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Large Power SystemsStability EnhancementUsing a Delayed OperationFuzzy Logic Power SystemStabilizerS. A. Gawish, F. A. Khalifa, W. Sabry, M. A. L.BadrPublished online: 30 Nov 2010.

To cite this article: S. A. Gawish, F. A. Khalifa, W. Sabry, M. A. L. Badr (1999)Large Power Systems Stability Enhancement Using a Delayed Operation FuzzyLogic Power System Stabilizer, Electric Machines & Power Systems, 27:2, 157-168,DOI: 10.1080/073135699269361

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Electric Machines and Power Systems, 27:157–168, 1999Copyright c° 1999 Taylor & Francis, Inc.0731-356X / 99 $12.00 + .00

Large Power Systems Stability EnhancementUsing a Delayed Operation Fuzzy Logic

Power System Stabilizer

S. A. GAWISHF. A. KHALIFAW. SABRY

Dept. of Elec. Power & EnergyM.T.C.Cairo, Egypt

M. A. L. BADR

Dept. of Elec. PowerFaculty of Eng.Ain-shams Univ.Cairo, Egypt

This paper presents a novel control operation of fuzzy logic power system sta-bilizer (FLPSS) for stability enhancement of a large-scale power system. TheFLPSS is applied for each machine in the system while its operation is de-layed for a short period almost equal to the �rst half cycle of the power systemelectromechanical oscillations. The application of this controller is successfulin damping large-scale power system oscillations. In order to accomplish bestdamping characteristics, two signals are chosen as inputs to the FLPSS; de-viation of power angle ( D Ç6) and deviation of speed derivative ( D Ç!) of eachsynchronous machine in the system. These two variables have e� cient eŒectson damping the oscillations of both frequency and terminal voltage signals andhence the system gives better stability. The eŒectiveness of this delayed oper-ation FLPSS controller is demonstrated by a digital computer simulation of alarge-scale power system.

Keywords fuzzy logic, power system stabilizer, large-scale power system,power system stability

1 Introduction

In the last decade, considerable eŒorts have been directed toward the enhancementof the stability problem of power systems. DiŒerent approaches have been discussedin literature to provide the damping required for improving the system stability.The main approaches have led to the development of two types of controllers;the power system stabilizers (PSSs) and the static VAR compensators (SVCs) [1].

Manuscript received in �nal form on November 25, 1997.Address correspondence to Mohamed A. L. Badi.

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158 S. A. Gawish et al.

Design of PSSs and SVCs have employed many diŒerent control techniques such asconventional controllers with lead-lag compensators, adaptive controllers using PIand PID algorithms, optimal controllers, etc.

Also, with the development of computer technologies and their applications,new branches of arti�cial intelligence (AI) and expert systems (ESs) have beengenerated and applied in power systems control. DiŒerent �elds have stemmedfrom AI such as arti�cial neural network (ANN) approaches and genetic algorithms(GAs) [2]–[4].

ESs are built on the basis of the knowledge gained from the �eld experience. Infuzzy logic techniques, this knowledge is generally expressed in linguistic expressionscontaining fuzzy descriptions. Therefore, fuzzy logic is a natural choice for thispurpose and may be considered acceptable for such a purpose [5, 6].

In recent controllersdesign, fuzzy logic controllershave received more attention,since they are robust, model-independent, and adaptable. Fuzzy logic controllersare mainly used for power systems exciters, AVRs, PSSs, SVCs, and convertercontrollers.

In many sources of the previously published work, the FLPSSs are used toimprove frequency oscillations neglecting their eŒect on other important signalssuch as the terminal voltage. This paper presents a new addition in the continuousdevelopment of the FLPSSs. The proposed FLPSS is delayed in operation for aperiod approximately equal to the �rst half cycle of the �rst swing of the powersystem electromechanical oscillations. The in�uence of the proposed FLPSS schemeon the dynamic characteristics of the controlled system is investigated. Simulationresults to illustrate the eŒectiveness of the proposed controller are presented. Theseresults have been obtained as an outcome of a detailed simulation study on athree machine power network. In the simulation study, the power network has beensubjected to a severe type of disturbance, namely, sudden short circuit at the endof one of the system busbars. This test can demonstrate the enhancement of thetransient stability of the system.

2 Power System Model

A typical power system is to be studied. It consists of three synchronous machinesconnected to a nine-bus network as shown if Figure 1. An IEEE type 1-S exciter hasbeen used as an excitation system for each one of the synchronous machines. Thestate-space equations of each synchronous machine and the associated excitationsystem are written as obtained in diŒerent literature sources [7, 8]. The system datais illustrated in Appendix A [7, 8].

