Genetically Optimized Neuro-Fuzzy IPFC For

1140 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 4, NOVEMBER 2002

Genetically Optimized Neuro-Fuzzy IPFC forDamping Modal Oscillations of Power System

S. Mishra, P. K. Dash, P. K. Hota, and M. Tripathy

Abstract—An integrated approach of radial basis functionneural network (RBFNN) and Takagi-Sugeno (TS) fuzzy schemewith a genetic optimization of their parameters has been devel-oped in this paper to design intelligent adaptive controllers forimproving the transient stability performance of power systems.At the outset, this concept is applied to a simple device suchas thyristor-controlled series capacitor (TCSC) connected in asingle-machine infinite bus power system and is then extended tointerline power-flow controller (IPFC) connected in a multima-chine power system. The RBFNN uses single neuron architectureand its parameters are dynamically updated in an online fashionwith TS-fuzzy scheme designed with only four rules and triangularmembership function. The rules of the TS-fuzzy scheme are de-rived from the real- or reactive-power error and their derivativeseither at the TCSC or IPFC buses depending on the device. Fur-ther, to implement this combined scheme only one coefficient inthe TS-fuzzy rules needs to be optimized. The optimization of thiscoefficient as well as the coefficient for auxiliary signal generationis performed through genetic algorithm. The performance of thenew controller is evaluated in single-machine and multimachinepower systems subjected to various transient disturbances. Thenew genetic-neuro-fuzzy control scheme exhibits a superiordamping performance as well as a greater critical clearing timein comparison to the existing PI and RBFNN controller withupdating of its parameters through the extended Kalman filter(EKF). Its simple architecture reduces the computational burden,thereby making it attractive for real-time implementation.

Index Terms—Damping modal oscillations, FACTS, fuzzy, ge-netic, intelligent controller, neural, power system, stability.

I. INTRODUCTION

I N A MODERN integrated power network, transient anddynamic stability is of increasing importance for secure

operation of power systems. The recently developed flexibleac transmission system (FACTS) devices with proper con-trol strategy can significantly improve the transient stabilitymargin. Amongst the available FACTS devices, the interlinepower–flow controller (IPFC) is the most versatile one [1] andcan be used to enhance system stability. As an IPFC consistsof one shunt converter and many series ac/dc converters it canreplace more than one unified power-flow controller (UPFC)and is capable of regulating real- and reactive-power flows indifferent transmission lines simultaneously through injectionof series voltages of variable magnitude and phase angle and,thus, improves the transient stability limit [1].

Manuscript received February 7, 2002; revised June 6, 2002. This work wassupported by AICTE under Grant No. 8018/RDII/R&D/BOR(217).

S. Mishra, P. K. Hota, and M. Tripathy are with the Department of ElectricalEngineering University College of Engineering, Burla, India.

P. K. Dash is with Multimedia University, Cyberjaya, Malaysia.Digital Object Identifier 10.1109/TPWRS.2002.804958

A common dc capacitor is connected between the series andshunt converters to provide the required dc voltage for the oper-ation of converters. Besides, the shunt converter can exchange acurrent of controllable magnitude and power factor angle withthe connected bus to maintain the desired voltage profile. It isnormally controlled to balance the real power absorbed from orinjected to the power system by the series converters plus thelosses by regulating the dc bus voltage at a desired value. Var-ious control strategies to control the series voltage magnitude,angle, and the shunt current magnitude have been presentedin [2]–[6]. The series converter voltage phasor can be decom-posed into in-phase and quadrature components with respect tothe transmission-line current. The in-phase and the quadrature-voltage components are more readily related to the reactive-and real-power flows in the transmission system [1]. Duringshort-circuit and transient conditions, the variation in real powercan be arrested by proper injection of quadrature componentsof the series converter voltage and, hence, the improvement intransient stability. The PI regulators used for the purpose haveinadequacy of providing robust control and transient stabilityover a wide range of power system operating conditions.

