Fuzzy Based Power System Stabilizer

7/28/2019 Fuzzy Based Power System Stabilizer

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FuzzyBasedPowerSystemStabilizer

Abstract - A new type of Power System

Stabilizer based on fuzzy set theory is

proposed to improve the dynamic

performance of a single machine power

system. To have good damping characteristicover a wide range of operating conditions,

speed deviation ( ) and acceleration ( ) of

a machine are chosen as the input signals to

the fuzzy stabilizer on the particular machine.

These input signals are first characterized by

a set of linguistic variables using fuzzy set

notations. The fuzzy relation matrix, which

gives the relationship between stabilizer

inputs and stabilizer output, allows a set of

fuzzy logic operations that are performed on

stabilizer inputs to obtain the desiredstabilizer output. In this the effect of

variations of of defuzzification techniques on

the performance of FLPSS (fuzzy logic power

system stabilizer) has been investigated.

Key words - PSS, Dynamic stability, fuzzy

based PSS, Single machine infinite bus power

system.

I. INTRODUCTION

Power System Stabilizer (PSS) have beenextensively been used in modern power system

for enhancing stability of the system. The PSS

extends system stability limits by modulating

generator excitation to provide damping to theoscillations of the synchronous machine rotors

with respect to one another. The conventional

Power System Stabilizer (CPSS), introducednearly five decades ago, comprising a cascade

connected lead-lag network with rotor speed

deviation as input signal has made great

contributions in enhancing stability of the system[1].

The conventional fixed structure PSS,designed using a laniaries model provides

optimum performance for a nominal set of

operating and system parameters. However, the

performance becomes sub optimal followingvariations in system parameters and loading

conditions from their nominal values. [2]-[4].In

recent years, adaptive self tuning PSS genetic

algorithm based PSS, artificial neural network

based PSS and Fuzzy Logic based Power SystemStabilizer (FLPSS) [3-5] have been proposed to

provide optimum damping to the system

oscillations under wide variations in systemparameters and operating conditions. An

adaptive self-tuning PSS suffers from a major

drawback of requiring model identification in

real-time, which is possible only with fastmicrocomputers. Although realization of a

variable structure PSS is simple, it results in

frequent change over of PSS structure and henceresults in the problem of chattering. In ANN

based PSS the ANN is trained by using a training

set obtained from off line studies consideration

the laniaries model of the system over thecomplete range of operating conditions.

Thus, the knowledge of the system model isprerequisite for designing ANN based adaptive

PSS. Fuzzy Logic controllers (FLC) are suitable

for systems that are structurally difficult tomodel due to naturally existing non-linearity and

other model complexities. Fuzzy Logic Power

System Stabilizers unlike other power systemstabilizers do not require a mathematical model

of the system.In construct to a conventional PSS, which isdesigned in the frequency domain, a fuzzy logic

PSS is designed in the time domain [4]. The

fuzzy controllers determine the operating

conditions from the measured values and selectthe appropriate actions from rules. Depending on

the system state, the controllers operate in the

range between no action and full action in anextremely nonlinear manner in order to damp out

the oscillations. The fuzzy controller in it has no

dynamic component, i.e. it can immediatelyperform the desired control action.

II.SYSTEMINVESTIGATEDA machine infinite bus system with

synchronous generator provided with IEEE

TypeST1 static excitation system is considered.Nominal parameters of the system are taken from

ref [6]


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III. DYNAMICMODELOFTHE

SYSTEM

Following assumptions have been made in

developing the dynamic model of the system.

1. The mechanical power input remainsconstant during the period of the transient.

2. Damping or a synchronous power is

negligible.3. The synchronous machine can be represented(electrically) by a constant voltage source

behind a transient reactance.

4. The mechanical angle of the synchronousmachine rotor coincides with the electrical

phase angle of the voltage behind transient

reactance.5. If a local load is fed at the terminal voltage of

the machine, it can be represented by a

constant independence (or admittance) toneutral.

The non-linear model of the system is obtained

as follows

( )

2

m ed T T

dt H

=

(1)

02 ( )d

fdt

=

(2)

11( ) /t R

dvE V T

dt

=

(3)

2 [ ]fd fd

fd fd fd

adu

d Ef R R L

dt L

=

(4)

a linear model of the system is obtained by line

arising the nonlinear model around a nominal

operating point(transfer function model is givenin the Fig. (1). The dynamic model of the

liberalized system in the state space form is

obtained from the transfer function model in the

form: X AX p= + &

(5)

Where

1 2

0

3 4 3

3 3 3

5 6

02 2 2

2 0 0 0

10

10

D

A

R R R

K K K

H H H

f

A K K K K

T T T

K K

T T T

=

1

fd

X

v

=

,

1

2

0

0

0

H

=

,

P= [ mT ]

Fig1.ModelforConstantEfd

Fig. 2. Shows that transfer function of the systemwith PSS. The linear state space model is given

in the form

X AX p= + &

(6)

1 2

3 4 3 3

3 3 3 3

5 6

1 2

1 51 1 52 1 53 1 55

2

2 2 2 2 2

0 0 02 2 2

2 0 0 0 0 0

10 0

10 0 0

. . . 10 0

2 2 2

10

D

A A

R R R

STAB D STAB STAB

R

K K K

H H H

f

K K K K K K

T T T T A K K

T T T

K K K K K K

H H H T

T a T a T a T aT

T T T T T

=

+


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X =

2

1

fd

t

v

v

u

,

3

3

1

2

10

2

0 0

0

02

02

A

STAB

STAB

H

K K

T

K

H

T K

T H

=

m

ref

Tp

v

=

Fig2.SystemModelwithCPSS

IV. FUZZYLOGICPSS

Selection of Input Signals to Fuzzy Logic PSS:For the present investigations generators

speed deviation ( ) and acceleration ( ) arechosen as the input signals to the FLPSS.

