Electric Power Systems Research Volume 40 Issue 2 1997 [Doi 10.1016_s0378-7796(96)01139-x] M.G. Rabbani; J.B.X. Devotta; S. Elangovan -- A Fuzzy Set Theory Based Control

8/14/2019 Electric Power Systems Research Volume 40 Issue 2 1997 [Doi 10.1016_s0378-7796(96)01139-x] M.G. Rabbani; J.

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ELSEVIER Electric Power Systems Research 40 (1997) 107-l 14

kEi41CSYSTErnSAESECIRCH

A fuzzy set theory based control of superconductive magneticenergy storage unit to improve power system

dynamic performance

M.G. Rabbani *, J.B.X. Devotta, S. ElangovanDepartment of Electrid Engineering, National Lhioersit,vof Singapore. Singapore 051 I, Singupovr

Received 21 June 1996; accepted 24 July 1996

Abstract

At present fuzzy logic control is receiving increasing emphasis in process control applications. The paperdescribes heapplication of fuzzy logic control in a power system that uses a 12-p&e bridge converter associated with superconductivemagnetic energy storage (SMES) unit. The fuzzy control is used in both the frequency and voltage control loops, replacing theconventional control method. The control algorithms have been developed in detail and simulation results are presented. Theseresults learly indicate he superior performance of fuzzy control during the dynamic period of energy transfer between he powersystem and SMES unit. 0 1997 Elsevier Science S.A.

Kw~w&: SMES; Fuzzy controller: Computer simulation

1. Introduction

Power system oscillations occur when there are sys-tem disturbances such as sudden load-changes or faults.The damping of the system must be such that thesynchronous generators can return to their steady stateconditions after the disturbances [l]. Especially whenthe load-end of the transmission line experiences sud-den load perturbations. the generators need continuouscontrol to suppress undesirable oscillations in the sys-tem. Many countermeasures have been suggested byresearchers to increase the damping. These includepower system stabilizers [2,3], optimal control of theturbine-governor system [4], and the use of static phaseshifters [S].

Since the successful commissioning test of the BPA30 MJ unit [6], superconductive magnetic energy stor-age (SMES) systems have received much attention inpower system applications. Although the original pur-pose of the SMES unit is load leveling, an additionalfunction of the SMES unit is the improvement of thesystem performance, by providing appropriate power

* Corresponding author.

037%7796/97: 17.00 0 1997 Elsevier Science S.A. All rights reserved.PII SO378-7796(96)01 139-X

modulation [7] during the dynamic period. The SMEScan be applied for both active and reactive powercompensation at suitable locations of the transmissionline for both static and dynamic voltage control andsystem stability preservation [8,9]. However, some is-sues associated with the use of SMES unit still remainto be resolved. Two of these issues are: (i) the effectiveuse of P-Q modulation, (ii) the evaluation of theirperformance after sudden disturbance.

One way to address these issues s to investigate theuse of alternative control techniques. At present, theuse of fuzzy logic is finding much application in severalareas [lO,ll]. In this paper, the conventional SMEScontroller proposed [8] is replaced by a rule based fuzzycontroller. To demonstrate the effectiveness of the pro-posed fuzzy controller, its performance is comparedwith the conventional one. The results show that theSMES unit responds very quickly following a suddenload change due to the effective use of its P-Q modula-tion capability. The paper begins by outlining the mainproblems associated with conventional control schemeand then describes the details of the proposed fuzzylogic control scheme. The controller is applied to a testnetwork and the simulation results are presented anddiscussed.


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108 M.G. Rabbuni et (11. /Electric

2. Problems associated with the use of conventionalcontrol

2.1. Review of control strategy

Fig. 1 shows a typica l configuration of a single area

power system equipped with a SMES unit. Applicationof a sudden load results in load-voltage and frequencydeviations. Following these variations, the SMES unitresponds to improve the performance subject to itslimita tion. The input to the SMES unit is a d.c. voltageEd. This voltage is continuously varied by a 12-pulsecascaded bridge type ac/dc converter. The converterd.c. output current 1, being unidirectional, the controlfor the direction and magnitude of the inductor powerflow Pd, is achieved by continuously regulating thefiring angle a. Fig. 2 shows a diagram of the conven-tional controlled system and the controller is shown inFig. 3. A switched capacitor bank is also placed at theload end to provide additional VAr as required forreactive power compensation. The control proceduredescribed in detail in [S] can be summarized as follows:

(i) At first the required inductor voltage Ed is calcu-lated by using the equation

Ed = K,Af - KidAId (2.1)

Pd = EdId (2.2)

where K,, and KiYid re the gains corresponding to thefrequency variation (Af) and the inductor current vari-ation (AI,) respectively.