Use of artificial neural networks (ANNs) for plant identifi-cation and control is gaining interest. A potential advantage ofthe ANN is its ability to handle the nonlinear mapping of input-output space. The difficulty in designing an ANN controller isto generate the training patterns of the controller. To overcomethis problem, a reinforcement learning controller has been pro-posed [7]. Dashet al. [7] have designed a single neuron ra-dial basis function neural network (RBFNN) unified power-flowcontroller (UPFC) with extended Kalman filter (EKF) updatingof its parameters in a multimachine power system. But it hasthe limitation that three constants are to be optimized for cre-ating the error surface and proper choice of EKF parameters.Further, as EKF involves complex mathematical operations, itrequires fast computational facility for its online implementa-tion. On the other hand, the TS-fuzzy UPFC proposed by Mishraet al. [8] has proved its superiority over its conventional coun-terpart. As any functional representation of inputs can be takenas a consequence of the rules, it is more nonlinear compared tothe Mamdani- type fuzzy scheme. But this scheme presents thedifficulties of deciding the number of coefficients of the con-troller in order to have acceptable performance.

Therefore, in this paper, a trial has been made to combinethe advantages of the TS-fuzzy scheme and RBFNN to developa neuro-fuzzy control strategy. The TS-fuzzy scheme is usedto update the parameters of the RBFNN in an online fashionwith reinforcement learning avoiding the requirement of EKF.As this newly designed controller involves less mathematical

0885-8950/02$17.00 © 2002 IEEE

MISHRA et al.: OPTIMIZED IPFC FOR DAMPING MODAL OSCILLATIONS OF POWER SYSTEM 1141

Fig. 1. Multimachine power system with IPFC.

operations, it is more realistic to implement it as an online con-troller with reinforcement learning. Besides, the genetic algo-rithm, which has global optimizing capacity basing upon a fit-ness function [11], is used to optimize the coefficients of theTS-fuzzy scheme as well as that of the auxiliary damping signal.To prove the efficiency of the new genetic-neuro-fuzzy (GNF)controller, transient disturbances at different operating condi-tions are created in single-machine and multimachine powersystems and are compared with conventional PI as well as theRBFNN controller, updating its parameters through extendedKalman filter (EKF) [NEKF] as proposed in [7].

II. SYSTEM MODEL WITH IPFC

To study the new control strategy for the IPFC, the multima-chine power system presented in references [7]–[9] is consid-ered for transient stability simulations. The power system andits detailed circuit model are shown in Fig. 1.

In Fig. 1, ST and ShT represent the series and shunt trans-formers whereas ShCon and SeCon are for the shunt and se-ries converters, respectively. Each synchronous generator of themultimachine system is simulated using a third-order model andthe IPFC is simulated using a power-injection model. As theIPFC consists of many series converters and one shunt converter,the injection model is derived based upon the UPFC injectionmodel [10].

If the shunt branch of the IPFC is connected to Bus-s withBus- , Bus- , Bus- , and Bus- representing the buses afterthe series transformers and an in-phase currentwith the Bus-svoltage drawn by the shunt converter, then the active powerof the shunt converter can be represented as

(1)

The power-injection model of the series voltage source con-nected between Bus-s and Bus-r has been presented in [8]–[10].As the system of Fig. 1 contains four series transformers to rep-resent the IPFC, the model can be formulated by adding all thepowers of the series injection model corresponding to Bus-sto represent the total Bus-s power and the powers of Bus-,Bus- , Bus- , and Bus- can be obtained directly. Further,as the exact real-power balance between the series and shuntconverter is never possible, the actual power in Bus-s will bethe sum of total Bus-s power and the real power drawn by theshunt converter. Hence, the IPFC injection model is constructed

Fig. 2. IPFC injection model.

