8/13/2019 199606 Stabilizer

1/7

IEEE Transactions on Energy Conversion,Vol. 11, No. 2 June 1996 435

A Neural Network-Based Power System Stabilizerusing Power Flow Characteristics

Young-Moon Park, Senior member, IEE EMyeon-SongChoi, member, IEEEDepartment of Electrical Engineering

Seoul National UniversitySeoul 15 1-742

Korea

Absf rad - A neural network-based Power System Stabilizer(Neuro-PSS) is designed for a generator connected to a multi-machine power system utilizing the nonlinear power flowdynamics. The usesof power flow dynamics provide a PSS for awide range operation with reduced size neural networks. TheNeuro-PSS consists of two neural networks: Neuro-Identifierand Neuro -Controller. The low-frequency oscillation is modeled

by the Neuro-Identifier using the power flow dynamics,then a G eneralized Backpropagation-Thorough-Time (GBTT)algorithm is developed to train the Neuro-Controller. Thesimulation results show that the Neuro-PSS designed in thispaper performs well with good damping in a wide operationrange compared with the conventionalPSS.

Keywords - Neuro-PSS, Neural networks, Power systemstabilizer, Low-frequency oscillation. Power flowcharacteristics.

I. INTRODUCTION

One of the most important problems arising from large-scale electric power system interconnection is the low-

frequency oscillation [l] . For this problem, there has been aconsiderable research into the Po wer System Stabilizer(PSS)design [I]. The conventional design was first proposed bydeMello and Concordia [2] on the basis of thesingle-machine infinite-bus linearlized model [3]. In their approach,the PSS was designed as a lead-lag compensater whichprovides a supplementary control signal to the excitationsystem.

96 WM 036-4 EC A paper recommended and approved by the IEE E EnergyDevelopment and Power Generation Committee of the IEEE PowerEngineering Society for presentation at the 1996 IEEE/PES Winter Meeting,January 21-25, 1996, Baltimore, MD. Manuscript submitted July 19, 1995;made available for printing January 4, 1996.

Kwang Y. Lee, Senior member, IEEE

Departmentof Electrical EngineeringThe P ennsylvania S tate University

University Park,PA 16802U S A

A practical PSS must be robust over a wide rangeofoperating conditions and capable of damping the oscillationmodes in a power system [4]. From this perspective, theconventional PSS design approach based on a single-machineinfinite-bus linearlized model in the normal operatingcondition has som e deficiencies:

1) There are uncertainties in the linearized model resultingfrom the variation in the operating condition, since thelinearlization coefficients are derived typically at normaloperating condition.

2) To implement the PSS for a multi-machine power system;its parameters need to be tuned to coordinate with othermachines and utilities.

Consequently, a realistic solution f or stabilizing the low-frequency oscillation of a multi-machine system is a stabilizerdesigned from a nonlinear multi-machine model in the firstplace [ I ] . Fig 1 shows the schematic diagram of a generatorconnected to a power system network. Difficulties in a powersystem stabilizer design come from the handling ofnonlinearities and interactions among generators. D uring thelow-frequency oscillation, rotor oscillates due to theunbalance between mechanical and electrical powers. Theelectrical power, P, shown in Fig. 1, has the properties of thenonlinearty and this interactionis the key variable affectingthe rotor dynamics. Thus, handling the nonlinear power flowproperly is the key to the PSS design for a multi-machinepower system. Unfortunately, itis not that easy to handle the

-_---Electnc Power Flow

II

P, +JQ,

External Power System

Fig. 1.A generator connectedto power system network.

0885-8969/96/ 05.00Q 1996IEEE

8/13/2019 199606 Stabilizer

2/7

436

nonlinear interaction variables in control by conventionalanalytical methods.

Recently, a new approach has emerged in control area tohandle nonlinea rities utilizing the neural networks' learningability. The use of neural networks' learning ability avoidscomplex mathematical analysis in solving control problems

when plant dynamics are complex and highly nonlinear,which is a distinct advantage over traditional controlmethods.

Nguyen and Widrow [5] showed the possibility of usingneural networks in controlling a plant with highnonlinearities. They exploited the neural networks' self-learning ability in the Truck-Backer problem. Iiguni andSakai [6] constructed a neural network controller combinedwith a linear optimal controller to compensate foruncertainties in model parameters. Recently,Ku and Lee [7]proposed an architecture of diagonal recurrent neural networkfor identification and control of dyna mic systems, and appliedit to a nuclear power plant model[SI.

