IEEE Transactions on Energy Conversion, Vol. 12, No. 4, December 1997 375

NEURO-FUZZY CONTROLLER OF LOW HEAD HYDROPOWER PLANTS USING ADAPTIVE-NETWORK BASED FUZZY INFERENCE SYSTEM

Miodrag B. Djukanovid Milan S. dalovid Bogdan V. VeSovid Dejan J. Sobajid Institute “Nikola Tesla” University of Belgrade Institute “Mihajlo Pupin“ Power System Control Department of Power Systems Dept. of Electrical Engineering Dept. of Automatic Conirol EPRI Belgrade, Yugoslavia Belgrade, Yugoslavia

ABSTRACT - This paper presents an attempt of nonlinear, multivariable control of low-head hydropower plants, by using adaptive-network based fuzzy inference system (ANFIS). The new design technique enhances fuzzy controllers with self- learning capability for achieving prescribed control objectives in a near optimal manner. The controller has flexibility for accepting more sensory information, with the main goal to improve the generator unit transients, by adjusting the exciter input, the wicket gate and runner blade positions. The developed ANFIS controller whose control signals are adjusted by using incomplete on-line measurements, can offer better damping effects to generator oscillations over a wide range of operating conditions, than conventional controllers. Digital simulations of hydropower plant equipped with low-head Kaplan turbine are performed and the comparisons of conventional excitation-governor control, state-feedback optimal control and ANFIS based output feedback control are presented. To demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired neuro-fuzzy controller, the controller has been implemented on a complex high-order non-linear hydrogenerator model.

Kev words: Neuro-Fuzzy Control, Temporal Back Propagation, ANFIS

1. INTRODUCTION

The study of the dynamic properties of closed-loop systems has inspired a number of theoretical developments, as well as practical achievements. Applications of modem control system design methods, using the multivariable systems theory and linear optimal regulator concepts in plant control are well documented [l]. Surveys of learning control methods (essentially those based on pattem recognition techniques) were given in the reference [2]. Although several learning and adaptive control schemes were proposed (model reference adaptive control, betterment method, table look-up method, etc.) they were, at the most, dependent on learning schemes. Intelligent control concepts are mainly based on following three approaches: (a) expert systems as adaptive elements in a control system; (b) fuzzy calculations as decision-producing elements in a control system; (c) neural-nets as compensation elements in control systems.

PE-23%-EC-0-02-1997 A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted July 15, 1996; made available for printing February 10, 1997.

Belgrade, Yugoslavia Palo Alto, CA 94304, USA

Fuzzy approaches to intelligent control schemes [3-71 treat situations, where some of the defining relationships can be described by fuzzy sets and fuzzy relational equations. Most knowledge-based systems depend upon the algorithms which are cumbersome to implement and require extensive computational time. Fuzzy logic provides an inference that enables approximate human reasoning capabilities to be applied to knowledge-based systems.

On the other hand, improved learning algorithms, coupled with advances in microelectronics, have stimulated considerable renewed interest in neural-nets across a spectrum of research areas [S-161. For control engineelring, neural nets are attractive in several aspects. They possess the capability for nonlinear plant modeling, can handle large amounts of sensory information, perform collective processing and learning, and offer the potential for highly parallel computation [15]. Neural controllers are high dimensional nonlinear controllers, with the capability of providing a desired performance, but difficult for suitable tuning. However, in contrast to controllers which rely on specific functional relationships, the strength of this approach lies in the adaptability of the network structure. Their functionality is synthesized implicitly by the weights, thresholds and activation functions. ,4s examples change, that is as the net learns through more and more observations, the mapping from input to output is also adaptively refined.

However, it should ble noted that, when a control problem involves dynamic nonlinear systems, the two techniques (fuzzy logic and neural-nets) worlcing together as neuro-fuzzy systems, can help to manage the comp1t:xity and to reduce the design time. Both of them are powerful design techniques with their own strengths and weaknesses. Neural-nets require prohibitive computational effort, they lack an easy way to verify and optimize a solution, and the solution itself remains a “black box”. On the other hand, fuzzy systems are inherently approximate systems, which lack a general solution to the tuning problem. To overcome these problems neuro- fuzzy approaches, using extended fuzzy logic inference method have been developed based on filzzy associative memories [ 17,181.