(ii) The desired reactive power Qdem can be calculated

as

(2.3

Qdem Qc, Qc (2.4)where Qd is reactive power provided by the SMES unitand Qc is the reactive power supplied by the switchedcapacitor; K, is the gain corresponding to load voltagedeviation.

(iii) The SMES unit provides P, and Q, to improvethe system performance by controlling the firing anglesof the 12-pulse converter.

UNIT

Y-f

Fig. I. Single line diagram for the test network.

Power Systems Research 40 (I 997) 107-I 14

1 1 1 Switched CapacitorBank-

CONTROLLER

System Volage andFrequency Zrg %

g.EJ w?asv

4 Y-Y/At-6

Trnnsformer

III12-P&e

Bridge Converter

Fig. 2. Schem atic diagram of the conventional controlled system.

2.2. Problems arising f+om the conventional controlstrategy

The use of Af (error) signal alone is insufficient todetermine the desired value of real power Pd modula-tion required by the SMES unit. In addition to thiserror signal, the change in error between successivesamples should be used to determine Pd. The absence ofthis additional signal makes the SMES unit less sensi-

tive to the disturbance. This will in turn result in alarger value of A in the SMES unit. A similar prob-lem arises when only load voltage deviation (AI,) isconsidered to determine the desired value of reactivepower modulation Qd, instead of the change in AV,between successive samples.

3. The proposed fuzzy logic control

The proposed controller along with SMES unit isshown in Fig. 4. The Af and AVL are the inputs to

the corresponding fuzzy controllers. The output of theFuzzy Frequency Controller (FFC) is Pdem, while Qdemis the output of the Fuzzy Voltage Controller (FVC).At any instant, the P-Q modulation of the SMESunit depends on the present value of inductor current1,. The P-Q regulator decides the actual amountof (Pd, Qd) to be provided by SMES, and Qc byswitched capacitor bank. Once Pd and Qd are selected,the firing angles of the 12-pulse converter can be calcu-lated.

Unlike the conventional controller, in the proposedmethod, the changes in Af and AVL signals are also


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M.G. Rabbani et al. /Electric Ponfer Systems Research 40 (1997) I OF I14 109

KnowledgeBase

Inputs . v v 1

- Fuzzitication - Decision Making - Defuzzification- Interface Logic

Output and States

Fig. 3. Basic fuzzy logic controller.

Pde*n

P-Opd

Qdem Regulator c),-H Estimator

Generator Y-Y/ATransformer

12-p&e Couverter

Fig. 4. Fuzzy controller for the SMES unit.

considered as explained below. In general, the inputvariables considered in the fuzzy rule base are

E(k) = R(k) - C(k)

CE(k) = E(k) - E(k - l),

where E(k) is the loop error (present deviation), CE(k)is the change in loop error, R(k) is the reference signal,C(k) is the present signal, and k is the sampling interval.

The structure of a general rule can be given as:

IF E(K) is X AND CE(K) is Y THEN U(K) is Z.

Here U(K) is either Pdem MW) or Qdem MVAr).The variables can be expressed as per unit quantities

as follows:

e(p.u.) = E(k)/GE

ce(p.u.) = CE(k)/GCE

where GE and GCE are the respective gain factors of thecontrollers. Fig. 5 shows the membership functions ofe(p.u.), ce(p.u.) and their respective output variable.

Note that the fuzzy subsets for output variable has anasymmetrical shape causing more crowding near theorigin. This allows precision control near the steady stateoperating point. Also large number of subsets s selectedto obtain accurate control.