There are cases where neural networks are applied forpower system stabilizing control [9],[101. However, thesecases are limited to a system with a single generatorconnected to an infinite bus to avoid the complexity of theinterconnected power system dynamics.Yu [11 pointed outthat it is desirable in the PSS controller design to considerinteraction variables describ ing mutual interactions am onggenerators networked in a power system.

This paper introduces a new approach for handling thenonlinear interaction variables, i.e., the power flow. Byutilizing the neural networks' learning ability in mapping thepower flow dynamics, a PSS (Neuro-PSS) is designed for agenerator connected to a multi-machine power system. Theproposed neural network-based PSS architecture is composed

of two parts. First, a Neuro-Identifier is designed for agenerator to emulate the characteristics of the power flowbetween the generator and the power system network.Seco nd, a Neuro-C ontroller is constructed for the generator toproduce the supplementary excitation signal which minimizesa quadratic cost function in speed deviation and controleffort. The Neuro-Identifier is trained by the usualBackpropagation Algorithm (BPA), and the Neuro-Controlleris trained with the equivalent error backpropagated throughthe Neuro-Identifier using a newly developed GeneralizedBackpropagation-Through-Time algorithm to minimize thequadratic cost function in speed deviation and control effortof the generator.

11. PROBLEM FORMULATION

A. Characteristicsof Rotor Dynamics

The choice of model is very important for a controllerdesign. In designing a PSS, the simplicity of the Heffron-Phillips linear model and its ability to represent the transient

behavior of the synchronous machine is well known[3].However, the parameters of the linearized model arefunctions of the operating condition [ l ] . Therefore, it isdesirable to use a nonlinear model in designing a nonlinearNeuro-PSS for a wide range operation.

To study the low-frequency oscillation, a third-order

model is considered for a synchronous generator connected toa network at b us j [I]:

do- T, G , T , = P, / o , G = P, 1 0

d t

d6d t

( I >

- O h W - l ) , O b = 271f O = 1 ( 2 )_

dei 1~ [ E ,e; - xd -x . e:, - v, cos(6 - e,)], 3)

dt TA

where 6 a n d o are rotor position an d velocity, e; is thevoltage behind the transient reactance, and other variables aredefined in [11.

In equation 3 ) , dynamics of e; is controlled by the fieldexcitation voltage, which is the output of a conventionalexciter. A supplem entary control signal will be added to thisexcitation voltage for stabilization[11.

The generator connected to a network should satisfy thealgebraic power balance constraint:

(4)P, ( e ; , v, A e , ) + s v , > e , ) =p N / mQ < ~ ~ v ~ Q I QAV,,Q,> = Q ~ ~ , G > ,= 1,2, . . . , N ,

where P, and Q, are the real and reactive powers of the

generator, Pw and QW are the net power injections at the j-t h

bus, and pi and Qt are the local loads, whicn are nonlinearfunctions of system variables. The rotor dynamics 1) isrepresented in terms of the power flow,P, In a conventionalmethod, it is difficult to design aPSS for a wide rangeoperation due to the nonlineartyof the power flow. However,a Neuro-PSS can be designed since one of the characteristicsof artificial neural networks is to learn the nonlinear mappingwith input-output pair [5].

Since the rotor dynamics is simply represented byequations (1) and 2) with known inertia constant, it onlyremains to learn the nonlinear power flow usinga neuralnetwork. Since the neural network needs not to learntheknown rotor dynamics (1) and (21, a smaller size neuralnetwork can be used and consequently, training time can be

reduced.To train a neural network, it needs to kno w the information

on the dynamics in terms of the input-output relationship. Inview of equations (1)-(4), the power flow can be representedas a function of e;, 6 and ~ i s input variables. However, the

voltage behind the transient reactance, e; , is not easy to

8/13/2019 199606 Stabilizer

3/7

437

measure and to use as a feedback variable. Since the voltagebehind the transient reactance only affects the power flow, itcan be included in the power flow variable.

Following the above observation, and by shifting theorigin to the normal operating po int ,it can be shown that therotor dynamics of a generatoris modeled as

- -@=I >dAw 1

dt M

dt

( 5 )

O ~ A O 6)dA6

Fig. 2. A neural network-based power system stabilizer@ , u , A 6 , Aw ) , 7)dt

where U is a supplementary excitation signal from PSS.