(Fig. 2) where the notations are the same as that of [10]. Thedynamics of the dc link voltage neglecting losses can be repre-sented by

(2)

In Fig. 2, the coefficient corresponds to ,where the “ ” stands for the series converter number. Thevoltage ratios () and phase angles () of all of the series-in-jected voltages with respect to the Bus-s are controllable from

and 0 to 2 , respectively. The injection modelof IPFC presented in Fig. 2 modifies the admittance matrix( -Bus) of the power network. The controllable loads at theth and th bus of IPFC are

(3)

These controllable admittances are added to theandelements of the -Bus matrix of the power network withoutIPFC. Further, the and are related to the series controlvoltages in phase and quadrature with the line current

after the series transformers of IPFC as

(4)

tan

tan tan (5)

which have also been presented in [7]. Similarly, automaticvoltage regulators (AVRs) are connected to each generator.No damper winding is modeled, as we are investigating theperformance of the IPFC. The dynamics of the machines andthe data are given in [8], [9].


Fig. 3. Single neuron RBFNN structure.

III. GENETIC-NEURO-FUZZY CONTROLLER

Recently, researchers have begun to examine the use of ra-dial basis function network for nonlinear control of plants andsystems since they offer a simple topological structure. Further,for real-time implementation of a FACTS controller, a singleneuron RBFNN will be adequate [7].

Fig. 3 shows the structure of the RBFNN, where the hiddenlayer comprises a single neuron referred to as a computing unit.The hidden layer neuron in the network uses a Gaussian basisfunction that has two parameters called a center “” and spread“ ” associated with it. The response of one of these units to thenetwork input “ ” is expressed as

(6)

and the network output is obtained as

(7)

A Takagi—Sugeno (TS) rule scheme has been designed toupdate the parameter matrix of theRBFNN. For updating the parameters, the following procedureis adopted. The active or reactive power deviations are fuzzifiedusing two input fuzzy sets named positive (P) and negative (N)and the membership functions are

(8)

where denotes error at theth sampling instant given by

or and

(9)

For the negative set

(10)

The membership functions for the error and difference oferror are shown in Fig. 4.

The TS fuzzy scheme uses four simplified rules as follows.: If is positive and is positive, then

.: If is positive and is negative, then

.: If is negative and is positive then

.: If is negative and is negative, then

.

Fig. 4. Membership function.

In the rule mentined before, base and representthe output of TS fuzzy scheme. Using Zadeh’s rules forAND

operation and the general defuzzifier, we get

(11)

However, for , we get the centroid defuzzifier withgiven as

where (12)

and

(13)

Therefore, the updating of parameters at any instant dependson error and its difference. This output(required change inparameter matrix of RBFNN) from the fuzzy scheme is al-ways added to the predisturbance parameter matrix to decide thepresent value of the parameters. Therefore

(14)

where and isthe predisturbance parameter matrix of RBFNN. Before theupdating of parameters is carried out, the output signal fromthe RBFNN will be generated as

(15)

Therefore, in this scheme, the output is immediately decidedbased on the input and previous value of parameter matrix,whereas the updating of the parameters are performed duringthe sampling time to make the controller ready for the next op-eration. In order to use a limited knowledge of the power systemdynamics to design the controller, a reinforcement method ofweight adaptation (continuously in an online fashion) whichwill avoid network training dataa priori to its implementation[7], will be used in this paper.

A. Control Scheme for TCSC

To introduce the concept at the outset, a single-machinepower system with a thyristor-controlled series capacitor(TCSC) as presented in Fig. 5 will be considered.

The TCSC reactance is modeled as

(16)

wherevirtual reactance of the TCSC;


Fig. 5. Single-machine power system with TCSC.

reactance of the TCSC capacitor;degree of voltage boost across the capacitor.

The TCSC reactance is varied by the real-power erroras the series capacitor directly controls the real-

power flow in the transmission line.

B. Control Scheme for IPFC

Since the components and of series injection voltageof IPFC (Fig. 1) are at quadrature and in phase to the line current,it can regulate the real-power and reactive-power flow in theline, respectively. Therefore, the real-power error (

) and the reactive-power error ( ) are used togenerate and , respectively. Besides, a modulating signalgenerated from the speed of the machines is used to damp thepower system oscillations. In that case, the signal is to bereplaced by

for series converter-1 (17)

where


where


where


where .In the expressions just shown, and are the

predisturbance power and actual power flowing out from theth-bus and is the speed of th machine. The choice of

( ) is taken for conveter-1 and 2 as these converters maybe employed for damping inter-area mode of oscillation in thepower system. Similarly, for the other two converters, theirerror signals are augmented with ( ) for faster dampingof local mode of oscillations. Only one coefficient has beenconsidered for auxiliary signal generation, since it will simplifythe design strategy.