Table 1 gives the rule base matrix for the frequency andvoltage controllers. The steps for frequency control canbe summarized as follows:1. Sample the reference frequency f* and the actual

frequency f,,,.2. Compute error (e) and change of error (ce) in theirrespective p.u. values are as follows:

e(k) = (f*(k) -f(k)hGE

cc(k) = (e(k) - e(k - I))/GCE

3. Identify the interval indices for e(p.u.) and ce(p.u.)respectively, by the comparison method.

4. Compute the degree of membership of e(p.u.) andce(p.u.) for the relevant fuzzy subsets.

5. Identify the four valid rules in Table 1 and calculatethe degree of membership pRi using MIN operator.


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110 M.G. Rnbbuni et al. / Elecrric Power Sysrrms Research 40 (1997) 107- 114

-30 -24 -18 -12 -6 0 6 I1 18 24 304p.u.)

NVB NB NM NS NVS 2 PVS PS PM PB PVB

-5 -4 -3 -1 -1 0 I 2 3 4 5

lJ (Pdcm )

ce(p.u.)

NVB NB NM NS PVS PS PM PB PVB

-6 -4.5 -3 -1.5 -.5 0 .5 1.5 3 4.5 6 pdem (MW)

Fig. 5. Membership functions of the fuzzy frequency controller

(FFC).

6.

7.

Retrieve power demand Pdem or each rule fromTable 1.Calculate the crisp value of Pdc,,, by height defuzzifi-cation method as follows:

P ~RIpdl + pR2pd2 + pR3pd3 + pR4pd4dem =

iURl + 1uR2 + pR3 + pR4 (3.1)The control of the voltage loop is done in the same wayexcept that the gain factors GE and GCE are different.

The actual real and reactive power consumed by theSMES unit (Pd, Qd) determined by the P-Q regulator,depend on the present value of the inductor current Id.Limitations on the firing angle z to the regions 5 I

Table 1

Rule base for frequency and voltage controllers

ce e

NVB NB

NVBNB

NMNS

NWZ

PVSPSPM

PBPVB

NVB NVBNVB NVBNVB NVBNVB NVB

NVB NVBNVB NBNB NM

NM NS

NS NVS

NVS Z

Z PVS

NM

NVBNVBNVB

NVBNBNM

NSNVSZ

PVSPS

d min(a,=a,=16S0)

Fig 6. A typical Pa-Q modulation diagram under two quadrantoperation.

Ia) I 165 restrain the (Pd, Qd) consumption of theSMES unit. The region of available for(Pd, Qd)for twoquadrant operation is shown in Fig. 6. Four quadrantoperation [12] can be exercised when capacitive VAr isrequired for compensation. The switched capacitorbank provides additional VAr (Q,.) when required.Therefore, the net reactive compensation provided bySMES unit along with switched capacitor is

Qnrt= Qd + Q, (3.2)For a particular value of Id, maximum P, is obtained

at c( = 5 and minimum P, at LX 165. The P-Qmodulation shows that the maximum Qd can be ob-tained in equal a mode (when a, = ti2) and the mini-mum Qd curve has a bend at the intersection point of

the two semicircular loci . For a particular value ofP,,if the desired value of Qd falls outside the availablearea, it is restricted to the nearest point of the boundaryof the curve. It is desirable to set the rated inductorcurrent 1, such that the maximum allowable energyabsorption equals the maximum allowable energy dis-charge. This makes the SMES unit equally effective indamping swings caused by sudden increase or decrease

NS NVS Z PVS PS PM PB PVB

NVBNVBNVBNB

NMNS

NVSZPVSPS

PM

NVBNVBNB

NMNSNVS

ZPVSPS

PMPB

NVBNBNM

NSNVSZ

PVSPSPMPB

PVB

NBNMNS

NVSZPVS

PSPMPB

PVBPVB

NMNSNVSZ

PVSPSPM

PBPVBPVB

PVB

NSNVSZ

PVSPSPM

PBPVBPVBPVB

PVB

NVSZPVSPS

PMPBPVBPVBPVB

PVBPVB

ZPVSPSPM

PBPVBPVBPVB

PVBPVBPVB


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M.G. Rabbani rr cd. /Electric Power Systems Research 40 (1997) 107- 114

Frequency Deviation (Hz)Load Voltage Deviation (p.u.)

-4.5 10 15 0 5 10 15

set set

Fig. 7. Response of the power system without SMES unit due to a step loading of (0.005 + jO.005) p.u. [case I].

x fo-3

set

Fig. 8. Response of the power system without SMES tmir due to a step loading of (0.008 + jO.008) p.u. [case 4.

-2voad Voltage Deviation (p.u.)

