a new fuzzy logic power system stabilizer

8/13/2019 A New Fuzzy Logic Power System Stabilizer

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Abstract-- This paper describes the performances of a new

power system stabilizer, the Fuzzy Logic PSS (FLPSS). It is

basically a PID (proportional-integral-derivative) type FLPSS

with adjustable gains added outside in order to keep a simple

structure. The FLPSS uses the generator speed deviation as

primary input from which the accelerating power is derived as a

secondary input. In order to validate the FLPSS, it has been

compared with two reference stabilizers, the IEEE PSS4B and

IEEE PSS2B from the IEEE Std 421.5. Conclusions are

supported by a range of small and large signal analyses,

performed on a four machine two areas test system (with two

configurations).

Index Terms-- Electromechanical modes, fuzzy logic, large

signal stability, power system stabilizer, small signal stability.

I. INTRODUCTION

N the context of modern interconnected electricalnetworks, power systems stabilizers are considered an

essential control mean to improve stability and transmissioncapacity. Extensive network interconnections tend tointroduce new electromechanical modes of oscillationbetween electrically coherent power plants or areas. When

large electrical areas are involved, corresponding inter-areamodes may be as low as 0.2 Hz. However, inter-machinesoscillations inside a given power plant may reach frequenciesas high as 4.0 Hz when machine inertia are small and excitergains are high. Power system stabilizers are facing such awide range of oscillating modes that they must ideally dampefficiently.

Most power system stabilizers in use in electric powersystems are derived from the classical linear control theory.This theory is based on a linear model of a fixed powersystem configuration. In other words, a fixed-parameterspower system stabilizer, called a conventional PSS is

optimum for one set of operating conditions and may not beas effective for drastically different set of operatingconditions and/or network configurations.

Indeed, power systems are nonlinear systems and theiroperation is basically of a stochastic nature. Therefore, systemconfiguration is dynamic with frequent topological changes

M. Dobrescu and I. Kamwa are with Hydro-Qubec, IREQ, 1800 Boul.Lionel-Boulet, Varennes, Quebec, Canada, J3X 1S1 (e-mail:[email protected] , [email protected] )

either due to switching actions in the short term or systemenhancements in the long term.

With the conventional fixed-parameters stabilizers, thegains and other parameters may not ideally suit the entirespectrum of operation. The main objective of PSS is to insuresystem stability and good performances for all operatingconditions and network configurations.

Nowadays, with the development in digital technology, ithas become possible to develop and implement new

controllers based on modern and more sophisticated synthesistechniques. Indeed, controllers based on robust optimalcontrol, adaptive control, artificial intelligence are beingdeveloped. Among these methods, fuzzy logic is particularlyattractive because it does not require a mathematical systemmodel to be controlled. It is, therefore, well-suited when thesystem to be controlled is complex, nonlinear and difficult tomodel. This powerful tool was used in different fields ofapplication including, recently, power systems dynamicperformance.

The Fuzzy Logic PSS concept was derived to provide anoriginal and efficient solution to this wide range modesdamping problem. The core of the paper is divided in three

sections, one to describe the FLPSS itself, a second one tobring some results based on small signal stability simulationsand a third one to present some large signal stability results.In order to emphasize the FLPSS performances we willcompare this novel fuzzy logic PSS results with two referencestabilizers results: the IEEE PSS2B [7] and IEEE PSS4B [1].

The IEEE PSS2B is an integral of generator acceleratingpower using a three-stage lead-lag transfer function while theIEEE PSS4B is built on a flexible multi-band transfer functionstructure to provide more degrees-of-freedom for achieving arobust PSS tuning over a wide frequency range. Both of themare included in the new IEEE Std-421.5 [2]. These IEEE PSS

have the same external inputs (speed and electrical powerdeviations). Those models and parameters are presented in theAppendix.

The reference system data and contingencies analysis, thePSS structures and settings used in this paper wereimplemented in Matlab/SimPowerSystems software [8].

II. DESCRIPTION OF THE FLPSS

The FLPSS model is shown in Fig.1. As for a conventionalPSS, the FLPSS comprises three main blocks, the filters

A New Fuzzy Logic Power System StabilizerPerformances

M. Dobrescu,Non Member,and I. Kamwa, Senior Member, IEEE

I


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(WO), the fuzzy logic controller (FLC) and the limiter. Oneadjustable limiter (0.15) is provided for the FLPSS output.The filters WO are two washout filters with time constants ofTw=10 seconds.

