A Neural Network-Based Power System Stabilizer using Power Flow Characteristics. External Power System

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1 EEE Transactions on Energy Conversion, Vol. 11, No. 2, June A Neural Network-Based Power System Stabilizer using Power Flow Characteristics Young-Moon Park, Senior member, EEE Myeon-Song Choi, member, EEE Department of Electrical Engineering Seoul National University Seoul Korea Absfrad - A neural network-based Power System Stabilizer (Neuro-PSS) is designed for a generator connected to a multimachine power system utilizing the nonlinear power flow dynamics. The uses of power flow dynamics provide a PSS for a wide range operation with reduced size neural networks. The Neuro-PSS consists of two neural networks: Neuro-dentifier and Neuro-Controller. The low-frequency oscillation is modeled by the Neuro-dentifier using the power flow dynamics, then a Generalized Backpropagation-Thorough-Time (GBTT) algorithm is developed to train the Neuro-Controller. The simulation results show that the Neuro-PSS designed in this paper performs well with good damping in a wide operation range compared with the conventional PSS. Keywords - Neuro-PSS, Neural networks, Power system stabilizer, Low-frequency oscillation. Power flow characteristics.. NTRODUCTON One of the most important problems arising from largescale electric power system interconnection is the lowfrequency oscillation [l]. For this problem, there has been a considerable research into the Power System Stabilizer (PSS) design []. The conventional design was first proposed by demello and Concordia [2] on the basis of the singlemachine infinite-bus linearlized model [3]. n their approach, the PSS was designed as a lead-lag compensater which provides a supplementary control signal to the excitation system. Kwang Y. Lee, Senior member, EEE Department of Electrical Engineering The Pennsylvania State University University Park, PA USA A practical PSS must be robust over a wide range of operating conditions and capable of damping the oscillation modes in a power system [4]. From this perspective, the conventional PSS design approach based on a single-machine infinite-bus linearlized model in the normal operating condition has some deficiencies: 1) There are uncertainties in the linearized model resulting from the variation in the operating condition, since the linearlization coefficients are derived typically at normal operating condition. 2) To implement the PSS for a multi-machine power system; its parameters need to be tuned to coordinate with other machines and utilities. Consequently, a realistic solution for stabilizing the lowfrequency oscillation of a multi-machine system is a stabilizer designed from a nonlinear multi-machine model in the first place []. Fig 1 shows the schematic diagram of a generator connected to a power system network. Difficulties in a power system stabilizer design come from the handling of nonlinearities and interactions among generators. During the low-frequency oscillation, rotor oscillates due to the unbalance between mechanical and electrical powers. The electrical power, P, shown in Fig. 1, has the properties of the nonlinearty and this interaction is the key variable affecting the rotor dynamics. Thus, handling the nonlinear power flow properly is the key to the PSS design for a multi-machine power system. Unfortunately, it is not that easy to handle the 96 WM EC A paper recommended and approved by the EEE Energy Development and Power Generation Committee of the EEE Power Engineering Society for presentation at the 1996 EEE/PES Winter Meeting, January 21-25, 1996, Baltimore, MD. Manuscript submitted July 19, 1995; made available for printing January 4, External Power System Electnc Power Flow 1 P, +JQ, -_--- Fig. 1. A generator connected to power system network /96/$05.00 Q 1996 EEE