P-Modulation of SMES Unit (MW)Converter Q-Modulation (MVAr)

5 10 15 0 5 10 15

15 0 5 10 15set set

Fig. 9. Response of the power system after addition of the SMES unit using fuzzy logic control [case I]. .. Conventional; ~ Fuzzy.

in load. When the inductor current reaches either of theselimits, the Pd-Af control loop is discontinued til l thefrequency deviation swings to the other side.

4. Results of the proposed P-Q control

The single area system of Fig. 1 is considered as a testnetwork. The purpose is to highlight the behavior ofSMES under fuzzy logic control scheme and its econom-

ical advantage over the conventional scheme. The degreeof impact on the power system would depend on the typeof the power system and the nature of the load. Thesection begins with system modeling followed by thesimulation results and performance evaluation. Finally,economic aspects are presented. The following aspectsare discussed in details in the sub-sections:

(a) system behavior without SMES unit;(b) its performance with SMES unit using non-fuzzycontroller;


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112 M.G. Rabbani et al. /Electric Power Systems Research 40 (1997) 107-114

x 1o-3

0 5 10 15

Or 1

I Converter Q-Modulation (MVAr)0 5 10 15

P-Modulation of SMES Unit (MW)

0 5 10 15

Q From Capacitor Bank (MVAr)

-4I

0 5 10 15

&I Icqc---g-1 .,.

... Inductor Current Deviation (kA)-10 Net Q-Modulation of SMES Unit (MVAr)

-4 t0 5 10 15

-150 5 10 15

set

Fig. IO. Response of the power system after addition of the SMES unit using fuzzy logic control [case 21. .. Conventional; ~ Fuzzy.

(c) its performance with SMES unit using fuzzycontroller.

4.1. System modeling 1141

The following assumptions are made in the systemmodeling:1. The reheat turbine type thermal plant supplies to a

single generator whose capacity is 2000 MW.2. The generator is equipped with automatic voltage

Table 2Performance comparison of fuzzy and non-fuzzy controlled power

system with SMES unit (Case 2)

System behav- Without SMES (con-ior SMES ventional)

SMES (fuzzy)

FrequencyDeviation AJ -0.023

VW

Settling time >I5(s)

Overshoot 0.018 (max.)

(Hz)

Inductor currentDeviation Ald ._.

(k.4Settling time

6)Overshoot

GA)

Q, (MVAr) .,.

-0.0186 -0.0174

8.963 7.042

0.0075 (max.) 0.005 (max.)

3.06 2.72

11.1 9.86

0.2 0.1

4 (max.) 3.4 (max.)

regulator (AVR) with stabilizing speed feedback.3. The generator is cylindrical rotor type and the resis-

tances of the generator and the line are neglig ible incomparison with the reactances.

4. Strong coupling is present between P-f and Q-Vloops. The coupling effect can be shown as follows.

In general, the active and reactive power taken by aload are functions of frequency and voltage. Hence,

(4.1)

where AP and AQ are the changes in the real andreactive loads as caused by relatively small variationsAf and AlV1 in frequency and voltage.

Let the step load change causing the disturbance be(AP, + jAQL). The consequent changes in frequencyand voltage , Af and AV,, would in turn affect theloading. Therefore, the net change in real and reactiveloading APLN and AQLN can be expressed as

APL, ap,-AP,+vAf+alv,l fP,AjVLI

AQLNzAQL+FAf+- aQL AlV,lWLI

(4.2)

dQ,/df is neglected because of its less practical impor-tance [ 131.

The net incremental power AP, out of the syn-chronous machine is given by the sum of AP, (the


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M.G. Rabbani et al. /Electric Power Systems Research 40 (1997) 107- I14 113

incremental generator power due to governor action) and- (2H/fO)(d/dt)Af(the power derived out of the inertiaof the rotor through speed change). Hence,

2H dAP,=AP,-s,dtAj

With the addition of SMES unit at the load end, theactive and reactive powers balance at the generator buscan be represented as

AP, = AP,, + AP, (4.4)

AQ,= AQm + AQd+ AQ, (4.5)where AQ, is the change of reactive power loss in thetransmission line.

Using Eqs. (4.2), (4.3) and (4.4), the following isobtained:

(4.6)

4.2. Simulat ion results

Non-linear dynamic equations are used in the solutionprocess. They are solved using 4th order R-K method.The time interval chosen is 0.0015 s.