A 3-phase short circuit fault is assumed to take place at the end of tie-line 5–7near bus [Eq. (7)] at zero time. The fault is assumed to be cleared and the line isconnected back successfully after 12 cycles of the power frequency. This correspondsto 0.24 Sec. for a 50 HZ system.

3 FLPSS Controller Design

The �rst step in designing the FLPSS is the determination of the state variableswhich represent the performance of the system. The input signals to the FLPSSare to be chosen from these variables. Since the main objective of the PSS is tolimit the variations in the power angle, deviation of power angle derivative ( D DZ)

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Large Power Systems Stability Enhancement using FLPSS 159

Figure 1. A multimachine power system model.

and deviation of speed derivative ( D Ç!) of the synchronous machine are taken asinputs to the FLPSS.

( D DZ) and ( D Ç!) of the synchronous machine can be computed directly fromreal-time measurements and the set point. Their values at any instant of time canbe expressed in a discrete form as:

D DZ(kT ) = !(kT ) !o (1)

D Ç![(k + 1)T ] =D ![(k + 1)T ] D !(kT )

T(2)

where T is the sampling interval and K is an integer expressing the multiple ofsampling interval.

The second step in the design is to decide on the linguistic variables. Thesevariables fuzzify the numerical input variables. For good control actions, sevenvariables are chosen as [9]:

a- Large positive: “LP”.b- Medium positive: “MP” .c- Small positive: “SP” .d- Very small: “VS” .e- Small negative: “SN”.f - Medium negative: “MN”.g- Large negative: “LN”.

The membership functions are chosen to be trapezoidal if the input signal is“LP” or “LN” and triangular for the others. Table 1 shows the domain for the twoinput signals.

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160 S. A. Gawish et al.

Tab

le1

Fuzz

ylo

gic

cont

rol

rule

s

Sign

alL

NM

NSN

VS

SPM

PL

P

DÇ ±

[0.

03,

0.01

25]

[0.

02,

0.00

5][

0.01

,0.

0][

0.00

5,0.

005]

[0.0

,0.

01]

[0.0

05,

0.02

][0

.012

5,0.

03]

DÇ

!´

104

[6.

0,3.

25]

[5.

25,

1.25

][

2.5,

0.0]

[1.

25,

1.25

][0

.0,

2.5]

[1.2

5,5.

25]

[3.2

5,6.

0]

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Large Power Systems Stability Enhancement using FLPSS 161

Table 2Fuzzy logic control rules

D DZ= D Ç! LN MN SN VS SP MP LP

LN LN LN LN LN MN SN VSMN LN LN MN MN SN VS SPSN LN MN SN SN VS SP MPVS MN SN VS SP SP MP LPSP MN SN VS SP SP MP LPMP SN VS SP MP MP LP LPLP VS SP MP LP LP LP LP

Table 3Crisp outputs w.r.t. fuzzy subsets

Fuzzy sets LN MN SN VS SP MP LP

Crisp value 1.2 0.8 0.2 0.0 0.2 0.8 1.2

Table 2 shows the rules controlling the fuzzi�ed output signal.For appropriate control signals, we de�ne crisp values for the control output

corresponding to the diŒerent fuzzy subsets LN, MN, SN, VS, SP, MP, or LP. Thesecrisp values are given in Table 3.

The �nal step is the defuzzi�cation of the fuzzy variables into crisp outputsand is done with the help of the center of gravity (COG) method [9].

4 Control Strategy

Each machine of the power system is assumed to be equipped with an FLPSS.The control strategy is to delay the operation of all FLPSSs of all machines un-til the �rst half cycle of the power system oscillations vanishes, i.e., about 0.5seconds. The main point behind this delay can be found from the experience onpower system stability. Just after a sudden disturbance on a system, a major vari-ation in the terminal voltage takes place. Usually the AVR responds fast and ef-�ciently corrects this variation. The changes in speed, and hence in angle are notthat sharp in the �rst instants after sudden disturbance. However, the unbalancein power tends to vary the steady state speed of the machine after a short pe-riod of time. Several values of delay time have been tested for the start of oper-ation of the PSS. An estimate of 0.5 seconds has shown best results. The AVRpractically makes a forcing excitation during this period to reestablish the lostpower balance after the clearance of the fault. The PSS does not interfere duringthis period. As the PSS comes into action, its eŒect will be quite signi�cant be-cause of the e� cient changes associated with speed and acceleration. This periodof delay is somewhat close to that of half cycle electromechanical oscillation ofthe system.

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162 S. A. Gawish et al.

5 Simulation Results

In order to validate this new control strategy as discussed in the latter section,a digital computer simulation program is developed using the MATLAB package.The obtained results are shown in the following �gures.

Figures 2(a)–(c) represent the rotor speed in p.u. for machines 1, 2, and 3,respectively. Figures 3(a)–(c) represent the terminal voltage in p.u. for machines 1,2, and 3, respectively. Figures 4(a)–(c) represent the power angle in electric degrees

Figure 2. (a) Machine (1) rotor speed—time response.