This paper presents the neuro-fuzzy control implemented on low-head hydropower ]plant nonlinear mathematical model, equipped with Kaplan turbine and static (STl) excitation system with multivariable voltage regulator. To control the plant’s trajectory, the back-propagation-type gradient descent method called “temporal back propagation” (TI3P) is applied to propagate the error signal through different time stages. To assess their dynamic performances, when the system is subjected to large disturbances, three control configurations (conventional, state- feedback and adaptive network-based fuzzy inference system (ANFIS)) are then implemented on the non-linear simulation model. The effectiveness of the proposed neuro-fuzzy controller is illustrated through the comparison, obtained by observing system dynamic performances, when using these three types of controllers.

0885-8969/97/$10.00 0 1997 IEEE

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2. PROBLEM FORMULATION

An outline of a single Kaplan turbine-generator unit system of a low-head hydro power plant (€PP), connected to the infinite bus power system is illustrated in Figure 1.

SYNCHRoNoUS TRANSMISSION LINE ........................................................... GENERATOR

INFINITE

S,M I 1 LOAD + I

t OUTPUT - - FEEDBACK "gov [ INTERFACE 1

4-1 ; LOOP .................................

Figure 1: Coordinated stabilizing control scheme for the exciter and governor loops of low-head hydro power plant.

The well known reduced third-order synchronous generator model [5,11] has been widely used in many power systems slow- speed dynamics studies. This model incorporates the change in flux linkage of the field winding and equations of mechanical masses rotation. It can be described by the set of three first-order differential and two algebraic equations. The generator is equipped with the static-type (ST1) excitation system, with the addition of the power system stabilizer-type AVR. This excitation system includes multivariable voltage regulator with four channels (generator terminal voltage, first derivative of voltage, frequency and first derivative of frequency). The dual control of a hydroelectric power plant with Kaplan turbine is performed by controlling both, the wicket gate and runner blade positions. The mathematical model of the turbine governor includes the temporary speed-droop and constant feedback taken from the auxiliary servomotor The complete non-linear plant model in the state space, described by a set of 16 first-order differential equations and appropriate algebraic equations is given in [12]. Since the design procedures of the optimal controllers are based on the theory of linear systems, it is necessary to linearize model non-linearities around a steady-state reference operating point. The discrete linear state space model of the system can be organized in the following matrix form:

x(m + 1) = Ax(m) + Bu(m) + (1) where x, U and w are state, control and disturbance vectors, respectively, while A, B and F are constant system matrices of appropriate dimensions. The state vector is defined as

x = LAO, A% Ae,, a,, Ax,,.,, AxzU, AX3u, (2)

AX,f,AX2€, A%€, A%€, Aq, AY,, A h AY, AVlT 9

mth individual state variables, as indicated on the block-diagram of the complete linear model given in Figure 2. The design technique for optimal state-feedback controller (having in mind that the stabilizing signals will be of discrete type and renewed at every sampling instant ATav) of this plant is presented in [12]. It defines the control vector in the form

(m); mAcw L t < (m+1)Aqw;m=1,2 ... N , (3)

where K is the feedback gain matrix. Model (I), (2) has two independent inputs, the excitation ( um) and speed control ( ugov), so #at

U = [u..'ugm]T . (4) The disturbance W=Tload in (1) is one-dimensional quantity. This state-feedback optimal controller was used in this study as: (i) the benchmark for comparison with the ANFIS controller, (ii) the source of pattems that are used in the training process of neuro- fuzzy controller.