C. Genetic Optimization of Coefficients

Recently, the genetic algorithm (GA) has gained momentumin its application to optimization problems. Unlike strict math-ematical methods, the GA does not require the condition thatthe variables in the optimization problem be continuous and dif-ferent; it only requires that the problem to be solved can be com-puted. So, the GA has an apparent benefit to adapt to irregularsearch space of an optimization problem [11]. Therefore, in thispaper, the GA has been used for optimization of only the coeffi-cient of TS fuzzy scheme () for single-machine power system

with TCSC and the coefficients of TS fuzzy scheme () andauxiliary signal ( ) for the multimachine power system. Thebasic operators in the GA include reproduction, crossover, andmutation. The coefficients and , taken as individuals inGA, are represented by a binary string of length 28 with thefirst 14 bit corresponding to and next to , respectively.The ratio of maximum value of these coefficients to 2 willrepresent the least count of the solution. The fitness function forthe multimachine power system is taken as

(21)

which is the ITAE of the speed signals corresponding to theinter-area and local mode of oscillations. On the other hand, thefitness function for a single-machine power system is simplytaken as

(22)

where is the base speed of the generator. The integration isreplaced by summation in the simulation of transient stabilityproblem. To select the maximum limits of the coefficients to beoptimized, the transient stability program written in MATLABis run and the values are chosen so that the system is unstableat the particular operating condition and type of fault. Two ran-domly generated numbers between 0 and 1 are multiplied bythe maximum limits of the coefficients to decide the coeffi-cient values for the present simulation. In this manner, a setof 50 random pairs of the coefficients are created, discardingthe unstable cases. These 50 pairs of coefficients are convertedinto binary codes to construct the initial population termed as“oldpop.” From this grouped population and by using the usualGA operators, equal numbers of new populations are gener-ated. A specific probability of each operator is fixed, keepingthe “mutation” probability sufficiently small. The crossover andmutation probabilities are taken as 0.6 and 0.03, respectively[11]. To select two strings of population for either mutationor crossover, the roulette wheel technique is used [11]. Thetechnique specified that for selection, a random number be-tween 0 and 1 is multiplied with the sum of fitness of all the“oldpop” strings. When this value is greater than or equal to thecumulative fitness of theth string, this string is selected fromthe “oldpop.” In this manner, two strings (mate-1 and mate-2)are selected to the mating pool. Using the GA operators, twonew strings (child-1 and child-2) are created out of these mates.This process is continued until 50 new strings of population aregenerated. Out of the original 50 strings and newly created 50strings (a total of 100 strings), the most-fit 50 population stringsare retained. These strings are replaced into the “oldpop” to rep-resent the second generation “oldpop.” In this manner, 25 gen-erations are continued, before the algorithm converges into thefit unique solution. The binary data in the solution are decodedto provide the optimized coefficient values of or both and

, depending on the type of power system considered. Thesevalues are used in the neuro-fuzzy scheme to present the GNFcontroller. The schematic diagram of the GNF controller is pre-sented in Fig. 6 ( is the shift operator).


Fig. 6. GNF IPFC.

In case the PI regulator is used in controlling theand ,the equations are

(23)

The integration values are limited to0.25 pu, which yieldsthe best performance.

IV. SIMULATION RESULTS

Both the multimachine and single-machine infinite bus powersystems depicted in Figs. 1 and 5 are taken for digital simulationstudies. The gains of all of the PI and NEKF control schemes areoptimized through the ITAE criteria whereas the value ofusedin the fuzzy membership function is decided based upon themaximum value of error and its difference. Further, as presentedin [7], the error surface required for NEKF is taken as

, where will be replaced by realpower or reactive power, depending upon the type of controller.In the real- and reactive-power error surfaces, the value of thecoefficient is considered to be the same for ease of optimization.The EKF updating equations, single-machine, and the multi-machine data are presented in [7]. At the predisturbance condi-tion, the value of of the RBFNN con-troller is initialized to or (dependingon whether it is a real-power or reactive-power controller).