2 436 nonlinear interaction variables in control by conventional analytical methods. Recently, a new approach has emerged in control area to handle nonlinearities utilizing the neural networks' learning ability. The use of neural networks' learning ability avoids complex mathematical analysis in solving control problems when plant dynamics are complex and highly nonlinear, which is a distinct advantage over traditional control methods. Nguyen and Widrow [5] showed the possibility of using neural networks in controlling a plant with high nonlinearities. They exploited the neural networks' selflearning ability in the Truck-Backer problem. iguni and Sakai [6] constructed a neural network controller combined with a linear optimal controller to compensate for uncertainties in model parameters. Recently, Ku and Lee [7] proposed an architecture of diagonal recurrent neural network for identification and control of dynamic systems, and applied it to a nuclear power plant model [S. There are cases where neural networks are applied for power system stabilizing control [9], [ 101. However, these cases are limited to a system with a single generator connected to an infinite bus to avoid the complexity of the interconnected power system dynamics. Yu [ 11 pointed out that it is desirable in the PSS controller design to consider interaction variables describing mutual interactions among generators networked in a power system. This paper introduces a new approach for handling the nonlinear interaction variables, i.e., the power flow. By utilizing the neural networks' learning ability in mapping the power flow dynamics, a PSS (Neuro-PSS) is designed for a generator connected to a multi-machine power system. The proposed neural network-based PSS architecture is composed of two parts. First, a Neuro-dentifier is designed for a generator to emulate the characteristics of the power flow between the generator and the power system network. Second, a Neuro-Controller is constructed for the generator to produce the supplementary excitation signal which minimizes a quadratic cost function in speed deviation and control effort. The Neuro-dentifier is trained by the usual Backpropagation Algorithm (BPA), and the Neuro-Controller is trained with the equivalent error backpropagated through the Neuro-dentifier using a newly developed Generalized Backpropagation-Through-Time algorithm to minimize the quadratic cost function in speed deviation and control effort of the generator. 11. PROBLEM FORMULATON A. Characteristics of Rotor Dynamics The choice of model is very important for a controller design. n 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 are functions of the operating condition [l]. Therefore, it is desirable to use a nonlinear model in designing a nonlinear Neuro-PSS for a wide range operation. To study the low-frequency oscillation, a third-order model is considered for a synchronous generator connected to a network at busj []: do - 1 dt M -- -(T, - G), (T, = P, /o,g = P, 10) (> -_ d6 - Oh(W -l), (Ob = 271f,O = 1) (2) dt dei ~ [ E -e;, - (xd -x'.(e:,- v, cos(6 - e,)], (3) dt TA 4 where 6 ando are rotor position and velocity, e; is the voltage behind the transient reactance, and other variables are defined in [ 11. n equation (3), dynamics of e; is controlled by the field excitation voltage, which is the output of a conventional exciter. A supplementary control signal will be added to this excitation voltage for stabilization [ 11. The generator connected to a network should satisfy the algebraic power balance constraint: P,(e;,v,Ae,)+ s(v,>e,)= pn/(m Q,<~~,v,,~,Q, + QAV,,Q,> = Q ~(~,G>, (4) j = 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-th bus, and pi, and Qt are the local loads, whicn are nonlinear functions of system variables. The rotor dynamics (1) is represented in terms of the power flow, P,. n a conventional method, it is difficult to design a PSS for a wide range operation due to the nonlinearty of the power flow. However, a Neuro-PSS can be designed since one of the characteristics of artificial neural networks is to learn the nonlinear mapping with input-output pair [5]. Since the rotor dynamics is simply represented by equations (1) and (2) with known inertia constant, it only remains to learn the nonlinear power flow using a neural network. Since the neural network needs not to learn the known rotor dynamics (1) and (21, a smaller size neural network can be used and consequently, training time can be reduced. To train a neural network, it needs to know the information on the dynamics in terms of the input-output relationship. n view of equations (1)-(4), the power flow can be represented as a function of e;, 6 and ~i) as input variables. However, the voltage behind the transient reactance, e;, is not easy to