3. ADAPTIVE NETWORK-BASED FUZZY INFERENCE SYSTEM

In the interest of completeness some important aspects of ANFIS systems are presented in sequel, based on [IS]. Fuzzy inference systems (fuzzy associative memories) are called neuro- fuzzy controllers, when used as fuzzy controllers implemented on architecture of an adaptive network. An adaptive network, shown in Figure 3, is a multilayer feedfonvard network where each node performs a particular function (node function) on incoming signals. It is characterized with a set of parameters pertaining that node. To reflect different adaptive capabilities, both square and circle node symbols are used. A square node (adaptive node) has parameters, while a circle node (fixed node) has none. The parameter set of an adaptive network is the union of the parameter sets associated to each adaptive node. To achieve a desired input-output mapping, these parameters are updated according to given training data and a gradient-based learning procedure. Assuming the given training data set has P entries, the error measure is defined for the pth ( l l p l p ) entry of training data, as the sum of squared errors

m=l

where Dmp is the mth component ofpth target output, and Okp is the mth component of actual output vector produced by the involvement of the pth input vector. If ct is a parameter of the given adaptive network, then

(6) zp a*

O"€S a*& -=c-- B P

where S is the set of nodes whose outputs depend on a. The derivative of the overall error measure E with respect to a is

p=l

The update formula for the generic parameter c1 is & a2 Aa=--7/-,

where q is a learning rate, expressed as

(7)

(9)

where k is the step size, representing the length of each gradient transition in the parameter space. The value of k can be changed to vary the speed of convergence. If we assume that fuzzy inference system under consideration has three inputs and two outputs, and that the rule base contains 64 fuzzy if-then rules of Takagi and Sugeno's type, as described in the Appendix, then the node hc t ions are as follows:

377

I ‘ I I Figure 2: The structural blockdiagram of linearized HPP plant equipped with the static ST1 excitation system with multivariable voltage regulator and temporary

speed-droop HPP governor.

(13) - w w, =I , i := 1, ...U .

For convenience, outputs of this layer will be called

Laver I : Every node ‘ i ’ in this layer is a square node with a node

(lo) where x is the input to node ‘i’, and AI is the linguistic label associated with this node function. The bell-shaped ph(x) is used:

C I W 1 function 0: = P&) >

“normalized firing strengths”.

1 1

PA*(.) = (11) I+[(YJT ’

where {ui, bi, ci} is the parameter set. Parameters in this layer are referred to as premise vurumeters. Laver 2: Every node in this layer is a circle node labeled P which

multiplies the incoming signals and sends the product out. For example:

W, =pAj(x~)xpgk(x~)xp~,(xg),i=l ,... 64; j , k , h = l , ... 4. (12) Each node output represents the firing strength of a rule (in

fact, other T-norm operators that perform generalized AND can be used as the node function in this layer). Laver 3: Every node in this layer is a circle node labeled N. The ith

node calculates the ratio of the ith rule’s firing strength to the sum of all rules’ firing strengths:

ov

Figure 3: Three input-two output ANFIS adaptive network for HPP control.

378

Laver 4: Every node 'i' in this layer is a square node with a node function

of = = ~ ( p ~ x ~ + qlxz + r,x3 + 4) , (14) where W , is the output of layer 3, and b,, ql, fi, s} is the parameter set. Parameters in this layer will be referred to as conreaaenf parameters.

Laver 5: The single node in this layer is a circle node labeled C that computes the overall output as the sum of all incoming signals, i.e.,

c WI fl

1 c w , 0: = overau output = Cw,fl = L--. (15)

1

In the forward pass of the hybrid learning ANFIS algorithm, functional signals go forward until layer 4 and the consequent parameters are identified by the least squares estimate. In the backward pass, the error rates propagate backward and the premise parameters are updated by the gradient descent. Consequently, this hybrid approach is much faster than the strict gradient descent algorithm.

INATED STABILIZING HPP CONTROL USING ANFIS

In this section, a generalized control scheme for WPP control is proposed, which can construct a fuzzy controller through temporal back propagation, such that the state variables can follow a given desired trajectory. The basic idea is to implement both the controller and the plant at each time stage as a stage adaptive network, and to cascade these stage adaptive networks into a trajectory adaptive network to facilitate the temporal back propagation learning process [17]. Given the state of the plant at time t=mAt, the controller Will generate an input to the HPP and the HPP will evolve to the next state at time (m+l)At. By repeating this process starting from t=O, a HFP state trajectory is obtained, determined by the initial state and the parameters of the controller. The principles of trajectory adaptive networks are explained in [ 181. To minimize differences between adaptive network inputs and desired outputs, defined through corresponding error measure, the back propagation gradient descent algorithm is applied within this network:

where %(mAt) is the desired trajectory at t=mAt. To tune the ANFIS controller for a wide range of operating points, we applied adaptive fuzzy system based on Unsupervised Learning (UL) of neural-nets (explained in detail in [SI), as shown in Figure 4. This system consists of neural-net classifier (NNC) and a number of M I S modules. The role of the NNC is to identify operating point and to activate an appropriate ANFIS. The training samples for the classifier are collected &om the off-line closed-loop system operation, controlled by optimal state-feedback controller. In consulting stage, the classifier decides which M I S module should be used. If the prediction error is smaller than prespecified tolerance, the control is continued with current ANFIS module. Otherwise, the NNC activates on-line re-clustering process that identifies ANFIS module, which will produce adequate (near optimal) control signals. Consequently, the NNC serves as the real time pointer to the "best" ANIFIS module that contains the sequence of control signals for near-optimal trajectory (memorized in the

consequent parameters of membership functions). In this work we f i s t specified controller's input and output variables. The input variables are specified as the deviation of generator speed from synchronous speed (Xl), the derivative of generator speed ( X 2 ) and the terminal voltage deviation from its reference (X3) i.e.

Xl(m)=loOO.[w(m) - w,] (17) X2(m)=SO.[u(m) - w(m- l)]IAT,, (18)

X3(m)=lO0.[V(m)-Vref] (19)

Figure 4: Block diagram of ANFIS based control of a Kaplan turbine HPP.

As it is specified in (4) the output variables are control inputs to the excitation and speed goveming systems:

(20) where A<- is sampling time. The excitation and govemor control signals u,(m) and ugOv(m) are output fuzzy variables of discrete type and renewed at every sampling instant, depending on the input fuzzy variables.

The controller blocks in Figure 4 are implemented as ANFIS with three inputs; each of them contains four membership functions, so it is the fuzzy controller with 64 fuzzy if-then rules of Takagi and Sugeno's type. The consequent parameters of the M S are all set to zero. As a conventional way of setting parameters in a fizzy controller, the premise parameters are set in a way that the membership functions can cover the domain interval (or universe of discourse) completely, with sufficient overlapping. This is illustrated in Figure 5.

The 200 stage adaptive networks are employed to construct the trajectory adaptive network, and each stage adaptive network corresponds to the time transition of 5 ms.

U = [u,(mXu,,(m)]T; mATsmnp st (m+WT,,, ,

5. THE RESULTS OF THE A.NFIS CONTROLLER TESTING

To demonstrate the efficiency of the proposed M I S controller, several simulation tests were perfomed, where the proposed controller was confronted to a number of small and large disturbances.

379

Due to the limited space, in this paper only results of a simulation of a 3-phase short-circuit on generator terminal bus, cleared after 0.10 s, will be presented in detail. The maximum excitation voltage EPDm was 2.73 p.u. The sampling interval in this study was specified to 0.05 s, while the step of numerical integration of differential equations (solved by using Runge-Kutta method) is taken to be 0.01 s. For the purpose of comparison, the response curves for the system's variables

Initial membership functions v. U. 1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0 0.5 1 .o

Final membership functions: ACCELERATION OF GENERATOR SPEED (radk2)

1 0.0 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0

-2.5 0 2.5 5

0.9 0.95 1.00 1.05 1.09

DEVIATION OF GENERATOR SPEED (rad/s)'lO 1

0.0 0.8 0.7 0.8 0.5 0.4 0.3 0.2 0.1

0

-5 0 5 10

Figure 5: Initial and final membership functions.

equipped with conventional multivariable voltage regulator, optimal complete state-feedback controller and ANFIS controller are shown in Figures 6 and 7. In these figures, generator terminal voltage, rotor speed, excitation control signal, turbine flow, governor control signal and mechanical torque curves are presented.