A. Single-Machine Infinite-Bus Power System With TCSC

The single-machine infinite-bus power system depicted inFig. 5 is considered for simulation studies. The initial value ofTCSC reactance and are taken as 0.1 and 0.5 pu, respec-tively. The controller data are given in the Appendix.

Case 1: The generator is operated at a low-power-outputcondition of p.u. and p.u. and a three-phasefault of 120-ms duration occurs near the infinite bus. Fig. 7shows the transient response of the system with different con-trol schemes. It is observed that the performance of each controlscheme is almost the same. This is due to the fact that the coef-ficients of the controllers are optimized at this operating condi-tion. To quantify the performance, the ITAE value that is foundup to 10 s in (22) is presented below: PI-3.1622, NEKF-2.6102,GNF-2.7508.

Case 2: The operating condition of the generator is changedto a new level of pu and pu and the samethree-phase fault is initiated near the infinite bus to evaluate the

Fig. 7. Transient response atP = 0:4 pu andQ = 0:2 pu.



performance of different control schemes and is presented inFig. 8. At this operating condition, it is found that the PI controlscheme is unstable whereas the GNF and NEKF are stable intheir operation which clearly establishes the superiority of anintelligent control scheme. The ITAE value for the two stablecontrol schemes of NEKF and GNF are 138.7366 and 59.1578,respectively.

Case 3: The operating condition of the generator is changedto a higher power level of pu and pu and athree-phase fault of 120-ms duration is simulated near the in-finite bus. The transient performance of the different controlscheme is depicted in Fig. 9. From the response, the suitability ofthe newly designed controller is well established, which makesthe unstable case stable.

B. Multimachine Power System With IPFC

The multimachine power system of Fig. 1 is taken for digitalsimulation. The different control schemes are used to producethe desired amplitude of voltage components and forall of the series voltage-source converters. The current of theshunt converter is obtained from a PI controller with the error as( ), where the voltage is the dc capacitorvoltage. Therefore, the equation for the in-phase shunt currentwith respect to the shunt converter bus voltage will be

(24)


Fig. 10. Inter-area mode of oscillation.

Fig. 11. Local mode of oscillation.

The following large disturbance cases are considered for eval-uating the performance of these controllers. The IPFC data andthe controller data are given in the Appendix. Taking machine–1as a reference and the predisturbance operating condition in perunit as , , , ,

, and , the response of the network to dif-ferent disturbances are presented to establish the superiority ofGNF controller over the NEKF and PI controller. The followingcase studies are undertaken for evaluating the performance ofthe proposed controller in the multimachine environment.

Case 1: A three-phase fault of 100-ms duration is simulatedat the middle of line connecting bus 6 and bus 1. The perfor-mance of the conventional PI controller, NEKF, and GNF con-troller in damping the inter-area ( ) and local mode (

) of oscillations of the generators is presented in Figs. 10 and11, respectively. In this case, the performances of each controlscheme are almost the same. This is because the parameters ofall of the controllers are tuned at this operating condition withthe previously mentioned fault. Further, to quantify the con-troller performance, the ITAE value found up to 15 s in (21)is presented below: PI-8.8262, NEKF-9.6467, GNF-9.0404.

Case 2: The duration of the same fault is increased from 100to 220 ms at the previous operating condition. The performanceof each control scheme is depicted in Figs. 12 and 13. In this sit-uation, the PI controller becomes unstable in the modal oscilla-tions whereas both NEKF and GNF controllers are stable in theiroperation. To have a quantitative insight to the modal oscilla-tions, the ITAE value was up to 15 s according to (21) for the twostable control schemes of NEKF-25.6824 and GNF-25.1329.