In practice, only shaft speed deviation ( ) isreadily available. The acceleration ( ) isderived from the measured at twosuccessive sampling instants

(KT) =( ) [( 1) ]KT K T

T

Where T is the sampling period.

SelectionofLinguisticVariables:The number of linguistic variables

determines the quality of the control, which canbe achieved using Fuzzy Logic Controllers. As

the numbers of linguistic variables increases, the

quality of control improves at the cost of

increased computational time and computermemory. A compromise is needed between the

two. For the power system under study, seven

linguistic variables for each of the inputs and the

output signals are considered. These seven

linguistic variables are PB (positive big), NS(negative small), NM (negative medium) and NB

(negative big). A choice of 7 linguistic variables

results in a set of 49IF-THEN rules (Table.1)shows the decision table. This table is obtained

from the expert knowledge of the operators.

In order to obtain the minimum and themaximum values of the stabilizer inputs thedynamic performance of the system without PSS

is obtained for different magnitudes of

perturbations. After choosing the linguisticvariables, it is required to determine the

membership functions for these linguistic

variables. Generally gauss Ian, triangular ortrapezoidal membership functions are prevalent.

Here triangular membership function is used to

define the degree of membership (Fig. 3.).Degree of membership plays a very important

part in designing a fuzzy controller.

Fig3.SymmetricalTriangularMembership

function

Now it is required to find the fuzzy regionfor the output for each fuzzy rule, for which

Madman implication is used.

Decisiontable1.


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1

Fig4.SystemModelwithFLPSS

V COMPARISON OF PERFORMANCE OF

THESYSTEMWITHCPSSANDFLPSS

Fig. 5 and 6 shows the transient response

for and respectively following a 5 % stepchange in mechanical torque with conventionalPSS and FLPSS obtained considering a linear

model of the system. The scaling factors for

and.

the stabilizing signals are respectively

5000, 350 and 500. Examination of the responses

clearly shows that dynamic performance of the

system with FLPSS is very close to that withconventional PSS and is in fact slightly better in

terms of settling time. Further, in order to

compare the dynamic performancesquantitatively a quadratic performance index is

evaluated

2 2

00[ ( )] [ ( )]

kJ t kt t

== =

Fig5.SpeeddeviationVsTimeTable 2. Shows the value of J for CPSS and

FLPSS.it also shows the peak overshoot of the

dynamic response for and . COGdefuzzifier has been used and symmetrical

triangular membership functions with equal basewidths have been considered.

Table2


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Fig.6. Rotor angle deviation Vs

Time

VI. EFFECT OF VARIATION IN

COORDINATES OF MEMBERSHIP

FUNCTIONAn attempt has been made towards gain

tuning of the fuzzy logic controller by altering

the coordinates of the membership functions.

Center of Gravity / Area (COG/COA) defuzzifieris used in the analysis.

Fig.7 shows a triangular membership

functions, , , are the coordinates of the

function. denotes the left coordinate of the

base denotes the abscissa of the peak and

denotes the right coordinates of the base. Let 1 ,

2 and 3 be the X coordinates of the peaks of

the membership functions PS, PM and PB

respectively.

For the membership functions PS let 1c = 1

For the membership functions PM let y = 2 -

1

For the membership functions PB let

z = 3 - ( 1 + 2 )

=3-(y + 1c )

Fig.7.

Fig.8.Trangular Membership Function

At this stage, we assume that the separation

between the peaks vary in geometric ratio i.e.

1

y z

c y= .It can be clearly seen from Fig (9) that

the coordinates of PS, PM and PB are1 2 1 2 3(0, , ), ( , , ) and 2 3( , ,...) . 3 =3.0,

the positive limit of the universe of discourse(universe of discourse is 3.0 to 3.0.

The value of 1c is varied over a wide

range in order to obtain its optimum value. Figs.(9) and Fig(10) show the transient response for

and for a step increase in mechanicaltorque i.e. Tm = 0.05 pu for 1c = 1.2,1.0 and0.4.Examination of the responses shows that the

maximum peak overshoot is nearly the same for1c = 1.2and 1c = 1.0 and increases slightly for1c = 0.4 whereas there is considerable reduction

in setting time as 1c is reduced to 0.4 whereasthere is considerable reduction in setting time for

1c is equal to 0.4.Examination shows that the

performance index J decreases slightly while thesettling time decreases to about 50% with change

in 1c from 1.2 to 0.4.The change in peak

deviation is quite insignificant.Fig. 9.Speed deviation Vs Time


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Fig.10. Rotor angle deviation Vs Time

VII CONCLUSION

A systematic approach for realizing Fuzzy

Logic PSS has been presented. An attempt hasbeen made to study the effect of variation of co-

ordinates of the membership functions and

scaling factors on performance of the FLPSS.

Performance of the FLPSS has been comparedwith CPSS. Following are the significant results

of the investigations carried out in this paper:

1. Performance of an optimum conventionalPSS is similar to that of FLPSS.

2. Unsymmetrical triangular membership

functions with 1c = 0.4 provides the bestdynamic performance of the FLPSS.

3. The scaling factors decrease inversely withincrease in magnitude of perturbation.

4. FLPSS using adaptive scaling factors provide

good performance.

Fuzzy Based Power System Stabilizer

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