Comparison of optimization technique of power system stabilizer by using gea

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME
225
COMPARISON OF OPTIMIZATION TECHNIQUE OF POWER SYSTEM
STABILIZER BY USING GEA /PHASE COMPENSATION TECHNIQUE
Mrs. Babita Nanda
Associate Professor EEE Department,
Malla Reddy College of Engineering for Women, Hyderabad, India
ABSTRACT
Power system stability is the ability of an electrical power system, for given operating
conditions, to regain its state of operating equilibrium after being subjected to a physical disturbance,
with the system variables bounded, so that the entire system remains intact and the service remains
uninterrupted”. Traditionally the excitation system regulates the generated voltage and there by helps
control the system voltage. The automatic voltage regulators (AVR) are found extremely suitable for
the regulation of generated voltage through excitation control. But extensive use of AVR has
detrimental effect on the dynamic stability or steady state stability of the power system as
oscillations of low frequencies (typically in the range of 0.2 to 3 Hz) persist in the power system for
a long period and sometimes affect the power transfer capabilities of the system. The power system
stabilizers (PSS) were developed to aid in damping these oscillations by modulation of excitation
system and by this supplement stability to the system .The PSS is designed by taking the
consideration of gain block, signal washout and two identical phase lead compensators and the
parameter are optimized by two alternative approach i.e. Phase compensation Technique & Genetic
And Evolutionary Algorithm.
Keywords-Power system stabilizer; Genetic algorithm; Matlab
1.INTRODUCTION
The stabilizer parameters are selected in such a manner to damp the power system oscillation.
In this paper optimization technique has been compared by using phase compensation and GEA
algorithm. The objective function allows the selection of the stabilizer parameters to optimally place
the closed-loop Eigen values in the left hand side of the complex s-plane. The single machine
connected to infinite bus system is considered for this study. The effectiveness of the stabilizer tuned
using the best technique; in enhancing the stability of power system. PSS is used to damp oscillations
by controlling its excitation using auxiliary stabilizing signals.
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
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ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 4, July-August (2013), pp. 225-231
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226
up
∆ w
Gain Signal washout Phase compensator
Fig-1 Transfer function model of conventional PSS
2.SYSTEM INVESTIGATED
The step-by-step procedure for optimizing PSS parameters by
2.1. Phase compensation technique is as follows:
2.1.1 Computation of natural frequency of oscillation (ωn) from the mechanical loop: Neglecting the
effect of damping D, the characteristic equation of the mechanical loop is written as:
2
o 1M s + ω K = 0
The roots of equation are: 1 o
1 2
K ω
s , s = ± j
M
Thus the natural frequency of oscillation is: 1 o
n
K ω
ω =
M
2.1.2. Computation of ∠GEP (Phase shift between stabilizing signal u and ∆Te)
The transfer function relating stabilizing signal up and ∆Te, setting ∆δ = 0 is :
e
p
∆T
GEP(s) =
u
Let γ be the phase angle of GEP(s) at ns = jω
2.1.3. Design of phase compensator Gc
The phase compensator Gc is designed to provide required degree of phase
compensation. For 100 % phase compensation:
∠Gc(j ωn ) + ∠GEP(j ωn ) = 0
The transfer function of phase compensator of the damping controller is given as:
1
2
1+sT
Gc(s) =
1+sT
1 2T = a T
Where,
1+sinγ
a =
1-sinγ
and 2
n
1
T =
ω a
Depending upon the phase shift one or two stages of the phase compensator are connected in
cascade.
Ks w
w
s T
1 + s T
1 3
2 4
(1 + s T )( 1 + s T )
(1 + s T )( 1 + s T )

227
2.1.4. Computation of optimum gain Ks of damping controller
The required gain setting Ks for the desired value of damping ratio ξ, is
obtained from:
n
s
c
2 ξ ω M
K =
|GEP| |G |
Where |GEP| and |Gc| are evaluated at ns = jω
Damping ratio ξ = 0.5 is assumed for electromechanical mode. The washout
time constant Tw = 10 seconds is chosen in present studies. Assuming two
identical cascade connected lead blocks where T1=T3 and T2=T4. Only three
parameters are to be optimized i.e. Kp, T1, T2.The optimum parameters of
PSS obtained using Phase Compensation Technique are
T1 = T3 = 0.2977 sec T2 = T4= 0.0972 sec Kp = 14.3
2.2. GEA (Genetic and Evolutionary Algorithm)
The Genetic and Evolutionary Algorithm is as follows:
2.2.1. Creation of initial population:
The initial population is created randomly within the upper and lower bounds of
the variables specified.
2.2.2. Evaluation of individuals:
A performance index J is defined to evaluate the individuals. For each chromosomes, the
value of performance index is obtained ,which is assigned to it as its fitness value .The
chromosomes are ranked in the descending order of the fitness value in the population.
2.2.3. If the optimization criteria (i.e. specified value of J and / maximum number of generations) is
not satisfied ,the creation of new generation starts as following (step 2.2.4-2.2.8):
2.2.4. Selection:
On the basis of the ranking, the chromosomes are selected for recombination .Each
individual in the selection pool receives a reproduction probability depending on its own
performance index and the performance indices of the other individuals in the selection pool.
Different methods for selectionare,Roulette-wheel selection ,stochastic universal sampling
,local selection ,truncation selection and tournament selection .
2.2.5. Recombination:
Recombination produces new individuals by combining the information contained in the
parents (mating population).This is done, by combining the variables value of the parents.
Depending on the representation (i, e, binary, real valued etc.) of the variables different
methods are used .Discrete Recombination can be applied to all the variable representations.
2.2.6. Mutations:
By Mutation the individuals are randomly altered. These variations (mutation step)are mostly
small and applied to the variables of individuals with low probability specified by mutation
rate. The mutation of real values means, that the randomly created values are added to the
variables with a low probability.
2.2.7. Reinsertion:
Reinsertion scheme determines which individuals are to exist in the new population. The
selection of reinsertion scheme depends on the selection scheme used.
The elitist reinsertion scheme produces less offspring than parented and replaces the worst
parents. However, the fitness-based reinsertion scheme produces more offspring than needed
for reinsertion and reinsert only the best offspring. The Elitist reinsertion combined with