It is, as we can see, a PID (proportional-integral-derivative) type stabilizer [6] which uses the speed deviationof the machine as primary input. The core of the FLPSS is afuzzy logic controller (FLC). Gains have been added outside

the FLC, on the one hand, to normalize input variables of thefuzzy logic controller and, on the other hand, to achieve thePID function. Let's note that the addition of these gainsoutside fuzzy logic controller permits to keep a simplestructure. The FLC uses the speed and the acceleration powerdeviations as inputs, the latter being derived from the speed.

Fig.1. PID type FLPSS model

In what follows, we will describe how the FLPSS has beensynthesised. In a first place, we are going to show how thefuzzy logic controller was realised from concepts of fuzzylogic [5]. Thereafter, we will present the tuning gainsmethodology.

A. Fuzzy logic controller

The design process of the fuzzy logic controller may be

split into five steps: the selection of control variables, themembership function definition, the rule creation, the fuzzyinference and the defuzzification strategy.

The fuzzy inference method is minimum-maximum type(Mamdani). The defuzzification strategy used is the fuzzycentroid method.

The two input variables membership functions have beenchosen identical because of the normalization achieved on thephysical variables. The normalization is important because itallows the controller to associate an equitable weight to eachof the rules and, therefore, to calculate correctly the stability

signal.Each of the input variables is classified by seven

trapezoidal fuzzy membership functions. The following fuzzysets were chosen: BN(Big Negative)= [-5.0 1.0 0.2 0.1],MN(Medium Negative)= [-1.0 -0.2 -0.1 0.2], LN(LowNegative)= [-1.0 -0.1 -0.03 1.0], Z(Zero)= [-1.0 -0.03 0.031.0], LP(Low Positive)=[-1.0 -0.03 0.1 1.0], MP(MediumPositive)= [-0.2 0.1 0.2 1.0] and BP(Big Positive)= [-0.1 0.21.0 5.0].

The output variable is classified by triangular fuzzymembership functions: BN (Big Negative) = [ -1.0 -0.51-0.439], MN(Medium Negative)= [-0.515 -0.439 -0.302],LN(Low Negative)= [-0.439 -0.302 0.0], BZ (Big Zero) =[-0.302 0.0 0.302], LZ(Low Zero)= [-0.0015 0.0 0.0015],LP(Low Positive)=[0.0 0.302 0.439], MP(MediumPositive)= [0.302 0.439 0.515], BP(Big Positive)= [0.4390.515 1.0].

The output signal was obtained using the followingprinciples:- If the speed deviation is important, but tends to decrease,

then the control must be moderated. In other words, whenthe machine decelerates, even though the speed isimportant, the system is capable, by itself, to return tosteady state.

- If the speed deviation is weak, but tends to increase, thenthe control must be significant. In this case, it means that,if the machine accelerates, the control must permit toreverse the situation.

The inference mechanism of the FLC is represented by a

7x7 decision table. The entire set of rules (49 if-then rules) ispresented in Table I.TABLE I.

FLPSS DECISION TABLE

w/

PaBP MP LP Z LN MN BN

BN BZ LN MN MN BN BN BN

MN LP BZ LN MN MN BN BN

LN MP LP BZ LN LN MN BN

Z BP MP LP LZ LN MN BN

LP BP MP LP LP BZ LN MN

MP BP BP MP MP LP BZ LN

BP BP BP BP MP MP LP BZ

B. Tuning FLPSS gains strategy

The FLPSS was obtained by combining the fuzzy logiccontroller with proportional-derivative action (FL-PD) and thefuzzy logic controller with proportional-integral action (FL-PI). The gains of the proportional, derivative and integralactions of the FLPSS are given by the following relations:

{ } { }

{ }

{ }

s p s wPR 2 1

s wINT 2

s pDER 1

PIDPR INT DER

K K F K K F K

K K F K

K K F K

Vs K K dt K Pa

= +

=

=

= + +

(1)

In (1) we used the following notations:- KPRis the proportional action gain.- KINTis the integral action gain.- KDERis the derivative action gain.- The F{} term represents the fuzzy operation.

VS

Pa

Kw FLC

Kp

s-1 Ks2

Ks1

2Hs

PD

PI

WO


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For obtaining the gains Kw, Kp, Ks1 and Ks2 a three stepsmethod has been used. This consists in adjusting only oneparameter at a time and is designed with the following steps:

1. Normalize input variables (the adjustment of Kw and Kpgains).

2. Tune the FL-PD control first without using PI control.

3. Keep input gains Kwand Kpunchanged after adding FL-PI control. Adjust the output gains Ks1and Ks2 in FL-PI(proportional-integral) and FL-PD (proportional-derivative) branches to obtain a good result.