Two case-studies were conducted on the system: case

1 corresponding to sudden load change of (0.005 +jO.005) p.u. and case 2 corresponding to (0.008 + jO.008)p.u. The parameters are given in Appendix B.

The frequency and load voltage deviations of thepower system without SMES unit for the above two casesare shown in Figs. 7 and 8 respectively. In case 1, themaximum frequency and load-voltage deviations are- 0.0126 Hz and - 0.00306 p.u. respectively. The max-imum frequency and load-voltage deviations in the case2 are - 0.023 Hz and - 0.00428 p.u. respectively.Finally, the load-voltage deviation tends to stabilizes at- 0.00173 p.u. in case 1 and 0.002 p.u. in case 2respectively. The performance of the AVR shows that it

is fast enough to pul l back the voltage following a suddenapplication of load (see Figs. 7 and 8).

The coupling effect between the Q- V and P-f loopsis the main cause for the oscillations.

The responses of the power system with a 4 MJ SMESunit under the same disturbances for both the casesmentioned above are shown in Figs. 9 and 10 respec-tively.

In both these cases, the P-modulation by the SMESunit reduces the oscilla tion in the frequency while Q-modulation along with the reactive power provided bythe switched capacitor bank improves the load voltage

profiles. However, Fig. 10 clearly show the advantage offuzzy logic controller over conventional controller inevery aspect. The performance comparison is shown inTable 2.

4.3. Performance evaluation

4.3.1. Case 1 [load change (0.005 + j 0.005) PA.]When conventional controller is used, the maximum

frequency devia tion is 0.0105 Hz; and this occurs at anexpense of change in the inductor current of - 1.5 kA.Meanwhile, the fuzzy controller limits the frequencydevia tion to 0.0093 Hz at the expense of inductor currentchange of - 1.48 kA. It is evident from Fig. 9 that thefuzzy controller can provide better compensation withless devia tion of inductor current. This ensures theeffective use of its power modulation. There is not muchgain in voltage control loop except that the reactivepower compensation provided by fuzzy controller is lessthan the conventional one for the similar load voltageprofiles.

4.3.2. Case 2 [Load change of (0.008 +jO.O08) p.u.]Compared to the results of case 1, the fuzzy controller

shows significant development for the larger disturbance.Fig. 10 shows that the P-modulation by the SMES uni twith fuzzy controller reduces the frequency oscillation byalmost 24.3% compared with 18.9% reduction by theconventional controller. Significant improvements in thefirst overshoot and settling time are also clearly observed.The inductor current deviation is much less than that of

conventional controller. Like the previous case, theeffective use of active and reactive power modulation isalso ensured.

With the help of switched capacitor bank, the Q,,,supplied by SMES unit substantially reduces the voltagedeviation. In Figs. 8 and 9, it is observed that due to fastAVR action, the load-voltage goes up within a fewseconds. During the init ial period immedia tely after thesudden increase in load, the slope of the voltage deviationis very large and negative. Notice that the maximumvoltage deviations are same with and without the SMESunit . It is as expected since compensation cannot beprovided due to propagation delay time. The negative

voltage deviation requires capacitive VAr and initi alvalues of Qdem are accordingly chosen by FVC aftersatisfying the requirement of Pd. Like FFC, the FVC alsoconsiders the change in A VL as a dominant factor in thefirst cycle. In the later stage mainly voltage deviationdetermines the desired compensation Qdem. It is seen thatwith less VAr compensation, the FVC is able to maintainsame voltage deviation like the conventional controller.The overall performance of fuzzy controller shows a clearedge over the non-fuzzy one.

When operated in the two quadrant mode, the SMESunit itself absorbs inductive VAr in addition to AQL


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114 M.G. Rabbani et al. /Electric Polzer Systems Research 40 (1997) 107-l 14

due to sudden load application. Therefore switching ofstatic capacitors are needed during the dynamic varia-tion of the load-voltage. But with four quadrant opera-tion the amount of switching capacitance needed ismuch less than that of two quadrant operation. In case1, it is observed that the four quadrant operation

obviates the use of switched capacitor bank. There is noadvantage on P-modulation in four-quadrant mode.