3 437 measure and to use as a feedback variable. Since the voltage behind the transient reactance only affects the power flow, it can be included in the power flow variable. Following the above observation, and by shifting the origin to the normal operating point, it can be shown that the rotor dynamics of a generator is modeled as daw 1 -- dt M - --(-@= > (5) da6 - = O ~AO, (6) dt * = f (@,u,a6,aw), (7) dt where U is a supplementary excitation signal from PSS. B. Neural Network Based-Power System Stabilizer A feedfonvard neural network with taped delays can represent the nonlinear dynamic system model [l ]. However, it requires a discrete model for training. The discrete model of the rotor dynamics of a generator with time step At corresponding to the equations (5), (6) and (7) is represented as 1 AO(k + 1) = -(-@,(k))at M + AO(k) A8(k + ) = O,,AW(k). At + A&k) AP,(k + ) = f(ae(k),ape(k - ),...,A&~ - n + ), AO(k),A6(k),U(k),U(k - l);..,u(k - m + 1)) (10) where, m and n are the delay orders for output and input variables. t should be noted that the order of the system that a neural network has to represent is reduced by two since only the power flow dynamics (10) needs to be modeled. Following the input-output relationship in the power flow dynamics, a Neuro-PSS is designed with two neural networks: A Neuro-Controller is constructed to generate adequate supplementary excitation signal to compensate for the Pow-frequency oscillation, and Neuro-dentifier is constructed to model the power flow dynamics and used to backpropagate an equivalent error or generalized delta to the Neuro-Controller for training. Fig. 2 shows the overall scheme for the neural network-based power system stabilizer for a wide range operation, where the operator, TDL, presents a memory element having the input or output history TRANNG OF NEURAL-NETWORKS The Neuro-PSS in this paper is composed of two multilayer feedforward neural networks, one for Neuro- dentifier and another for Neuro-Controller. The structure of (8) (9) Fig. 2. A neural network-based power system stabilizer a multilayer neural network represents a nonlinear function with multi-inputs and single output and has weight parameters and neurons, each with a nonlinear sigmoid function. The Neuro-dentifier s weight parameters are adjusted by the equivalent error with the BPA 651, and the Neuro-Controller s are adjusted by the GBTT algorithm. A. Training of the Neuro-dentijier The Neuro-dentifier represents the nonlinear dynamics of the power flow output of a generator connected to a power system network. t is later used to train the Neuro-Controller by backpropagating the equivalent error. The dynamics of the power flow of a generator in (1 0) can be viewed as a nonlinear mapping as following: where - X(k) = (A&k),AP,(k ~ l);..,ap,(k U,@ + 1) = f (Z(k)) ~ n Aw(k),A6(k),~(k),~(k ~ ),...,u(~ + ), ~ m + )) (1 11 Therefore, the Neuro-dentifier for the plant can be represented by a nonlinear network F A&k + 1) = F(Z(k),$), (12) where is the weight vector to adjust. nput-output training patterns are obtained from the operation history of the plant. The Neuro-dentifier learns to generate the same output responses as the plant does by using the BPA. The objective of training the Neuro-dentifier is to reduce the average error defined by J=---(hP,(k+l)-~,(k+,))*, 1 N k=12 (13) where N is the number of training sets in an epoch for adjusting the weight parameters. n the BPA, the equivalent error on the output node of the network for the k-th sampled data is defmed as

4 l),...,a&(k n 438 This error is then used backward to compute an equivalent error for a node in an arbitrary layer to update weight parameters in the BPA. The training is finished when the average error between the plant and the Neuro-dentifier outputs converges to a small value, and the Neuro-dentifier represents the plant characteristics approximately, i.e., 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 the sensitivities satisfy the following coupled equations: (19) &(k + 1) = f (*(k)) N k ( k + 1) = F(z?