At the end, the following values were obtained for theFLPSS gains: Kp=0.55, Kw=50*Kp, Ks1=1.2 and Ks2=0.12.

III. RESULTS BASED ON SIMULATIONS

We will start comparing the three PSS using a fourmachine two areas system called in this paper the Kundur testsystem [3-4]. In its basic symmetrical configuration, thissystem is available in the Matlab/SimPowerSystems software[8] as a demonstration. Despite its small size, it mimics veryclosely the behavior of typical systems in actual operation.

We have implemented the stabilizers: FLPSS (described inprevious section), IEEE PSS2B and IEEE PSS4B (describedin Appendix) on all generating units (G1, G2, G3 and G4).

The Kundur test system, shown in Fig.2, consists of twofully symmetrical areas linked together by two 230 kV lines of220 km length. Each area is equipped with two identical roundrotor generators rated 20kV/900MVA. The synchronousmachines have identical parameters, except for inertia whichis H = 6.5s for generators in area 1 and H = 6.175s forgenerators in area 2. Thermal plants having identical speedregulators are further assumed at all locations, in addition to

fast static exciters with a 200 gain. The reference load-flowwith generator G2 considered as the swing bus is such that allgenerators are producing about 700 MW each. Two stressedscenarios were considered with respectively, two tie-lines at a413 MW transfer level (K2L) and a single tie-line at a 353MW transfer level (K1L). The loads are assumed everywhereas constant impedance load models. The area 1 and area 2loads are 967 MW and 1767 MW respectively. The loadvoltage profile was improved by installing 187 Mvar morecapacitors in each area.

Fig. 2. Four Machine Two-Areas Kundur test system

A. Small signal analysis

Small-signal analysis provides a mean to compare thedamping of the different system modes. The values wereobtained with no stabilizer at either site first and then withFLPSS, IEEE PSS4B and IEEE PSS2B in closed-loop at thefour generators in Fig.2. In order to identify the open-loopsystem, a finite impulse (1% from reference voltage Vref for0.2 seconds) is injected in turn into each of the four machineswhile recording the output response signals. The linear MIMOmodel is constructed from a modal analysis of these timeresponses [9]. It allows the dominant modes to be identified.

To better understand the results, we have completed thesmall signal analysis by providing in Table II and Table III themodal performance of the three PSS on a single tie-linesystem (K1L) and on two tie-lines system (K2L). This fourmachines two areas system has a strong inter-area mode.

TABLE II.PSS DAMPING ON A SINGLE TIE LINE SYSTEM

Open Loop FLPSS IEEE PSS4B IEEE PSS2BMode

Hz Hz Hz Hz Inter-area

0.44 -0.015 0.37 0.26 0.33 0.37 0.46 0.19

Localarea 1

1.10 0.12 0.83 0.59 1.87 0.5 1.04 0.33

Localarea 2

1.15 0.095 0.86 0.61 1.99 0.45 1.07 0.32

TABLE III.PSS DAMPING ON A TWO TIE LINES SYSTEM

Mode Open Loop FLPSS IEEE PSS4B IEEE PSS2BHz Hz Hz Hz

Inter-area

0.64 -0.026 0.55 0.19 0.52 0.31 0.62 0.1

Localarea 1

1.13 0.096 0.83 0.6 1.92 0.47 1.06 0.32

Localarea 2

1.16 0.092 0.86 0.65 1.99 0.45 1.07 0.33

For the single tie line system K1L inter-area frequency is0.44Hz without PSS and for the two tie lines system K2Linter-area frequency is 0.64 without PSS. The closed loopinter-area frequency is quite different for FLPSS and PSS4B(Table II and II).

The damping performance of the FLPSS is compared inTable II and Table III against the IEEE PSS4B and IEEEPSS2B for these two systems. The IEEE4B PSS is clearly thebest for the inter-area modes. However, for the two localmodes the better damping is obtained with FLPSS. This goodperformances hold at both week (K1L) and strong (K2L)systems.

To illustrate the basic differences between thesestabilizers, a frequency response plot is shown on Fig.3 tocompare FLPSS settings with IEEE stabilizers (PSS4B andPSS2B type).


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Fig. 3. Frequency response of the three PSS type

As shown in Fig.3, in the interest frequency range [0.1 Hz4 Hz], the FLPSS, IEEE PSS2B and the IEEE PSS4B don'tpresent phase delay. Otherwise, it appears that, compared tothe other stabilisers, the FLPSS gain varies little between 0.04Hz and 0.3 Hz. In this frequency interval the gain of theFLPSS is located around 15p.u. However, beyond 1Hz, the

gain of the FLPSS increases quickly to reach 75p.u. around 4Hz. To this frequency, the other stabilisers gains are 55p.u.(PSS4B) and 60p.u.(PSS2B).