B. Neural NetworkBased-Power System Stabilizer

A feedfonvard neural network with taped delays canrepresent the nonlinear dynamic system model [ l I].However, it requires a discrete model for training. Thediscrete model of the rotor dynamics of a generator with timestep At corresponding to the equations 5), 6) and (7) isrepresented as

8 )

9 )

1M

AO(k+ 1 = -(-@,(k))At AO(k)

A8 k I) = O,,AW (k). t A k)

AP,(k + I) = f (Ae(k ) ,APe(k- I ) , . . . , A & ~ n + I ) ,

10)AO(k),A6(k),U(k),U(kl ) ; . . , U ( k - m 1))

where, m and n are the delay orders for output and inputvariables.

It should be noted that the order of the system that a neuralnetwork has to represent is reduced by two since only thepower flow dynamics(10) needs to be m odeled.

Following the input-output relationship in the power flowdynamics, a Neuro-PSS is designed with two neuralnetworks: A Neuro-Controller is constructed to generateadequate supplementary excitation signal to compensate forthe Pow-frequency oscillation, and Neuro-Identifier isconstructed to model the power flow dynamics and used tobackpropagate anequivalent error or generalized delta to theNeuro-Controller for training. Fig. 2 shows the overallscheme for the neural network-based power system stabilizerfor a wide range operation, where the operator,TDL, presents

a memory element having the input or output history.

111. TRAINING OF NEURAL-NETWORKS

The Neuro-PSS in this paper is composed of twomultilayer feedforward neural networks,one for Neuro-Identifier and another for Neuro-Controller. The structure of

a multilayer neural network represents a nonlinear functionwith multi-inputs and single output and has weightparameters and neurons, each with a nonlinear sigmoidfunction. The Neuro-Identifiers weight parameters areadjusted by the equivalent error with theBPA 651, and theNeuro-Controllers are adjusted by the GBT T algorithm.

A . Training o the Neuro-Identijier

The Neuro-Identifier represents the nonlinear dynamicsofthe power flow outputof a generator connected to a powersystem network. It is later used to train the Neuro-Controllerby backpropagating the equivalent error.

The dynamics of the power flow of a generator in(1 0) canbe viewed as a nonlinear mapping as following:

(1 11@ 1) = f ( Z ( k ) )where -

X ( k )= (A k) ,A P,(k l ) ; . . ,AP,(k n I ) ,

Aw(k) ,A6(k) ,~ (k ) ,~ (kI ) , . . . , u ( ~m + I ) )

Therefore, the Neuro-Identifier for the plant can berepresented by a nonlinear networkF

A k 1) = F(Z(k) , ) , (12)

whereInput-output training patterns are obtained from the

operation history of the plant. The Neuro-Identifier learns togenerate the same output responses as the plant does by usingthe BPA. The objective of training the Neuro-Identifier istoreduce the average error defined by

is the weight vector to adjust.

(13)J = - - - h P , k + l ) - ~ , k + , ) ) * ,

N k=12

where N is the number of training sets in an epoch foradjusting the weight parameters. In theBPA he equivalenterror on the output node of the network for the k-th sampleddata is defmed as

8/13/2019 199606 Stabilizer

4/7

438

This error is then used backward to compute an equivalenterror for a node in an arbitrary layer to update weightparameters in the BPA. The training is finished when the

average error between the plant and the Neuro-Identifieroutputs converges to a small value, and the Neuro-Identifierrepresents the plant characteristics approximately, i.e.,

(k 1 = f ( * ( k ) ) N k ( k 1 = F z? k),@) (15)

B. Training o the Neuro-Controller

The role of the Neuro-Controller is to stabilizelow-frequency oscillation when the speed of a generator deviatefrom its normal value. In order to solve this problem in afinite time horizon, a general quadratic cost function isdefined as

where u ( k ) is the supplementary excitation control input,and N is the numb er of time steps.

The characteristics of the Neuro-Controller can berepresented as a nonlinear networkH :

U ( k ) = f f ( A e ( k ) , A P , ( k ~ l ) , . . . , A ( k ~ n + I), -2 (17)

CO k) ,A6 k ) ,U k - l ) ; . . , U ( k ~ m + 1 ,w

where F? is the weight vector to adjust.Since the target value for the adequate supplementary

excitation control U k ) is not available for training, the usualbackpropagation method is not applicable. Therefore, the

Neuro-Controller has to learn the control law by trial anderror, by driving the Neuro-Identifier to generate theequivalent error for backpropagation.

