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# A Novel approach for tuning Power System Stabilizer (SMIB

## system) using Genetic Local Search technique

Department of Electrical Engineering
Government College of Technology
Coimbatore, INDIA

Dr.A.EBENEZER JEYAKUMAR
Department of Electrical Engineering
Government College of Technology
Coimbatore, INDIA

Abstract: - The genetic local search technique (GLS) hybridizes the genetic algorithm (GA) and
the local search (such as hill climbing) in order to eliminate the disadvantages in GA. The
parameters of the PSS (gain, phase lead time constant) are tuned by considering the single
machine connected to infinite bus system (SMIB). Here PSS are used for damping low
frequency local mode of oscillations. Eigen value analysis shows that the proposed GLSPSS
based PSS have better performance compared with conventional and the Genetic algorithm
based PSS (GAPSS). Integral of time multiplied absolute value of error (ITAE) is taken as the
performance index of the selected system. Genetic and Evolutionary algorithm (GEA) toolbox
is used along with MATLAB/SIMULINK for simulation.
Key-words: - Genetic local search, Power system oscillations, Power system stabilizer, Genetic
algorithms, SMIB, K-constants
power system utilities still prefer the
1. Introduction
reasons behind that might be the ease of onPower systems experience lowline tuning and the lack of assurance of the
frequency oscillations due to disturbances.
stability related to some adaptive or variable
These low frequency oscillations are
structure techniques.
related to the small signal stability of a
Unlike
other
optimization
power system. The phenomenon of stability
techniques,
Genetic
Algorithm
(GA)
works
of synchronous machine under small
with
a
population
of
strings
that
represent
perturbations is explored by examining the
different potential solutions therefore, GA has
case of a single machine connected to an
implicit parallelism that enables it to search
infinite bus system (SMIB). The analysis of
the problem space globally and the optima
SMIB  gives physical insight into the
can be located more quickly when applied to
problem of low frequency oscillations.
complex
optimization
problem.
These low frequency oscillations are
Unfortunately,
recent
research
has
identified
classified into local mode, inter area mode
some deficiencies in GA performance. This
and torsional mode of oscillations. The
degradation in efficiency is apparent in
SMIB system is predominant in local mode
applications with highly epistatic objective
low frequency oscillations.
These
functions, i.e. where parameters being
oscillations may sustain and grow to cause
optimized are highly correlated. In addition,
system separation if no adequate damping
the premature convergence of GA represents
is available. In recent years, modern control
a major problem.
theory have been applied to power system
In this proposed genetic local search (GLS)
stabilizer (PSS) design problems. These

approach, GA is hybridized with a local
search
algorithm to enhance its capability of
variable structure control, and intelligent
exploring
the search space and overcome the
control.
premature
convergence. The design problem
Despite the potential of modern
control techniques with different structures,

## with mild constraints and an eigenvaluebased objective function.

The GLS algorithm is employed
to solve this optimization problem and
search for the optimal settings of PSS
parameters. The proposed design approach
has been applied to SMIB system. Eigen
value analysis and simulation results have
been carried out to assess the effectiveness
and robustness of the proposed GLSPSS to
damp out the electromechanical modes of
oscillations and enhance the dynamic
stability of power systems.

Eq' =

K3
K3 K 4

fd
1 sTd' 0 K 3
1 sTd' 0 K 3

(3)
Vt K 5 K 6 E q'
(4)
The K-constants are given in appendix.
The system data are as follows :
Machine (p.u):
xd = 0.973 xd' = 0.19
xq = 0.55

Td' 0 = 7.765 s

(5)
D

2. System investigated
A single machine-infinite bus
(SMIB) system is considered for the
present
investigations.
A
machine
connected to a large system through a
transmission line may be reduced to a
SMIB system, by using Thevenins
equivalent of the transmission network
external to the machine. Because of the
relative size of the system to which the
machine is supplying power, the dynamics
associated with machine will cause
virtually no change in the voltage and
frequency of the Thevenins voltage
(infinite bus voltage). The Thevenin
equivalent impedance shall henceforth be
referred to as equivalent impedance (i.e.
Re+jXe).
The synchronous machine is
described as the fourth order model. The
two-axis
synchronous
machine
representation with a field circuit in the
direct axis but with out damper windings is
considered for the analysis. The equations
describing the steady state operation of a
synchronous generator connected to an
infinite bus through an external reactance
can be linearized about any particular
operating point as follows(eq:1-4):

d 2
Tm P M
dt 2
(1)
P K1 K 2 Eq'

(2)

= 0.0

H = 4.63

re = 0.0

xe = 0.997

(6)

## KA = 50.00 TA= 0.05 s

(7)

Exciter :
Operating point :

Vt 0 = 1.0

P0 = 0.9

Q0 = 0.1

0 = 65 0

(8)

## The interaction between the speed and

voltage control equations of the machine is
expressed in terms of six constants k 1-k6.
These constants with the exception of k3,
which is only a function of the ratio of
impedance, are dependent upon the actual
excitation levels in the machine.
angular speed deviation () as input signal
has been considered. Fig.1 shows the
linearized model of the single machine
connected to large system (SMIB) around the
operating point.