228
fitness-based reinsertion, which prevents the loosing of information is the recommended
method .At each generation, a given number of the least fit parents is replaced by the same
number of most fit offspring. The best individuals can live for many generations.
2.2.8. Migration:
The regional model divides the population into multiple subpopulations. These
subpopulations evolve independently of each other for certain number of
generations(isolation time ).After the isolation time is over a number of individuals is
distributed between the subpopulations .The migration rate ,the selection method of the
individuals for migration and the scheme of migration determines how much genetic diversity
can occur in the subpopulation .The most general migration strategy is that of unrestricted
migration .For each subpopulation, a pool of potential immigrants is constructed from the
other subpopulation. The individual migrants are then uniformly at random determined from
the pool.
2.2.9. Termination:
A number of methods are available for termination of the optimization, like maximum
number of generations, maximum computing time in minutes, minimal difference to defined
optimum, running mean of best objective values, minimal standard deviation of all current
objectives values etc. Once the predefined termination criterion is met, the optimization
algorithm terminated.
2.3. Steps of Algorithm Using MATLAB Tool Box
The optimization of controller parameters using GEA presented in this thesis is done using
GEA toolbox along with MATLAB software package .While applying GEA, a number of parameters
affects the speed of convergence of the algorithm. The typical parameters /options for applying GEA
are defined as follows:
2.3.1. Number of individuals:
An individual is string of variables (i.e. parameters to be optimized).The choice
of number variables depends on the problem. The larger and more complex a problem is the
higher the number of individuals ought to be.
2.3.2. Generation Gap:
It is the fraction of the population to be reproduced every generation .If
generation gap >1,more offspring than individuals in the population are
produced. However, if generation gap <1, less offspring than the individuals in
the population are produced, some parents survive in next generation.
2.3.3. Reinsertion rate:
This options defines how much parents are replaced by the produced offspring.
The reinsertion rate of 1 means all the parents may be replaced by offspring.
2.3.4. Mutation rate:
It is the factor of how many variables per individuals are mutated.
Mutation rate =1 means on an average 1 variable per individual is mutated.
2.3.5. Mutation range:
This option defines the range of the mutation steps for every variable depending on the size
of the domain of the respective variables.
2.3.6. Mutation Precision:
This option defines the precision of the mutation steps depending on the mutation range.
2.3.7. Migration interval:
This option defines the number of generations between successive migrations. It is also called
as isolation time.

229
3. FLOW CHART OF GEA
GEN=1
GEA (Genetic and Evolutionary Algorithm -- The optimum PSS parameters are obtained by using
GEA, minimizing the following performance index,
J 2
0
( )w dt
∞
= ∆∫
The range of the parameters over which search is carried out are given below:
0.1 < T1< 0.5 0.1 < T2 < 0.5 5 <Kp< 20 T1 = T3 T2 = T4
J is evaluated considering step increase in Pm by 5%.
Apply GA operators:
selection,crossover and mutation
NO
YES
Specify the parameters for GA
Generate initial population
Time-domain simulation
Find the fitness of each individual
in the current population
Gen.>Max.G
en?
Gen.=
Gen.+1
start
STOP

230
Fig-2: shows the variation of value of objective function J corresponding to best individual in each
generation with the generation number. The optimum parameters of PSS obtained using GEA are
T1 = T3 = 0.367 sec T2 = T4 = 0.1863 sec Kp = 11.58
Dynamic responses for the system are obtained with PSS optimized by two alternative
approaches considering a step increase in mechanical power Pm by 5%. (i.e. ∆ Pm = 5%)
The values are taken for showing the comparison is shown in the below:
Number individuals---------------10
Selection. Name-------------------selsus
Selection. Generation Gap-------0.9
Selection. Reinsertionrate-------0.8
Selection. Reinsertion Method --2
Recombination. Name------------recdis
Recombination. Rate--------------0.7
Mutation.Name--------------------mutreal
Termination. Running Mean------0
Termination. Method---------------4
VLUB=[1 1 -20 -10.5;10 10 10]
4. CONCLUSION
It is clear that the responses with GEA optimized PSS settles faster than the phase
compensation Technique. Hence the optimum parameters obtained by GEA are considered.
5. ACKNOWLEDGMENT
I would like to express sincere gratitude to my Guide Prof. M. L. Kothari. He is Emeritus
Professor in Electrical Department from IIT DELHI .It has been my proud privilege to work under
Prof. M. L. Kothari, a luminary in the field of power system engineering. I am very grateful for
continued guidance, valuable advice and suggestion and the co-operation extended throughout the
project work

231
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