The learning process by trial and error consists oftwoparts. First, from the given initial state the Neuro-Controllerdrives the Neuro-Identifier forN steps. Second, the weightparameters of the Neuro-Controller are updated using theaverage of corrections calculated for each step to reduce thecost function. In order to train the Neuro-Controller tominimize the general quadratic cost function 16), it isnecessary to extend the Backpropagation-Through-Time(BTT) algorithm [ l 11, which w as originally developed for thequadratic cost of the output errors alone. Since our costfunction 16) includes not only output errors, but also input

variables, the BTT method can not be used and has to begeneralized, resulting in the Generalized BTT (GB TT).

The equivalent errors for the cost function are defined asthe following sensitivities with respect to input variables:

for k-1 2, ... , N . (18)By differentiating the cost function 16) and using the

relationships 9), lo), 1 1) and 17), it can be shown that thesensitivities satisfy the following coupled equations:

(19)

s ,

Equations (19)-(22) show that the equivalent errorsbackpropagate and the sensitivity with respect to the input,6:, can be computed. Since u k ) is the output of the Neuro-

Controller H , the conventional backpropagation algorithmcan thus be used directly.

The process of the GBTT training algorithm i ssummarized as follows:

Set the weight parameters of the Neuro-Controller withsmall random numbers.

Set the load condition and initial state with randomnumbers in the operation region of the power plant.

Let the Neuro-Controller drive the generator and theNeuro-Identifier for teps forward.

From the operation result in step 3), evaluate theequivalent errors 6 ; backward using equ ations 19), 20),21)

and22),

and compute the weight parameteradjustment vector AW k .

Update the weight parameters in the Neuro-Controller byusing the average of weight parameter adjustment vectors

AW k found in step4).

Go to step 2).

8/13/2019 199606 Stabilizer

5/7

439

Training of the Neuro-Controller is finished when theaverage decrease of the cost function converges to a smallvalue for an arbitrary reference output and initial conditions.

IV. CASE STUDY

A. The Study Power System

The Neuro-Controller is applied to a simple power systemnetwork [12] shown in Fig. 3 to stabilize low-frequencyoscillations. The power system consists of three power plants:two are thermal units and one is hydro unit. The normaloperating conditions and line parameters of the network inp.u. on 100 MVA base are also shown inFig. 3. The powersystem has sustained low-frequency oscillations due todisturbances. The control objective is to improve systemdamping by using a supplementary excitation control appliedto the second generator. For the low-frequency oscillationproblem, parameters of the generator model (1)-(3) arepresented in Table 1.

T h e r m a l P l a n t )

Vol tage : 1.06+jO.O

0.08+ 0 .24 0 .025 0 .0 l+ j0 .03(0 .0 l )

0.02+j0.06(0.03)

+JO 1

Fig. 3. The power system with 3 generators and 5 buses

Table. 1 Parameters of generators

Typical IEEE governor and turbine models are used:TG OV l (2-nd order) for the thermal plant and IEEEG2 (3-rdorder) for the hydro unit[131. The IEEE exciter and voltageregulator model EXSTl (4-th order) is used for this study onwhich supplementary excitation control input is to beinjected. As a result, a 9-th order model for thermal plant anda 10-th model for hydro plant are used to present thenonlinear characteristics and the low-frequency oscillations insimuliations.

17. Training of the Neural Networks

The training patternsof the Neuro-Identifier are generatedby the power system simulations starting from the steady,state initial value in a wide range operating condition andrandomly generated control inputs history within theconventional PSS operation region.

During the low-frequency oscillation in the range of 1-2

[Hz], it was assumed that the exciter can be approximated asa second-order model. Therefore, the Neuro-Identifier isconstructed to emulate the power flow dynamics as a third-order model which includes the dynamics of exciter and theexcitation field voltage.

The discrete-time training patterns are obtained with thetime step of 0.04 [sec] in simulation. This allows at leasttwenty sampling points in a cycle [14] of the low-frequencyoscillation under 1.25 [Hz].

The structures of the neural networks are chosen by trialand error. The Neuro-Identifier consists of one hidden Payerwith 40 nodes, an input layer with7 input nodes and anoutput layer with one node. The three of the seven inputnodes are for its output history, h P e k ) ,A P e k- I ) , AP k - 2 ) ;two for control input history, ~ ( k ) , k - 1 ) ; and two forAmp), A&k). The Neuro-Controller has one hidden layerwith 40 nodes, an input layer with 6 input nodes and anoutput layer with one node. The three of the six input nodesare for output history, A P, k ) , A P e k- ), AP k - 2 ) ; one for

previous control input u ~I ) ; and two for Aa(k), A8p) .The cost function (1 6) for the N -step ahead controller is setwith the weightings Q = 1.0 and R = 0.02.