As a general observation, it is interesting to mention thatthe IEEE PSS4B frequency response is well balanced at bothends of the spectrum, limiting the gain on the high side andphase lead on the low side. On the other hand, IEEE PSS2Bphase in the interval [0.01Hz 0.04Hz] is too large.

B. Large signal analysis

We have implemented the FLPSS described in previoussections on G1, G2, G3 and G4 (as in the small signalanalysis), in order to analyze its behavior following largecontingencies (Table IV).

Two scenarios were considered respectively, two tie-linessystem (K2L) with a 413 MW transfer power and a single tie-line system (K1L) with a 353 MW transfer power. Thecontingencies applied to Kundur test system are presented intable IV.

TABLE IV.LARGE SIGNAL TESTS ON THE KUNDUR TEST SYSTEM

TEST SYSTEM CONTINGENCY DESCRIPTION

A K2Lsystem

15 cycles 3short-circuit at bus 8 clearedwith one tie-line outage (line 7-9);

B K1Lsystem

12 cycles 3 short-circuit at bus 1 (nearG1) normally cleared with no equipmentoutage;

C K2Lsystem

9 cycles 3short-circuit at bus 1 (near G1)normally cleared with no equipmentoutage;

The FLPSS performances are exposed by comparinganalysis with reference PSS: PSS2B and PSS4B.

A severe fault was applied at the middle of the tie lines,followed by one tie-line outage (test A, Table IV).

Test A results illustrating the FLPSS performances areshown in Fig.4. While all candidate devices perform well on atwo tie-line system, the FLPSS outperform the PSS4B andPSS2B.

Fig. 4. Test A: Inter-area angle shift, speed deviation and G1 terminal voltage ofthe K2L system

Test B results are shown in Fig.5. We can see that whenthe K1L test system is in closed-loop with the PSS2B, it lostthe stability. The two other stabilizers (FLPSS and PSS4B)succeeded in consolidating the network. For this contingency,we can say that the FLPSS and the PSS4B have broadlycomparable performances.

Fig. 5: Test B: Inter-area angle shift, speed deviation and terminal voltage (G1)of the K1L system

Test C results are shown in Fig. 6. The K2L test system isless oscillating with the PSS4B and the FLPSS. We also notethat the speed excursions are less pronounced with theFLPSS, allowing the steady state to be reached more quickly.


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Fig. 6. Test C: Inter-area angle shift, speed deviation and G1 terminal voltage of

the K2L system

C. Others important tests

Two other interesting contingencies for assessing PSSbehavior under mechanical power disturbances are described

Table V. In particular, Test D (Table V) results are shown inFig.7. The initial crest of the speed obtained with the FLPSS,is smaller than with the two other stabilizers. Meanwhile, theterminal voltage is not degraded too much which is a welcomeproperty. We also note that the FLPSS permits to reach thesteady state faster. This said, Fig.7 also shows that the PSS2Band PSS4B PSS have an equally acceptable performance forthis Test D.

TABLE V.OTHERS TESTS ON THE KUNDUR SYSTEM

TEST SYSTEM CONTINGENCY DESCRIPTION

D. K1L system Finite impulse (10% from referencemechanical power (Pref) for 1 second) appliedon a single unit (G4)

E K2L system Mechanical power negative ramp(1p.u./minute for 6 seconds) on a single unit(G1)

Fig. 7: Test D: PSS output signal, speed deviation and G4 terminal voltage of theK1L system

To complete this study, Test E results are shown in Fig.8.In the case of a mechanical power negative ramp applied tothe generator G1, the PSS4B has better performances than theother two stabilizers. On this type of event, the least powerfulstabilizer is the PSS2B because its stability signal is subject tovery low frequency oscillations, a probable side-effect of itsexcessive phase lead below 0.04Hz.

Fig. 8: Test E: PSS output signal, speed deviation and G1 Electrical power of theK2L system

IV. CONCLUSIONS

In this paper, fuzzy logic was used to synthesize a powersystem stabilizer in order to maintain the stability of thepower system over a wide operating range. The resultsobtained in simulations are promising. Indeed, they showedthat the Fuzzy Logic based PSS satisfies two essential

properties in the control system field: good robustness andgood damping performance. It is important to emphasize thatin this study no robust control technique was explicitly used.It demonstrates the potential and efficiency of fuzzy logic inthe power grid control field. Two modern PSS, the IEEEPSS2B and IEEE PSS4B have been used in order to validatethe new FLPSS concept.