4.4. Economic aspect

One of the most important criteria of using SMESunit either for load leveling and/or the improvement ofpower system performance is that it should be econom-ically viable. With the proposed mode of control thefluctuation of inductor current is smaller. This clearlyindicates that the SMES unit with fuzzy logic control isable to handle much bigger disturbances within thesame capacity as compared with other controllers. Fig.10 shows that the rating of switched capacitor bank canbe decreased with the proposed mode of control whichfurther decreases the cost of the SMES unit .

5. Conclusions

This paper presents a new method of controlling theSMES unit for improving the transient performance ofthe single area system. Fuzzy logic was used to designfrequency and voltage controllers to generate requiredcontrol signals for the SMES unit . Direct genera tion of

control signals for the 12-pulse converter from activeand reactive power modulation using both error signalsand change in successive error signals, makes the pro-posed controller more sensitive. As a result, P-Q mod-ulation is effectively used. Under smaller disturbances,fuzzy logic controller provides a little gain in systemfrequency damping and inductor current variations.However, when the degree of disturbance increases,fuzzy control shows its clear superiority in every aspectover the conventional controller.

In the proposed mode of control it is observed thatthe time taken to damp the system oscillations is com-

paratively smaller. Also this occurs with a smallerdeviation of the inductor current. This paper suggeststhat with the use of fuzzy logic control, the size of theSMES unit can be reduced and the rating of theswitched capacitor bank can be made smaller.

References

[I

PI

[31

[41

[51

@I

[71

P.M. Anderson and A.A. Fouad, Power System Control andStability, Iowa State University press, Ames, Iowa, 1977.E.V. Larsen and D.A. Swann, A pplying power system stabiliz-

ers, IEEE Trans. Power Appar. Syst., PAS-ZOO (1981) 3017-3046.O.P. Malik. G.S. Hope. S.J. Cheng and G. Hancock, A multi-

microcomputer based dual-rate self-tuning stab ilizer, Proc.IEEEjP ES Joint Powrr Generution Conj:, Portland, OR, USA,1986, Paper 86JPGC 652-2.S.C. Tripathy, T.S. Bhatti, C.S. Tha, et al., Sampled data

automatic generation control analysis with reheat steam turbinesand governor dead-band effect, IEEE Trans. Power Appur. Syst.,PAS-13 (1984) 1045-1051.

H. Stemmeler and G. Guth, T he thyristor controlled staticphase-shifter a new tool for power flow control in ac powersystem, Brown Boaeri Re oiew, 69 (1982) 73-78.

H.J. Boening and J.F. Hauer, Commission ing test of the Bon-neville 30 MJ super-conductive magnetic energy storage unit,IEEE T rans. Power Appar. Syst., PAS-104 (1985).

Y. Mitani, K. Tsu ji and Y. Murakami, Application of supercon-ducting magnetic energy storage to improve power system dy-namic performance, IEEE Trans. Power S JI.~~., 3 (1988)

1418-1425.[8] S. Banerjee, J.K. Chatterjee and S.C. Tripathy, Application o

magnetic energy storage unit as continuous VAr controller,IEEE Trans. Energ?, Conversion, 5 (1990) 39-45.

[9] S. Banerjee, J.K. Chatterjee and S.C. Tripathy, Application o

magnetic energy storage unit as load frequency stabilizer, IEEETrans. Energy Comersion, 5 (1990) 46-51.

[IO] C.D. S ousa and B.K. Bose, A fuzzy set theory based control oa phase controlled converter dc machine drive, IEEE Trans. Ind.A,@., 30 (1994) 34-43.

[I l] K. Rasool, and S. Alireza, Fuzzy power flow analysis, E r.Power Syst. Res., 29 (1994) 105-109.

[12] K.S. Tam and A. Yarali, Operation principle and application

multiterminal super-conductive magnetic energystorage systems,IEEE Trans. Energy Conversion, 8 (1992) 54-61.

[13] 0.1. Elgerd, Electric Energy Systems Theory, McGraw-Hill, NeYork, 1971.

[14] E.W. Kimbark, Direct Current T ransmiss ion, Wiley, New York1971.

Electric Power Systems Research Volume 40 Issue 2 1997 [Doi 10.1016_s0378-7796(96)01139-x] M.G. Rabbani; J.B.X. Devotta; S. Elangovan -- A Fuzzy Set Theory Based Control

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