## which depend on operating conditions.

Control matrix B depends on system
parameters only. Control signal U is the
PSS output. From the operating
conditions and the corresponding
parameters of the system considered, the
system eigenvalues are obtained.

## Fig.1 Linearized model of SMIB system

From the transfer function block diagram,
the following state variables are chosen for
single machine system. The linearized
differential equations can be written in the
form state space form as
0

(9)

## X(t) A.x(t) BU(t)

Where
X(t) = [ Eq Efd]T

(10)

A=

0
314
0
D M
K1 M
K2 M
K4
0
1 K 3T 'do
K A TA K 5
0
K A TA K 6
(11)

B 0

KA

TA

(12)

## System state matrix A is a

function of the system parameters,

## 3. Transfer function model of PSS

and design considerations
The exciter considered here is only
having the gain of KA and the time constant
of TA. The typical PSS consists of a washout
functions),and a gain. It is well known that
the performance of the PSS is mostly
affected by the phase compensator and the
gain. Therefore, these are the main focus of
the tuning process. Two first order phase
compensation blocks are considered. If the
degree of compensation required is small, a
single first-order block may be used.
Generally slight under compensation is
preferable so that the PSS does not contribute
to the negative synchronizing torque
component.
0 Wash out function (Tw) has the
value of anywhere in the range of 1 to 20
0
seconds. The main considerations are that it
should
1 T 'do be long enough to pass stabilizing
signals at the frequencies of interest relatively
1 TA
unchanged,
but not so long that it leads to
undesirable generator voltage excursions as a
result of stabilizer action during systemislanding conditions. For local mode of
oscillations in the range of 0.8 to 2 Hz, a
wash out of 1.5 sec is satisfactory. From the
view point of low-frequency interarea
oscillations, a wash out time constant of 10
seconds or higher is desirable, since lowtime constants result in significant phase lead
at low frequencies.
The stabilizer gain K has an
important effect on damping of rotor
oscillations. The value of the gain is chosen
by examining the effect for a wide range of
values. The damping increases with an
increase in stabilizer gain upto a certain point

## beyond which further increase in gain

results in a decrease in damping. Ideally,
the stabilizer gain should be set at a value
corresponding to maximum damping.
However the gain is often limited by other
considerations.
The transfer function
model of the SMIB system with the PSS is
given in Fig.2.
The transfer function of Power
System Stabilizer is given by,
10s
1 sT1 2
H1 (s) K *
*(
)
(1 10s) 1 0.05s

KPSS gain
Twwashout time constant
A low value of T2=T4=0.05 sec is chosen
from the consideration of physical
realization. Tw=10 sec is chosen in order to
ensure that the phase shift and gain
contributed by the wash out block for the
range of oscillation frequencies normally
encountered is negligible. The wash out time
constant (Tw) is to prevent steady state
(13)
voltage off
sets as system frequency changes.

Where,

## Fig.2 SMIB system with power system stabilizer

lead-lag networks for the PSS T1=T3 .
Hence now the problem reduces to the
tuning of gain (K) and T1 only.
The parameters of the PSS
obtained for the damping ratio of 0.3. The
0.8-2 Hz for the local mode of oscillations.
In this SMIB system only local mode of
oscillations are considered for the tuning of
PSS. The local mode of oscillation occurs
when a machine supplies power to a load
center over long, weak transmission lines.
Pole placement technique is used for the
tuning of CPSS design .