Comparing response curves of the conventional multivariable voltage regulator, with those of ANFIS controller, it could be concluded that the system performance is highly improved, if the proposed M I S controller is applied. At the same time comparison of ANFIS with the optimal state-feedback controller, used as a benchmark in this work, shows that the system performance is

I

-05 - : 0 1 2 3 4 5 0 7 8 0 10

T W W )

Figure 6: System response (terminal voltage, rotor speed, and exciter input) to a temporary short-circuit: _ _ _ _ _ conventional controller; - optimal state-feedback controller; . . . . . . . . neuro-fuzzy ANFIS co~itroller

similar. Very slight degradation of oscillatory processes with ANFIS was expected due to the fact that optimal state-feedback controller is based on full state feedback, while the ANFIS uses only three discrete-type measured signals, namely the speed deviation, speed derivative and voltage deviation of the generator. In our investigations we also tested the sensitivity of ANFIS against system topology changes. The ANFIS designed on a basis of patterns generated from a 3-phase short-circuit, cleared after 0.10 s has been tested for simple tripping of one of two outcoming parallel lines, with reclosing after 0.5 s. The studied case indicates the robustness of the proposed ANFIS controller. For the purpose of illustration, Figure 8 shows the results of a simulated line tripping causing the 100% increase in line reactance within 0.5 s. To test the ANFIS for a wide range of operation regimes, we applied adaptive fuzzy system based on Unsupervised Learning (UL) of neural-nets, as shown in Figure 4. The previously (off line) tuned ANFIS controllers are chosen to cover wide ranges of possible operating conditions, namely:

Figure 5 shows the initial, and final membership functions of rotor angle, angular velocity arid generator t m a l voltage. It could be observed that the final membership functions are quite different from the initial ones, being a consequence of learning process. A list of the fuzzy rules with numerical parameters can be found in

0.90 I V, Il .10 ; 0.20 SIP < 1.00 ; -0.145 I Q 5 0.52 .

380

Appendix. To demonstrate how the M I S controller can survive substantial changes of operating conditions, the results of light load and leading power factor operation tests are presented in the sequel.

0.815

j 081

0,

% + 0.8

P - OQOS

z

0.795 1 2 3 4 5 6 7 8 9 10

T M W )

0.7 I 0 1 2 3 4 5 E 7 8 9 10

T W W )

Figure 7: System response (turbine flow, governor input and mechanical torque,) following a temporary short-circuit: ----- conventional controller; - optimal state-feedback controller; ........ neuro-fuzzy ANFIS controller

1.015

0 1 2 3 1 5 6 7 8 9 10

THE($)

Figure 8: Rotor speed responses to a tie-line fault: ----- conventional controller, - optimal state-feedback controller; ........ neuro-fiuzy ANFIS controller

5.1 Lipht load test

With the generator operating with the output of 0.2 P.u., 0.95 power factor lag and a terminal voltage 1.00 p.u, , a 3-phase short- circuit was applied on generator terminal bus, and cleared after

0.10 s. The disturbance is large enough to cause the system to operate in nonlinear region. Responses with conventional multivariable voltage regulator, optimal state-feedback controller and M I S Controller are shown in Figure 9. The system with conventional controller is highly oscillatory, while the load rotor angle settles to its new value very smoothly and quickly when ANFIS is applied.

o m 6 Ogg7 9 0 1 2 3 4 5 8 7 8 9 i o

TIM e3 I Figure 9: Rotor speed responses to atemporary (0.10 s) short-circuit (P=0.2p.u, cosq~O.95 lagging V=1.00 PA): --_-- conventional controller, - optimal state-feedback controller; ......... neuro-fuzzy ANFIS controller

5.2 Leadinp Dower factor operation test

With the generator operating with the output of 0.3 P.u., 0.9 power factor lead and a terminal voltage 1.00 p.u. a 3-phase short- circuit was applied on generator terminal bus, and cleared after 0.10 s, as in 5.1 above.

0496 4 0 1 2 3 4 5 8 7 E 9 i o

T IMW)

Figure 10: Rotor speed responses to a temporaty (0.10 s) short-circuit (P=O.3p.u., cosCp=O.90 leading, V=l.OO pa): ----- conventional controller; - optimal state-feedback controller, ......... neuro-fuzzy ANFIS controller

Responses with conventional multivariable voltage regulator, optimal state-feedback controller and ANFIS controller are shown in Figure 10. The rotor angle response with the ANFIS shows fast damping and practically no overshoot. It should be noted that Figures 8,9 and 10 reveal robustness and fault tolerance of the ANFIS controller obtained from the temporal back propagation.