Figure 2. (b) Machine (2) rotor speed—time response.

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Large Power Systems Stability Enhancement using FLPSS 163

Figure 2. (c) Machine (3) rotor speed—time response.

Figure 3. (a) Machine (1) terminal voltage—time response.

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164 S. A. Gawish et al.

Figure 3. (b) Machine (2) terminal voltage—time response.

Figure 3. (c) Machine (3) terminal voltage—time response.

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Large Power Systems Stability Enhancement using FLPSS 165

Figure 4. (a) Machine (1) power angle—time response.

Figure 4. (b) Machine (2) power angle—time response.

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166 S. A. Gawish et al.

Figure 4. (c) Machine (3) power angle—time response.

for machines 1, 2, and 3, respectively. In all these �gures, the curve with dotted lineplot represents the machine when equipped with no controller, and the curve withsolid line plot represents the machine when equipped with the proposed control.

6 Conclusion

This paper demonstrates an application of a delayed control of FLPSS appliedfor a power system. The results discussed in the last section and the curves ofFigures 2 and 3 illustrate the quality of this controller to be a new addition overthe conventional controllers. Although the delay time of operation of PSS matcheswith half the period of oscillation, another investigation is necessary to state theirinterrelation. Also, results show that a control such as fuzzy logic control may notbe suitable for each machine at all times but a delayed control for some time ofoperation may be best suitable in some cases.

References

[1] Demello, F. P. and Concordia, C., 1969, Concepts of synchronous machines stability asaŒected by excitation control, IEEE Transactions on Power Apparatus and Systems,Vol. PAS-88, No. 4, pp. 316–329, April.

[2] Harvey, R. L., 1994, Neural network principles, Prentice-Hall, Inc.[3] Chen, J. L., 1993, A fuzzy expert system for fault diagnosis in electric distribution

system, Canadian Conference on Electrical and Computer Engineering, Vancouver,Canada, September 14–17.

[4] Jervanhaura, P. O., Verho, P., and Partanen, J., 1993, Using fuzzy sets to model theuncertainty in the fault location process of distribution networks, IEEE/ PES 1993 Sum-mer Meeting, Vancouver, B.C., Canada, 93 SN 4168 PWRD, July 18–22.

[5] Momoh, J. A., Ma, X. W., and Tomosovic, K., 1995, Overview and literature surveyof fuzzy set theory in power systems, IEEE Trans. on Power Systems, Vol. 10, No. 3,August.

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Large Power Systems Stability Enhancement using FLPSS 167

[6] Negoita, C. V., 1984, Expert systems and fuzzy systems, The Benjamin/ CummingsPublishing Company, Inc.

[7] Anderson, P. M. and Fouad, A. A., 1997, Power systems control and stability, Ames,Iowa: State University.

[8] IEEE Committee Report, 1968, Computer representation of excitation systems, IEEETrans., PAS-87, pp. 1460–1464.

[9] Hsu, Y. Y. and Cheng, C. H., 1990, Design of fuzzy power system stabilizers for multi-machine power systems, IEEE Proceedings, Vol. 137, Pt. C, No. 3, pp. 233–238, May.

Appendix A

Transmission Lines

Node No. Impedance (p.u.)

4–5 0.01 + j 0.0854–6 0.017 + j 0.0925–7 0.032 + j 0.1616–8 0.039 + j 0.177–8 0.0085 + j 0.0728–9 0.0119 + j 0.1008

Operating Conditions

Machine P (p.u.) Q (p.u.) V (p.u.) ± (rad.)

1 0.716 0.27 1.04 0.06252 1.63 0.067 1.025 1.06653 0.85 0.109 1.025 0.9458

Machines: (reactance’s in p.u. to a base of 100 MVA)

Machine 1 2 3

Rated MVA 247.5 192.0 128.0K V 16.5 18.0 13.8H 23.64 6.4 3.01Power factor 1.0 0.85 0.85Type hydro steam steamSpeed 180 rpm 3600 rpm 3600 rpmX d 0.146 0.8958 1.3125X ¢

d 0.0608 0.1198 0.1813X q 0.0969 0.8645 1.2578X ¢

q 0.0969 0.1969 0.25T ¢

do 8.96 6.0 5.89T ¢qo 0.0 0.535 0.6978

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168 S. A. Gawish et al.

Excitation System

Machine 1 2 3

K A 40.0 40.0 40.0TA 0.15 0.15 0.15K F 0.002 0.002 0.002TF 0.75 0.75 0.75

Loads

Load (p.u.)

A 1.26 j 0.5044B 0.8777 j 0.2926C 0.969 j 0.3391

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