Case 3: The fault duration is further increased to 272.5 msat the same operating condition. The modal oscillations are pre-sented in Figs. 14 and 15. At this condition, it is found that thePI and NEKF schemes are unstable, whereas the GNF scheme isstable in its operation. Therefore, the newly designed controllerfor IPFC claims a higher critical clearing time compared to theNEKF and PI controller. This increase in critical clearing time





will enable more time for the opening of the circuit breaker fol-lowing a fault. Also, it increases the transient fault duration thatthe system can withstand.

Case 4: The operating condition of the multimachine powersystem in per unit is changed to a higher power level of

, , , , , and. At this operating condition, it is found that the PI

control scheme becomes unstable in its operation whereas bothNEKF and GNF schemes are stable. Besides, the settling timeof both intelligent schemes is practically the same, althoughthere is slightly higher overshoot in the case of GNF, as depictedfrom the inter-area and local modes of oscillations presented inFigs. 16 and 17, respectively.

Case 5: The operating condition of the power network inper unit is further changed to , ,

, , , and , and the modaloscillations are presented in Figs. 18 and 19, respectively. From






the responses, the superiority of the GNF control scheme is wellestablished as the unstable case of NEKF and PI are made stablethrough GNF schemes. Besides, the settling time of GNF is al-most the same at all of the considered operating points.

Case 6: The fault location in the power system is changedto the middle of the transmission line connecting bus 3 and bus8. The same three-phase fault of 100-ms duration is simulatedwith the operating condition the same as that of case 1. Theperformance of all of the controllers are presented in Figs. 20and 21. From the performance, it is quite clear that the GNFcontroller overcomes the instability of both NEKF and PI con-trollers. Therefore, the newly designed controller is robust tochange in fault location.



V. CONCLUSIONS

In this paper, a combination of both TS-fuzzy scheme andRBFNN is adopted for nonlinear control of TCSC and IPFC.By combining both intelligent techniques, the control strategybecomes less mathematical and, hence, faster in computation.The new neuro-fuzzy-based control scheme adapts itself to gen-erate suitable variation of the control signals depending on theoperating condition of the power system and, hence, a supe-rior performance in comparison to the linear PI controllers isused for IPFC and TCSC. In the TS fuzzy scheme used, the ruleconsequently could be either a linear or a nonlinear functionof input variables and, hence, a suitable change in parametermatrix of the RBFNN can be obtained. Further, as RBFNN isused, it has tremendous power to incorporate the nonlinearitythrough training. On the other hand, the coefficient of TS fuzzyscheme and the auxiliary signal are optimized through the GA tominimize the fitness function globally. The performance of theIPFC and TCSC with the proposed GNF control scheme is eval-uated vis-à-vis the RBFNN controller with EKF updating of itsparameters (NEKF) and conventional PI control to validate itssuperior performance in respect to transient stability enhance-ment. This controller makes the unstable cases of NEKF and PIcontroller stable, hence, found to be robust to fault location andchange in operating condition. Besides, the critical clearing timeincreases for the newly designed controller compared to its con-ventional counterpart as well as the NEKF scheme provide moretime for the transient faults. Also, the inter-area and local modesof power system oscillations are damped much faster using thisnew controller.

APPENDIX

TCSC controller data: conventional PI controller.

Optimized coefficient: (Coefficient of the TSfuzzy scheme) (Coefficient of the NEKF errorsurface).


IPFC data in per unit.: All of the series transformers aswell as the converters have the same data of ,

, , ,, kV, and Fs.

Controllers data: Conventional PI controllers(Both P and Q controller

of all of the series converters)(in phase-current controller of shunt converter).Optimized coefficients: (Coefficient of theauxiliary signal) (Coefficient of the TSfuzzy scheme) (Coefficient of the NEKFerror surface) TS fuzzy scheme for (Change in param-eter matrix of RBFNN) (Both P and Q controllersof all of the series converters).

REFERENCES

[1] N. G. Hingorani and L. Gyugyi,Understanding FACTS. Piscataway,NJ: IEEE Press, , 2001.