6. CONCLUSIONS

A new design of the flexible, adaptive, multivariable output feedback, neuro-fuzzy coordinating stabilizing control of the exciter and govemor loops of a low-head hydropower plant has been proposed in the paper. The main feature of the proposed control is that it does not require a reference model, or inverse system model and avoids the use of probing signals.

381

2. Berger, K.M., Loparo K.A, ",A Survev of Techniaues to Handle Uncertainty and Complexitv with Adication to Intelligent Control", CWRU, Technical Report TR 87-139, October 1987. Hiyama, T., Kugimiya, M.,"Advanced PID Type Fuzzy Logic Power System Stabilizer", IEEE Trans. on Enern Conversion, Vol. 9, No. 3, Sep.

Lee C.C., "Fuzzy Logic irn Control Systems: Fuzzy Logic Controller", IEEE Trans. on SMC, Vol. 20, No. 2, March/April1990, pp.404-435. Hsu. Y.Y.. Chenc C.H.. "Desim of Fuzzv Power Svstem Stabilisers for

3.

1994, pp. 514-520. 4.

5.

A generalized controller design methodology, called "temporal back propagation" is applied for the construction of a self-leaming neuro-fuzzy controller. To " i z e the difference between an actual trajectory and given desired trajectory, this methodology employs the adaptive network, as a building block and the back- propagation gradient method, as the update procedure. The main advantages of the proposed ANFIS controller over neural and/or fuzzy controllers are: (i) A neural-net mapping, of "black box" type, which is difficult to

be interpreted, is avoided; (ii) The problem of tuning fuzzy controllers is eliminated; (iii) Combining neural-nets and fuzzy logic, the ANFIS controller

minimizes system cost by optimizing the number of rules and membership functions, reduces memory requirements and creates fuzzy solution in the form of if-then rules, which is more robust and reliable and can work well under a wider range of operating conditions.

Digital simulations of hydropower plant equipped with low- head Kaplan turbine and mutual comparisons of conventional excitation control, state-feedback optimal control and ANFIS based control show that ANFIS provides improved system transients with large stability margins, like state-feedback optimal controllers. Once trained, the ANFIS is able to provide the control action in real-time based on on-line measured operating conditions. The ANFIS controller performance compares well with state-feedback optimal controller under different operating conditions and a range of disturbances.

APPENDIX

This paper is a logical follow up to the previous paper [12]. Consequently, modeling background of this paper related to exciter and governor types, as well as the computation of the K-matrix in (3) can be found in this reference.

Each linguistic label used in the ANFIS is characterized by four parameters. The final if-then rules derived from the reference settings are: Rule 1: IfXl is A1 and X2 is B1 and X3 is C1, then:

u e ~ up"

= -0.1 006 *X 1+0.1150 *X2+0.294 3 *X3+0.73 63 and = 0.2756*Xl -O.O251*X2+ O.O951*X3+ 0.4997

Rule 64: If X1 is A4 and X2 is B4 and X3 is C4, then: ~x

ugov = -O.O076*Xl -0.0192rX2 -O.O048*X3 -0.0071 = -0.1092*Xl -0.1969rX2 -O.O719*X3 -0.1106 and

where: A1 ... A4, B1 ... B4, C1 ... C4 are the linguistic labels characterized by: {0.174,2.001,0.013} ... {0.181,2.001,0.980}, {0.207,2.004,0.069} ... {0.157,2.001, 1.002}, {0.158,2.001,-0.002) ... { 0.097,2.010,0.969},respectively.

ACKNOWLEDGEMENT

Authors gratefully acknowledges support &om Dr. J.S.R. Jang, from the University of California, Berkeley, by providing published papers and software from CMU Artificial Intelligence Repository.

7. REFERENCES

Mukknacke Po&r Systetn~",-IEE Roc..* Pt. C., Vol. 137, No. 3, May 1990. OD. 233-238.

6.

7.