To avoid oscillation during training stage, weightparameters in the Neuro-Identifier are corrected with theaverage of corrections calculated for ten patterns. Trainingofthe Neuro-Controller is done in two phases. First, training is

done with a smallN (=3) since in the beginning it has littleknowledge of control.A small number of steps prevents thesystem from diverging. Training is carried on with agradually increasingN until it reaches 8 so that the systemcan be controlled for a longer duration of time. Then, trainingis carried on withN fixed at 8. It takes about 30 minutes in anIBM-PC 486 computer to train two neural networks: theNeuro-Identifier and the Neuro-Controller.

C. Comparison of the Control Results

Fig. 4 shows the speed deviation of generator 2 for adisturbance of three-phase ground fault at midpoint of a halfthe line 4-5, which cleared after0.2 [sec]. It compares the

cases without a control and with supplementary excitationcontrols by the conventional PSS, STAB4 [13], and theNeuro-PSS. The parameters in the STAB 4 was optimized bythe PSS parameter optimization method in [15].

Fig. 5 shows the speed deviation for the same disturbancewhen the power system is in a light loading condition 0.5[P.u.] in generating power) and Fig. 6 shows for a heavy

8/13/2019 199606 Stabilizer

6/7

440

loading condition (1 O [P.u.]). The figures show that both thecontrollers work very well judging from small swings withlarge damping.

The performance o f the controllers are compared in Table2 with the integral-time-error (ITE) computed with the costfunction 16). Observations in the table show that the Neuro-PSS works very well judging from theITE performance inboth the heavy or the light load comparedto the normal loadcondition, however, the ITE performance of the conventionalshows larger variation to loading conditions for the Neuro-PSS because the parameters in the STAB4 were optimized inthe normal loading condition.

Fig. 7 shows the speed deviation for other disturbancecoming from stepwise loading condition (0.15 P .u.) changes:increased (at0.24 [sec]), decreased (at0.96 [sec]) and cleared(1.44 [sec]) when the power system is in the heavy loadingcondition. The figures show that both the controllers workvery well judging from small sw ings.

WI

V. CONCLUSIONS

I I I I II 1 I

A neural network-based power system stabilizer (Neuro-PSS) is developed for a generator connected to a multi-machine power system utilizing the power flow dynamics.The low-frequency oscillation is modeled by the Neuro-Identifier using nonlinear power flow dynamics, then aGeneralized Backpropagation-Thorough-Time algorithm isdeveloped to train the Neuro-Controller. Thetwo neuralnetworks constructed to learn and control the power flowdynamics avoid the need to identify the original rotordynamics. The performanceof the proposed Neuro-PSS wasdemonstrated by applying it to a typical multi-machine powersystem. Its comparison with a conventional PSS shows thatthe Neuro-PSS works very well in a wide range of operation.

0 1 2 3 4 5 6Time [Sec]

ry Without Control TAB4 _. Neuro PSS?___

Speed dev. of the 2 nd Gen. 0.5 [P.u.] )

0 . 4

1 2 3 4 5 6Time [Sec1

0. *

i x t ithoutontrd TAB4 eur o PSS

Fig. 5 . The speed deviation of generator2 for the line faultdisturbance in a light load condition.

Speed dev of the 2 nd Gen 1 O[p U 1 )0 5

I I I

IHzl I I I II I

0 1 3 4 5 6

~ Without Control TAB4 euro PSS

Time [Sec]

Fig. 6. The speed deviation of generator2 for the line faultdisturbance in a heavy load condition.

Speed dev. of the 2 nd Gen. 1 O[p.u.] )

0.1

-0.1

0.3

I I

I I

-0 5 I I0 1 2 4 5 6

Time [Sec]

w i t ontrol TAB4 euro PSS l

Fig. 4. The speed deviation of generator2 for the line fault Fig. 7. The speed deviation of generator2 for the load change-disturbance in a normal load condition. disturbance in a heavy load condition.

8/13/2019 199606 Stabilizer

7/7

44 1

Loading O S EP.u.1 0.75[P.u.l l .o b U . lWithout Control 6.04 loo(%) 12.03 loo(%) 22.24 loo(% )

STAB4 1.81 30.0(%) 2.19 18.2(%) 2.83 12.7(%)

[11]P. J. Werbos, Backpropagation through time: Whatitdoes and how to do it, proc, o IEEE, pp.1550-1560,vol . 78, No. 10, Oct. 1990.