(k),@). (15) B. Training of the Neuro-Controller The role of the Neuro-Controller is to stabilize lowfrequency oscillation when the speed of a generator deviate from its normal value. n order to solve this problem in a finite time horizon, a general quadratic cost function is defined as where u ( k ) is the supplementary excitation control input, and N is the number of time steps. The characteristics of the Neuro-Controller can be represented as a nonlinear network H : U(k) = f f(ae(k),ap,(k ~ ~ ACO(k),A6(k),U(k - l);..,u(k ~ + ), - m + 1),w) 2 (17) 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 usual backpropagation method is not applicable. Therefore, the Neuro-Controller has to learn the control law by trial and error, by driving the Neuro-dentifier to generate the equivalent error for backpropagation. The learning process by trial and error consists of two parts. First, from the given initial state the Neuro-Controller drives the Neuro-dentifier for N steps. Second, the weight parameters of the Neuro-Controller are updated using the average of corrections calculated for each step to reduce the cost function. n order to train the Neuro-Controller to minimize the general quadratic cost function (16), it is necessary to extend the Backpropagation-Through-Time (BTT) algorithm [l 11, which was originally developed for the quadratic cost of the output errors alone. Since our cost function (16) includes not only output errors, but also input variables, the BTT method can not be used and has to be generalized, resulting in the Generalized BTT (GBTT). The equivalent errors for the cost function are defined as the following sensitivities with respect to input variables: s", Equations (19)-(22) show that the equivalent errors backpropagate 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 algorithm can thus be used directly. The process of the GBTT training algorithm is summarized as follows: Set the weight parameters of the Neuro-Controller with small random numbers. Set the load condition and initial state with random numbers in the operation region of the power plant. Let the Neuro-Controller drive the generator and the Neuro-dentifier for N steps forward. From the operation result in step 3), evaluate the equivalent errors 6; backward using equations (19), (20), (21) and (22), and compute the weight parameter adjustment vector AWk. Update the weight parameters in the Neuro-Controller by using the average of weight parameter adjustment vectors AWk found in step 4). Go to step 2).

5 439 Training of the Neuro-Controller is finished when the average decrease of the cost function converges to a small value for an arbitrary reference output and initial conditions. A. The Study Power System V. CASE STUDY The Neuro-Controller is applied to a simple power system network [12] shown in Fig. 3 to stabilize low-frequency oscillations. The power system consists of three power plants: two are thermal units and one is hydro unit. The normal operating conditions and line parameters of the network in p.u. on 100 MVA base are also shown in Fig. 3. The power system has sustained low-frequency oscillations due to disturbances. The control objective is to improve system damping by using a supplementary excitation control applied to the second generator. For the low-frequency oscillation problem, parameters of the generator model (1)-(3) are presented in Table 1. ( Thermal Plant) 0.02+j0.06(0.03) 0 2+JO 1 Voltage : 1.06+jO.O 0.08+' l+j0.03(0.0l) Fig. 3. The power system with 3 generators and 5 buses Table. 1 Parameters of generators Typical EEE governor and turbine models are used: TGOVl (2-nd order) for the thermal plant and EEEG2 (3-rd order) for the hydro unit [ 131. The EEE exciter and voltage regulator model EXSTl (4-th order) is used for this study on which supplementary excitation control input is to be injected. As a result, a 9-th order model for thermal plant and a 10-th model for hydro plant are used to present the nonlinear characteristics and the low-frequency oscillations in simuliations. 17. Training of the Neural Networks The training patterns of the Neuro-dentifier are generated by the power system simulations starting from the steady, state initial value in a wide range operating condition and randomly generated control inputs history within the conventional PSS operation region. During the low-frequency oscillation in the range of 1-2 [Hz], it was assumed that the exciter can be approximated as a second-order model. Therefore, the Neuro-dentifier is constructed to emulate the power flow dynamics as a thirdorder model which includes the dynamics of exciter and the excitation field voltage. The discrete-time training patterns are obtained with the time step of 0.04 [sec] in simulation. This allows at least twenty sampling points in a cycle [14] of the low-frequency oscillation under 1.25 [Hz]. The structures of the neural networks are chosen by trial and error. The Neuro-dentifier