El-MeGwally, K.A, Malk, O.P., "Fuzzy Logic Power System Stabilizer", IEE Proc. , Pt.-C, Vol. 142, No. 3, May 1995, pp.277-281. Handschin, E., H o f f i q W., Reyer, F., "A New Method of Excitation Control Based on Fuzzy Set Theory", IEEE Trans. on Power Svstems, Vol. 9, No. 1, Feb. 1994, pp.533-539.

8. Pao, Y.H.,"AdaDtive uattetn recognition and neural networks", Addison Wesley Publishing Company Inc., 1989.

9. Djukanovic, M., Sobajic, D.J., and Pao, Y.H., "Prediction of Power System Frequency Response &er Generator Outages Using Neural-Nets", IEE Proceedings. Part C, Vol. 140, No.5, Sept. 1993, pp. 389398,

10. Djukanovic, M., Calovic, M., Milosevic, B., Sobajic, D.J., "Neural-Net Based Real-Time Economic Dispatch for Thermal Power Plants", Paper 96 SM 548-8 EC presented at 1996 PES Summer Meeting, Denver, CO, July

11. Djukanovic, M., Sobajic, D.J., and Pao, Y.H., "Neural-Net Based De- termination of Generator-Shedding Requirements in Eledric Power

12. Djukanovic, M., Novicevic, M., Dobrijevic, Dj., Babic, B., Sobajic, D., Pao, Y., "Neural-Net Baseti Coordinated Stabilizing Control for the Exciter and Governor Loops of Low Head Hydropower Plants", IEEE Trans. on Enern Conversion, Vol. 113, No. 4, Dec. 1995, pp. 760-768.

13. Hsu Y.Y, Chen, C.R., "Tuning of Power System Stabilizers Using an Artificial Neural Network", IEEE Trans. on Energy Conversion, Vol. 6, No. 4, December 1991, pp 612-619.

14. Weerasooriya, S., El-Sharkawi, M A , ""Identification and Control of a DC Motor Using Back-Propag,&tion Neural Networks", IEEE Trans. on Energy Conversion,Vol. 6, No.4, Dec. 1991, pp. 663-669.

15. Wu, Q.H., Hog& B.W., Irwin, G.W., "A Neural Network Regulator for Turbogenerators", m r a n s . on Neural Networks, Vol. 3, No. 1, Jan.

16. Zhang.Y., Malik, O..P., Chen., G.P., "Artificial Neural Network Power System Stabilizer in Multi-Machine Power System Environment",= Trans. on Energv Conversion- Vol. 10, No. 1, March 1995, pp. 147-155.

17. Jang, J.S.R., "Self-Learning Fuzzy Controllers Based on Temporal Back Propagation" IEEE Trans. on Neural Networks, Vol. 3, No. 5 , Sept. 1992,

18. Jang, J.S.R., "ANFIS: Adaptive-Network-Based Fuzzy Inference System" IEEE Trans. on Svstems, Idan and Cvbemetics, Vol. 23, No. 3, May 1993,

28 -August 1,1996.

system^", IEE ROC. Part Ck Vol. 139, NO. 5, Sept. 1992, pp. 427-436.

1992., pp. 95-100.

pp. 714-723.

pp. 665-685.

8. BIOGRAPHIES

Dr. Miodrae B. Diukanovic' is the researcb scientist at the Institute "Nikola Tesla", Belgrade, Yugoslavia, and adjunct professor of the University of Belgrade, Dept. of Electrical ]Engineering. His areas of interest include power system dynamic security and applications of artificial intelligence methods to

Dr. Milan S. Calovic'is the piofessor of electrical engineering at the University of Belgrade, Dept. of Electrical Engineering, Yugoslavia. His main fields of activities are within the frame of power system planning, analysis, operation and control. Boedan V. VeSoviC is the research associate at the Institute "Mihajlo Pupin" in Belgrade, working on the research in the field of power systems planning and operation. His current researclh works include optimization methods, fuzzy set theory and object-oriented anallysis and design. Dr. Deian J. Sobaiic' (M'80-SM189) is with Power System Control, EPRI. His current research interests include power system operation and control. Dr. Sobajic is a member of the IEEE Task Force on Neural Network Applications

power systems.,