[2] L. Gyugyi, C. D. Schauder, S. L. Torgerson, and A. Edris, “The unifiedpower flow controller: A new approach to power transmission control,”IEEE Trans. Power Delivery, vol. 10, pp. 1088–1097, Jan. 1995.

[3] M. Noroozian, L. Angquist, M. Ghandari, and G. Anderson, “Improvingpower system dynamics by series-connected FACTS devices,”IEEETrans. Power Delivery, vol. 12, pp. 1635–1641, Oct. 1997.

[4] M. Noroozian and G. Anderson, “Damping of power system by control-lable components,”IEEE Trans. Power Delivery, vol. 9, pp. 2046–2054,Oct. 1994.

[5] K. R. Padiyar and A. M. Kulkarni, “Control design and simulation ofunified power flow controller,”IEEE Trans. Power Delivery, vol. 13,no. 4, pp. 1348–1354, Oct. 1998.

[6] S. Limyingcharoen, U. D. Annakkage, and N. C. Pahalawaththa, “Fuzzylogic based unified power flow controllers for transient stability im-provement,”Proc. Inst. Elect. Eng. C, vol. 145, no. 3, pp. 225–232, May1998.

[7] P. K. Dash, S. Mishra, and G. Panda, “A radial basis function neuralnetwork controller for UPFC,”IEEE Trans. Power Syst., vol. 15, pp.1293–1299, Nov. 2000.

[8] S. Mishra, P. K. Dash, and G. Panda, “TS-fuzzy controller for UPFC ina multimachine power system,”Proc. Inst. Elect. Eng. Gener. Transm.Dist., vol. 147, no. 1, pp. 15–22, Jan. 2000.

[9] M. Noroozian, G. Anderson, and K. Tomsovic, “Robust near-optimalcontrol of power system oscillation with fuzzy logic,”IEEE Trans.Power Delivery, vol. 11, pp. 393–400, Jan. 1996.

[10] M. Noroozian, L. Angquist, M. Ghandari, and G. Anderson, “Use ofUPFC for optimal power flow control,”IEEE Trans. Power Delivery,vol. 12, pp. 1629–1634, Oct. 1997.

[11] D. E. Goldberg,Genetic Algorithm in Search, Optimization and MachineLearning. Reading, MA: Addison-Wesley, 1989.

S. Mishra received the B.Sc. (Engg.) degree from University College ofEngineering, Burla, Orissa, India, the M.Sc. (Engg.) degree from RegionalEnginering College, Rourkela, Orissa, and the Ph.D. degree from SambalpurUniversity, Orissa, in 1990, 1992, and 2000, respectively.

He is a Reader in the Department of Electrical Engineering at the UniversityCollege of Engineering, Burla. His interests are in fuzzy logic and ANN appli-cations to power system control and power quality.

P. K. Dash received the B.E. and M.E. degrees from the Indian Institute ofScience, Bagalore, in 1962 and 1964, respectively, and the Ph.D. degree fromSambalpur University, Orissa, India, in 1972.

He was a Postdoctoral Fellow with the University of Calgary, Calgary, AB,Canada, from 1975 to 1976. He was a Professor of electrical engineering andChairman, Center for Intelligence Systems, Regional Engineering College,Rourkela, India. Currently, he is on the Faculty of Engineering at MultimediaUniversity, Cyberjaya, Malaysia. His interests are in fuzzy logic and ANNapplications to power system control.

P. K. Hota received the B.E. degree from Regional Engineering College,Tiruchirapalli, Tamilnadu, India, the M.Sc. (Engg.) degree from UniversityCollege of Enginering, Burla, Orissa, India, and the Ph.D. degree from JadavpurUniversity, Kolkata, India in 1985, 1992, and 2000, respectively.

He is the Head of the Department of Electrical Engineering at the UniversityCollege of Engineering, Burla, India. His interests are in soft computing appli-cation to power system operational control and unit commitment.

M. Tripathy is pursuing the M. E. degree with a specialization in power systemsat the Department of Electrical Engineering, University College of Engineering,Burla, India.

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Genetically Optimized Neuro-Fuzzy IPFC For