more powerful than gradient descent, but requires
more memory of the computer. Since the training process is
done offline, this requirement does not degrade the
performance of the system. The Levenberg-Marquardt update
rule is
W  ( J T .J   I ) 1 J T e
→
(3)
where J is the Jacobian matrix of derivatives of each error to
each weight  is a scalar quantity, and e is the error vector. If
 is very large, the above expression approximates gradient
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descent, while if it is small then it becomes the Gauss-Newton
method. Since the Gauss-Newton method is faster, but tends
to be less accurate when near an error minimum,  is
adjusted during training.
V. CONVENTIONAL POWER SYSTEM STABILIZER
The input to the conventional PSS is speed deviation. The
PSS gain Ks is an important factor as the damping provided by
the PSS increase in proportion to an increase in the gain up to a
certain critical gain value, after which the damping begins to
decrease.
Speed deviation (pu)
International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
Time(s)
The basic structure of the CPSS consists of
 A phase compensation block
 A signal washout block
 A gain block
The conventional fixed power system stabilizer is designed
using a linearized model of the system using control theory.
Therefore, this provides optimum performance for a nominal
operating condition and system parameters with the input
being small enough to justify the linear model. However, its
performance becomes suboptimal following variations in
system parameters and loading conditions from their nominal
values or when the disturbance applied is large.
VI. SYSTEM DESCRIPTION
Time(s)
Figure 8: System response with Conventional PSS
Speed deviation (pu)
Figure 5: Block diagram of the Conventional PSS
Speed deviation (pu)
Figure 7: System response without Stabilizer
The model of system, consists of a 200MVA, 13.8KV Three
phase, 60Hz, 32 pole synchronous generator. The generator is
connected to the network (10000MVA, 230KV) through a
transmission line, as shown in Figure 6. The basic parameter
of the generator is shown in the appendix. Also the generator
is equipped with an AVR and a PSS.
Time(s)
Speed deviation (pu)
Figure 9: System response with Fuzzy controller
Time(s)
Figure 6: The model of Single-machine-connected to the network
Figure 10: System response with Neuro-Fuzzy controller
VII. SIMULATION RESULTS
The proposed methodology is implemented for a singlemachine connected to the network. To investigate the
effectiveness of the neuro-fuzzy controller, we set the three
phase short circuit fault during [0.1 0.2] of time in seconds.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
VIII. CONCLUSION
Power systems could lose synchronism if the low frequency
oscillations are not damped effectively. A conventional power
system stabilizer can provide sufficient damping for a limited
range around its tuning point. To improve the performance of
power system stabilizer, neuro-fuzzy controlling technique has
been proposed.
This proposed power system stabilizer (NFPSS) not only
reduces the settling time of the oscillations but also
minimizing both positive and negative overshoots very
effectively as shown in Figure 10. Thus it can be concluded
stability enhancement is greatly achieved by this neuro-fuzzy
based stabilizer compared with conventional PSS and FPSS.
IX. REFERENCES
[1]. S.M.Radaideh, I.M.Nejdawi, M.H.Mushtaha “Design of
power system stabilizers using two level fuzzy and adaptive
neuro-fuzzy inference systems”, Elsevier: Electrical Power
and Energy Systems Vol.35 (2012), pp. 47- 56.
[2]. D. K. Chaturvedi, O. P. Malik, “Neurofuzzy Power
System Stabilizer ”, IEEE Transactions on Energy
Conversion, Vol. 23, No. 3, (Sep. 2008), pp.887- 894
[3]. S. Kamalasadan, G. Swann, “A novel power system
stabilizer based on fuzzy model reference adaptive controller,"
in IEEE Power Energy Society General Meeting., PES '09.
(July 2009), pp. 1- 8.
[4]. Joe H. Chow, George E. Boukarim, Alexander Murdoch
“Power system stabilizers as undergraduate control design
projects" IEEE Transactions on Power Systems, Vol. 19,
No.1, (Feb. 2004), pp.144- 156
[5]. D. K. Chaturvedi, O. P. Malik, P. K. Kalra “Experimental
Studies with a Generalized Neuron-Based Power System
Stabilizer” IEEE Transactions on Power Systems, Vol. 19, No.
3, (Aug. 2004), pp. 1445- 1453
[6]. T. Hussein, M.S.Saad, A.L.Elshafei, A.Bahgat “Robust
adaptive fuzzy logic power system stabilizer” Elsevier: Expert
systems with applications, Vol. 36, (Dec 2009), pp. 12104–
12112
[7]. A.L. Elshafei, K.A.El-metwally, A.A.Shaltout, “A
variable-structure adaptive fuzzy-logic stabilizer for single and
multi-machine power systems” Elsevier: Control Engineering
Practice, Vol 13, (April 2005), pp. 413- 423
[8]. M.A.Abido, Y.L.Abdel-Magid, “A Hybrid Neuro-fuzzy
Power System Stabilizer for multi machine power systems”
IEEE Transactions on Power Systems, Vol. 13, No. 4, (Nov.
1998), pp. 1323- 1330.
[9]. B.Bayati Chaloshtori, S.Hoghoughi Isfahani, A.Kargar,
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[10]. P.Kundur., “Power system control and stability”," New
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X.APPENDIX
System Data
The Parameters of the Synchronous machine, Turbine and Governor system, Excitation system and Conventional PSS are as
follows.
[a] Synchronous machine constants:
Xd = 1.305 pu
Xd’ = 0.252 pu
Td” = 0.053 sec
Xd’ = 0.296 pu
Xl = 0.180 pu
Tq0" = 0.1 sec
Xq = 0.474 pu
-3
Rs = 2.85*10 pu
Xq"= 0.243 pu
Td’ = 1.01 pu
H = 3.2 sec
F = 60 Hz
[b] Turbine and Governor system constants:
Ka = 3.33
Ki = 0.105
T = 0.07 sec
Td = 0.01 sec
Rp = 0.05
Tw = 2.67sec
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Kp = 1.163
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
[c] Excitation system constants:
KA = 300
Tf
= 0.1 sec
TA = 0.001 sec
Efmax = 11.5 pu
TR = 0.02
Efmin = 11.5 pu
Kf = 0.001
[d] Conventional PSS data:
Kpss = 20
T1 = 0.154 sec
VsMin = 0.2 pu
Tw = 1.41 sec
T2 = 0.06 sec
VsMax = 0.2 pu
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