consists of one hidden Payer with 40 nodes, an input layer with 7 input nodes and an output layer with one node. The three of the seven input nodes are for its output history, hpe(k), APe(k - ), AP (k- 2) ; two for control input history, ~(k), u(k-1) ; and two for Amp), A&k). The Neuro-Controller has one hidden layer with 40 nodes, an input layer with 6 input nodes and an output layer with one node. The three of the six input nodes are for output history, AP,(k), APe(k - ), AP (k - 2) ; one for previous control input u (- ~ ) ; and two for Aa(k), A8p). The cost function (16) for the N-step ahead controller is set with the weightings Q = 1.0 and R = To avoid oscillation during training stage, weight parameters in the Neuro-dentifier are corrected with the average of corrections calculated for ten patterns. Training of the Neuro-Controller is done in two phases. First, training is done with a small N (=3) since in the beginning it has little knowledge of control. A small number of steps prevents the system from diverging. Training is carried on with a gradually increasing N until it reaches 8 so that the system can be controlled for a longer duration of time. Then, training is carried on with N fixed at 8. t takes about 30 minutes in an BM-PC 486 computer to train two neural networks: the Neuro-dentifier and the Neuro-Controller. C. Comparison of the Control Results Fig. 4 shows the speed deviation of generator 2 for a disturbance of three-phase ground fault at midpoint of a half the line 4-5, which cleared after 0.2 [sec]. t compares the cases without a control and with supplementary excitation controls by the conventional PSS, STAB4 [13], and the Neuro-PSS. The parameters in the STAB4 was optimized by the PSS parameter optimization method in [15]. Fig. 5 shows the speed deviation for the same disturbance when the power system is in a light loading condition (0.5 [P.u.] in generating power) and Fig. 6 shows for a heavy

6 Without 440 loading condition (1.O [P.u.]). The figures show that both the controllers work very well judging from small swings with large damping. The performance of the controllers are compared in Table 2 with the integral-time-error (TE) computed with the cost function (16). Observations in the table show that the Neuro- PSS works very well judging from the TE performance in both the heavy or the light load compared to the normal load condition, however, the TE performance of the conventional shows larger variation to loading conditions for the Neuro- PSS because the parameters in the STAB4 were optimized in the normal loading condition. Fig. 7 shows the speed deviation for other disturbance coming from stepwise loading condition (0.15 P.u.) changes: increased (at 0.24 [sec]), decreased (at 0.96 [sec]) and cleared (1.44 [sec]) when the power system is in the heavy loading condition. The figures show that both the controllers work very well judging from small swings. V. CONCLUSONS A neural network-based power system stabilizer (Neuro- PSS) is developed for a generator connected to a multimachine power system utilizing the power flow dynamics. The low-frequency oscillation is modeled by the Neuro- dentifier using nonlinear power flow dynamics, then a Generalized Backpropagation-Thorough-Time algorithm is developed to train the Neuro-Controller. The two neural networks constructed to learn and control the power flow dynamics avoid the need to identify the original rotor dynamics. The performance of the proposed Neuro-PSS was demonstrated by applying it to a typical multi-machine power system. ts comparison with a conventional PSS shows that the Neuro-PSS works very well in a wide range of operation. Speed-dev. of the 2-nd Gen. ( 0.5 [P.u.] ) 0.4,,,, Time [Sec1. * i x t Withoutontrd - STAB4 - Neuro-PSS Fig. 5. The speed deviation of generator 2 for the line fault disturbance in a light load condition. Speed-dev of the 2-nd Gen ( 1 O[p U 1 ) Hzl * Time [Sec] ~ - - Without Control - STAB4 - Neuro-PSS 1 Fig. 6. The speed deviation of generator 2 for the line fault disturbance in a heavy load condition. Speed-dev. of the 2-nd Gen. ( 1.O[p.u.] ) W,, Time [Sec] Control - STAB4 _. Neuro-PSS? ry ~ Fig The speed deviation of generator 2 for the line fault disturbance in a normal load condition. -0 5, Time [Sec] w i t Control - STAB4 - Neuro-PSS l1 Fig. 7. The speed deviation of generator 2 for the load change disturbance in a heavy load condition.