V. APPENDIX

A. IEEE PSS4B

TABLE VI. PSS4B PARAMETERSLow

FrequencyBand

Intermediate

FrequencyBand

High

FrequencyBandKB=20.0 KI=40.0 KH=160.0

KL1=66.0 KI1=66.0 KH1=66.0

KL2=66.0 KI2=66.0 KH2=66.0

TL1=0.4843 TI1=0.0969 TH1=0.0101

TL2=0.5812 TI2=0.1162 TH2=0.0121

TL7=0.5812 TI7=0.1162 TH7=0.0121

TL8=0.6974 TI8=0.1395 TH8=0.0145

VLmax=0.6 VImax=0.6 VHmax=0.6

VLmin=-0.6 VImin=-0.6 VHmin=-0.6

KL11=1; KI11=1; KH11=1; VST=0.15


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Fig.9: PSS4B

B. IEEE PSS2B

1sT6

1sT5

1sT4

1sT3

1sT2

1sT1

1sTw

sTwKs1PSS

+

+

+

+

+

+

+

=

Fig.10: PSS2B

TABLE VII.PSS2B PARAMETERS

PSS2B

parameters

Function PSS

parameters

Tw1(2,3)Tw4T8T9MN

Ks2Ks3

10.01000.500.10

51

0.991.0

Ks1TwT1T2T3T4T5T6

VST

20.03

0.120.0120.120.0120.250.75

0.15

VI. REFERENCES[1] R. Grondin, I. Kamwa, G. Trudel, L. Grin-Lajoie, J. Taborda, Modeling

and Closed-Loop Validation of a New PSS Concept, The Multi-BandPSS, Presented at the 2003 IEEE/PES General Meeting, Panel Sessionon New PSS Technologies, Toronto, Canada

[2] IEEE Standard 421.5, IEEE Recommended Practice for ExcitationSystems Models for Power System Stability Studies, August 1992.

[3] M. Klein, G.J. Rogers, S. Moorty, P. Kundur, Analytical Investigation ofFactors Influencing Power System Stabilizers Performance, IEEE Trans.on Energy Conv., 7(3), Sept. 1992, pp.382-390.

[4] P. Kundur, Power System Stability and Control, McGraw-Hill, NewYork, NY, 1994.

[5] C. C.Lee, Fuzzy Logic in Control Systems : Fuzzy Logic Controller, Part Iand II, IEEE Transactions on Systems, Man, and Cybernetics, vol. 20, no.2, pp. 404-435, 1990.

[6] H. X. Li, H. B. Gatland, Enhanced Methods of Fuzzy Logic Control, IEEE transactions on systems, man and cybernetics, pp.331-336, 1995.

[7] N. Martins, A.A. Barbosa, J.C.R. Ferraz, M.G. dos Santos, A.L.B.Bergamo, C.S. Yung, V.R. Oliveira, N.J.P. Macedo, "Retuning Stabilizersfor the North-South Brazilian Interconnection, " IEEE PES Summer

Meeting, 18-22 July 1999 , Vol. 1, pp. 5867.[8] MATLAB SimPowerSystem Software (version 6.5.1, 2004), MathWorks,

www.mathworks.com/products/simpower/[9] I. Kamwa, L. Grin-Lajoie, "State-Space Identification-Towards MIMO

Models for Modal Analysis and Optimization of Bulk Power Systems,"IEEE Trans. on Power Systems, 15(1), Feb. 2000, pp. 326-335.

VII. BIOGRAPHIES

Manuela Dobrescu received a B.Eng. (1989) in Electrical Engineering fromCraiova University, Romania and a M.Sc.(2003) from cole Polytechnique,Montreal University, Canada. In 1989, she joined RENEL-Romania, where shewas involved in the control and protection field for power plant generators andhigh voltage stations. Twelve years later, she joined Hydro-Qubec ResearchInstitute, where she is now involved as a Researcher in the field of power systemdynamics.

Innocent Kamwa (S'83, M'88, SM98) received a PhD in electricalengineering from Laval University, Qubec, Canada, 1988, after graduating in1984 at the same university. Since then, he has been with the Hydro-QubecResearch Institute, where he is at present a Principal Researcher with interestsbroadly in bulk system dynamic performance. Since 1990, he has held anassociate professor position in Electrical Engineering at Laval University wherefive students have completed their PhD under his supervision. A member ofCIGR, Dr. Kamwa is a recipient of the 1998 and 2003 IEEE PES Prize PaperAwards and is currently serving on the System Dynamic Performance CommitteeAdCom.

a new fuzzy logic power system stabilizer

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