VI. ACKNOWLEDGMENT

The work is supported in parts by Korea Science andEngineering Foundation (KOSEF) and the National ScienceFoundation NSF) under grants U.S.-Korea CooperativeResearch on Intelligent Distributed Control of Power Plantsand Power Systems (INT-9223030), and Research andCurriculum Development for Power Plant IntelligentDistributed Control (EID-92 1232).

VII. REFERENCE

[l] Yao-nan Yu, Electric Power System Dynamics,Academic Press, New Yo rk, pp. 114-118, 1983.[2] F. P. deMello and C. A. Concordia, Concept of

synchronous machine stability as affected by excitationcontrol, IEEE Trans. on PAS, Vol. PAS-103, pp. 316-319,1969.

[3] W. G. Heffron and R. A. Phillips, Effect of modernamplidyne voltage regulator on under excited operationof large turbine generators, Trans. on American Inst.Electrical Eng. Part 3 71, pp. 692-697, 1952.

[4] K. T. Law, D. J. Hill and N R. Godfrey, Robustcontroller structure for coord inate power system voltageregulator and stabilizer design,IEEE. Trans. on Control

Systems Technology, vol. 2, No.3, pp. 220-232,September 1994.[ 5 ] D. Nguyen and B. Widrow, The truck backer-upper: An

example of self-learning in neural networks,IEEEControl System Magazine, pp. 18-23, 1990.

[6] Y. Iiguni and H. Sakai, A nonlinear regulator design inthe presence of system uncertainties using multilayeredneural networks, IEEE Trans. on Neural Networks,

[7] C. C. Ku and K. Y. Lee, Diagonal recurrent neuralnetwork for dynamic system control,IEEE Trans. onNeural Networks, Vo1.6, pp. 144-156,Jan. 1995.

[8] C. C. Ku, K. Y. Lee and R. E. Edward, Imp roved nuclear

reactor temperature control using diagonal neuralnetworks, IEEE Trans. on Nuclear Science, vol. 39, pp.2298-2308, December 1992.

[9] Q. H. Wu, B.W. Hogg, and G.W. Irwin, A neuralnetwork regulator for turbogenerators,IEEE Trans. onNeural Networks, Vol. 3, No. 1, Jan. 1992.

V01.3,N0.4, pp. 410-417, July 1991.

Analysis, McGraw -Hill, pp. 387, 1968.

[13lT. E. Kostyniack, PSS/E Program Operation Manual,P.T.I., October 31, 1983.

[14lK. J. Astrom and, B. Wittenmark, Computer ControlledSystems: Theory and Design, Prentice-Hall International,

[15]M.R. Khaldi, A.K.Sarkar, K.Y. Lee, Y.M. Park, TheModal Performance Measure for Parameter Optimizationof Power System Stabilizers,IEEE. Trans. on EnergyConversion, Vol. 8, No.4, pp.660-666 , Dec., 1993.

pp. 30-31, 1984.

VIII. BIOGRAPHY

Yo u n g - M o o n Park was born in Masan, Korea on Aug.20, 1933. He received his B.S., M.S., and Ph.D. degrees inelectrical engineering from Seoul National University in1956,1959 and 1971, respectively.His major research fieldispower system operation and control, an d artificial intelligenceapplications to power systems. Since 1959, he has been afaculty of Seoul National University where he is currentlyaProfessor of Electrical Engineering. Heis also serving as thepresident of the Electrical Engineering and Science ResearchInstitute. Dr. Park is a senior member o f IEEE .

M y e o n - S o n g Choi received the B.S. and M.S. degrees inelectrical engineeringfrom Seoul National University, Seoul,Korea, in 1989 and 1991, respectively. He is currently aPh.D. candidate in Power System Laboratory, ElectricalEngineering, Seoul National University. His current researcbinterests include robust control theory, artificial neuralnetworks, and their ap plications to po wer system stabilizingcontrol.

K w a n g Y. L e e received the B.S. degree in electricalengineering from Seoul National University, Seoul, Korea, in1964, the M.S. degree in electrical engineering from NorthDakota State University, Fargo, ND, in 1967, and the Ph.D.degree in system science from Michigan State University,East Lansing, MI, in 1971. He has been on the faculties ofMichigan State, Oregon State, University of Houston, and the

Pennsylvania State University, University Park, PA, w here heis a Professor of Electrical Engineering. His current researchinterests include control theory, artificial neural networks,fuzzy logic systems, and computational intelligence and theirapplicationsto power system s. Dr. Lee is a senior memberofIEEE.