7 44 1 Loading OS EP.u [P.u.l l.o bu.l Without Control 6.04 loo(%) loo(%) loo(%) STAB (%) (%) (%) V. ACKNOWLEDGMENT The work is supported in parts by Korea Science and Engineering Foundation (KOSEF) and the National Science Foundation (NSF) under grants U.S.-Korea Cooperative Research on ntelligent Distributed Control of Power Plants and Power Systems (NT ), and Research and Curriculum Development for Power Plant ntelligent Distributed Control (ED ). V. REFERENCE [l] Yao-nan Yu, Electric Power System Dynamics, Academic Press, New York, pp , [2] F. P. demello and C. A. Concordia, Concept of synchronous machine stability as affected by excitation control, EEE Trans. on PAS, Vol. PAS-103, pp ,1969. [3] W. G. Heffron and R. A. Phillips, Effect of modern amplidyne voltage regulator on under excited operation of large turbine generators, Trans. on American nst. Electrical Eng. Part 3 71, pp , [4] K. T. Law, D. J. Hill and N. R. Godfrey, Robust controller structure for coordinate power system voltage regulator and stabilizer design, EEE. Trans. on Control Systems Technology, vol. 2, No.3, pp , September [5] D. Nguyen and B. Widrow, The truck backer-upper: An example of self-learning in neural networks, EEE Control System Magazine, pp , [6] Y. iguni and H. Sakai, A nonlinear regulator design in the presence of system uncertainties using multilayered neural networks, EEE Trans. on Neural Networks, V01.3,N0.4, pp , July [7] C. C. Ku and K. Y. Lee, Diagonal recurrent neural network for dynamic system control, EEE Trans. on Neural Networks, Vo1.6, pp , Jan [8] C. C. Ku, K. Y. Lee and R. E. Edward, mproved nuclear reactor temperature control using diagonal neural networks, EEE Trans. on Nuclear Science, vol. 39, pp , December [9] Q. H. Wu, B.W. Hogg, and G.W. rwin, A neural network regulator for turbogenerators, EEE Trans. on Neural Networks, Vol. 3, No. 1, Jan [ 1 1]P. J. Werbos, Backpropagation through time: What it does and how to do it, proc, of EEE, pp , vol. 78, No. 10, Oct Analysis, McGraw-Hill, pp. 387, [ 13lT. E. Kostyniack, PSS/E Program Operation Manual, P.T.., October 31, [ 14lK. J. Astrom and, B. Wittenmark, Computer Controlled Systems: Theory and Design, Prentice-Hall nternational, pp , [15]M.R. Khaldi, A.K.Sarkar, K.Y. Lee, Y.M. Park, The Modal Performance Measure for Parameter Optimization of Power System Stabilizers, EEE. Trans. on Energy Conversion, Vol. 8, No.4, pp , Dec., V. BOGRAPHY Young-Moon Park was born in Masan, Korea on Aug. 20, He received his B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University in 1956,1959 and 1971, respectively. His major research field is power system operation and control, and artificial intelligence applications to power systems. Since 1959, he has been a faculty of Seoul National University where he is currently a Professor of Electrical Engineering. He is also serving as the president of the Electrical Engineering and Science Research nstitute. Dr. Park is a senior member of EEE. Myeon-Song Choi received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1989 and 1991, respectively. He is currently a Ph.D. candidate in Power System Laboratory, Electrical Engineering, Seoul National University. His current researcb interests include robust control theory, artificial neural networks, and their applications to power system stabilizing control. Kwang Y. Lee received the B.S. degree in electrical engineering from Seoul National University, Seoul, Korea, in 1964, the M.S. degree in electrical engineering from North Dakota State University, Fargo, ND, in 1967, and the Ph.D. degree in system science from Michigan State University, East Lansing, M, in He has been on the faculties of Michigan State, Oregon State, University of Houston, and the Pennsylvania State University, University Park, PA, where he is a Professor of Electrical Engineering. His current research interests include control theory, artificial neural networks, fuzzy logic systems, and computational intelligence and their applications to power systems. Dr. Lee is a senior member of EEE.