## The eigenvalues of the above

A matrix are obtained using Matlab. It is
evident from the open loop eigenvalues, the
system without PSS is unstable and therefore
it is necessary to stabilize the system by
shifting these eigenvalues to the LHP and far
off from the imaginary axis. The location of
the desired eigenvalues is calculated by
choosing a damping factor for the dominant
root.
The real part is -n and the
imaginary part is
n 1
Where

## n is the undamped natural frequency of the

corresponding root.
For the determination of PSS parameters a
damping factor of =0.3 is chosen
(maximum damping). Corresponding to
this damping factor the desired eigenvalues
are obtained as.
2
1= -n+ n 1

2= -n- n 1
It is to be noted here that the some of the
eigenvalues need not be shifted since they
are placed for off in LHP. If any
electromechanical modes of oscillations are
present then PSS needs to be added to
enhance the dynamic stability of the
system. By using Decentralized modal
control (DMC) algorithm the parameters of
the conventional power system stabilizer
are found.
2

## 3.2. GA based design of PSS

Minimizing the following error
criteria the controller generates the
parameters of the gain and the phase lead
time constant.
In this paper Integral of time
multiplied absolute value of error (ITAE)
 will be minimized through the
application of a genetic algorithm, as will
presently be elucidated. The GA works on a
coding of the parameters (K, T) to be
optimized rather than the parameters
themselves. In this study Gray coding was
used where each parameter was represented
by 16 bits and a single individual or
chromosome
was
generated
by
concatenating the coded parameter strings.
In contrast to traditional stochastic search
techniques the GA requires a population of
initial approximations to the solution. Here
30 randomly selected individuals were used
to initialize the algorithm. The GA then
proceeds as follows:
3.2.1. Fitness determination
The first step of the GA
procedure is to evaluate each of the
them. Each individual was evaluated by

## decoding the string to obtain the Lead-lag

compensator parameters which were then
applied in a Simulink representation of the
closed-loop system.
1. The five fittest individuals were
automatically selected while the remainders
were selected probabilistically, according to
their fitness. This is an elitist strategy that
ensures that the next generation's best will
never degenerate and hence guarantees the
asymptotic convergence of the GA.
2. Using the individuals selected above the
next population is generated through a
process of single-point cross-over and
mutation. Mutation was applied with a very
low probability of 0.001 per bit.
Reproduction through the use of crossover
and mutation ensures against total loss of any
genes in the population by its ability to
introduce any gene which may not have
existed initially, or, may subsequently have
been lost.
3. This sequence was repeated until the
algorithm was deemed to have converged (50
iterations). As was indicated previously the
simulation and evaluation of the GA tuned

## 3.3. GLS Algorithm

Step 1: set the generation counter k=0 and
generate randomly n initial solutions, X0 =
{xi, i=1.n}. The ith initial solution xi
can be written as xi =[p1 p2pjpm], where
the jth optimized parameter pj is generated by
randomly selecting a value with uniform
probability over its search space [p imin ,pjmax].
These initial solutions constitute the parent
population at the initial generation x 0. Each
individual of x0 is evaluated using objective
function J. set x=x0;
Step 2: optimize locally each individual in x.
replace each individual in x by its locally
optimized version. Update the objective
function values accordingly.
Step 3: search for the optimum value of the
objective function, Jmin. set the solution
associated with Jmin as the best solution, xbest
with an objective function of Jbest.

## Step 4: check the stopping criteria. If one of

them is satisfied then stop, else set k=k+1 and
go to step 5.
Step 5: set the population counter i=0;
Step 6: draw randomly, with uniform
probability, two solutions x1 and x2 from x.
apply the genetic crossover and mutation
operators obtaining x3;
Step 7 : optimize locally the solution x3 and
obtain x3;
Step 8 : check if x 3 is better than the worst
solution in x and different from all solutions
in x then replace the worst solution in x by x 3
and the value of objective by that of x3;
Step 9: if i=n go to step 3, else set i=i+1 and
go back to step 6;
To demonstrate the effectiveness and
robustness of the proposed GLSPSS over a

## simulated using these Simulink diagrams

for 0.05 p.u step change in mechanical
torque Tm. The dynamic response curves
for the variables change in speed deviation
(), change in rotor angle deviation ()
and change in terminal voltage deviation
(Vt) of the single machine system with
PSS are plotted for three different types of
power system stabilizers (PSS) are shown
in Figs. 3 5. It is observed that the
oscillations in the system output variables
with PSS are well suppressed. The Table I
shows various types of PSS and its
parameters after tuned by conventional,
genetic and genetic local search technique.

Table 1

4. Comparision of various
design techniques
The linearized incremental state
space model for a single machine system
with its voltage regulator with four state
variables has been developed. The single
machine system without PSS is found
unstable with roots in RHP. The system
dynamic response without PSS is simulated
using Simulink for 0.05 p.u disturbance in
mechanical torque. MATLAB coding is
used for conventional PSS, Genetic PSS,
and Genetic local search (GLS) PSS design
techniques. The final values of gain (K),
and phase lead time constant (T) obtained
from all the techniques are given to the
curves for the variables , and Vt are
taken from the simulink. The system
responses curves of the conventional PSS
(CPSS), GA based PSS as well as GLS
based PSS are compared.
Shaft speed deviation is taken as the input
to the all the Power system stabilizers. So
the PSS is also called as delta-omega PSS.
The system dynamic response with PSS is

## PSS parameters of various pss for

single machine system.
PSS type

PSS parameters

CONVENTIONAL
GA BASED PSS

K = 7.6921
T =0.2287
K =26.5887
T=0.2186
K=35.1469
T=0.2078

## 4.1. Simulation results

1.Performance of fixed-gain CPSS is better
for particular operating conditions. It may not
yield satisfactory results when there is a
drastic change in the operating point.
2.
Dynamic response shows
that the GA based PSS has optimum response
and the response is smooth and it has less
over shoot and settling as compared to
conventional PSS.
3.
As
compared
to
the
conventional PSS & GA based PSS the
proposed genetic local search (GLS) based
design of PSS gives the optimum response

## and the response is smooth and it has reduced

settling time.
4.
The time multiplied absolute
value of the error (ITAE) performance index
is considered. The simulation results show
the proposed Genetic local search based PSS
can work effectively and robustly over a wide
conventional and GA based design of PSS.
5. The response curves shows that GLS PSS
has less over shoot and settling time as
compared to the GA PSS and the traditional

## Fig .5 Vt Vs time for normal load condition of the SMIB system

Conclusion
In this study, a genetic local
search algorithm is proposed to the PSS
design problem. The proposed design
approach hybridizes Genetic Algorithm
with a local search to combine their
different strengths and overcome their
drawbacks (i.e.) GA explores the search
space (spectrum of optimum location
points either maxima or minima) before it
gives data to the local search technique.
Then local search technique is the best
technique than GA to find the optima
(either maxima or minima). The potential
of the proposed design approach has been
demonstrated by comparing the response
curves of various power system stabilizer
(PSS) design techniques.
Optimization results show that the
proposed approach solution quality is
independent of the initialization step. Eigen
value analysis reveals the effectiveness and
robustness of the proposed GLSPSS to
damp out local mode of oscillations. In
addition, the simulation results show that
the proposed GLSPSS can work effectively

conditions and system configurations.

Appendix
Derivation of k-constants
All the variables with subscript 0
are values of variables evaluated at their predisturbance steady-state operating point from
the known values of P0 , Q0 and Vt0.
P0Vto
iq 0 =
(14)
2
( P0 x q ) (Vt 20 Q0 x q ) 2
vd 0 = iq 0 xq
(15)
vqo = Vt 20 vt20

id 0 =

Q0 xq iq20
vq 0

(17)
Eq 0 = vq 0 id 0 xq

(18)

(16)

1

0 = tan

(19)

(vd 0 xeiq 0 )
(vq 0 xeid 0 )

(20)
K1 =

xq xd'
xe x

'
d

iq 0 E0 sin 0

K2 =

E0 sin 0
xe xd'

K3 =

xd' xe
xd xe

K4 =

x q x d'
x e x d'

Eq 0 E0 cos 0
xe xq
(22)

(24)

K5=
xd ' vq 0
vd 0
E0 cos 0
E0 sin 0
xe x q Vt 0
xe xd' Vt 0
xq

(25)
K6 =

vq 0

xe
xe xd' Vt 0

## K6 Change in Vt with change in Eq

constant rotor angle

(21)

(23)

E 0 sin 0

K2
Change in Te for a change in d axis
K3
Impedance factor
K4
Demagnetising effect of a change in
rotor angle
K5
Change in Vt with change in rotor
angle for constant Eq

(26)

Nomenclature
All quantities are per unit on
machine base.
D
Damping Torque Coefficient
M
Inertia constant

Angular speed

Rotor angle
Id, Iq Direct and quadrature components of
armature current
Xd, Xq Synchronous reactance in d and q axis
Xd, Xq Direct axis and Quadrature axis
transient reactance
EFD
Equivalent excitation voltage
KA
Exciter gain
TA
xciter time constant
Tm,Te Mechanical and Electrical torque
Tdo
Field open circuit time constant.
Vd,Vq Direct and quadrature components of
terminal voltage
K1
Change in Te for a change in with
constant flux linkages in the d axis

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