Direct neural adaptive control applied to synchronous generator

Direct Neural Adaptive Control Applied t o Synchronous Generator Payman Shamsollahi, Student Member, IEEE, and Om P. Malik, Fellow, IEEE Department of Electrical and Computer Engineering The University of Calgary, Calgary, Alberta, Canada T2N 1N4

Abstract-

This paper investigates t h e application

of neural networks to control a synchronous generator based on direct adaptive control scheme. Use of a neural network t o model t h e dynamic system is avoided by making use of the sign of t h e Jacobian of t h e plant.

This will substantially reduce the complexity and the computation time of t h e control algorithm. T h e controller is trained on-line using the back-propagation aigorithm which gives an adaptive attribute to t h e controller. Simulation results are presented t o complement the theoretical discussion.

bilizer (NAPSS) is introduced. Only the inputs and out.puts of the generator are measured and there is no need to determine the states of the synchronous generator. The on-line version of the back-propagation training method is used in this paper. Thus, the NAPSS is not designed for a specific point and is able to track the plant variations as they occur.

11. DIRECTNEURALADAPTIVECONTROLLER The structure of the system is shown in Fig. 1. The input vector to the NAPSS is formed as:

I. INTRODUCTION Power System Stabilizer (PSS) is a supplementary controller to damp low frequency oscillations and to improve dynamic performance of the generating unit. Over the past two decades, various control methods have been proposed for PSS design. .Among these, Conventional PSS (CPSS) of the lead-lag compensation type has been adopted by most utility companies because of its simple structure, flexibility and ease of implementation [l]. The CPSS works well if its parameters are tuned carefully and the system is operating within a certain range of the design point, However, for a nonlinear plant like power system with a wide range of operating conditions and time-varying configuration and parameters, this fixed parameter stabilizer may not be the optimal one for the whole set of possible operating points and configurations. In recent years, there have been new approaches for PSS design using modern control techniques. Many of these approaches lack one or more of the three basic and important features that a PSS should have, i.e. simplicity of structure, fast acting ( low computation time ) and adaptivity. Recently. neural networks have been successfully applied to the identification and control of dynamical systems [2] specially in the field of adaptive control by making use of on-line training [3]. Among various types of neural networks used in control systems, feed-forward multi-layer neural network is the most common one. This is mainly due to the computational efficiency of the backpropagation algorithm [4]and the versatility of the three layer feed-forward neural network in approximating an arbitrary static nonlinear function [5]. However little work is reported on the use of neural networks for power system real-time control. In this paper, the Xeural Adaptive Power System Sta0-7803~39464/97/510.00 0 1997 IEEE.

[ A ~ ( k ) , A w (k l),. . . , A u ( ~ m), 4Pe( I C ) , AP,(k - 1), . . . ,APe(k - n ) ]

(1)

where Aw(IC) is the generator speed deviation and 4Pe(k) is the accelerating power, b&h at the time step IC. The output of the controller is the PSS control action, u ( k ) . which is fed to the plant to damp the oscillations of the generator speed deviation. As it is clear in ( l ) ,m 1 samples of the speed deviation as well as n 1 samples of the accelerating power are fed as input to the controller. This helps the controller to consider the dynamic nature of the plant. The setup shown in Fig. 1 is very simple and there are no blocks of reference model and/or identifier in its structure. There is also no need to measure the plant states. To obtain the best performance, i.e. minimum oscillations in the plant output, a cost function is defined for the system as:

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1 h -2[ A w d ( k ) - Au(IC)]~ -u(k)’ 2

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(2)

~

where e ( k ) = A w d ( k ) - A w ( k ) is the output error, Aud(k) is the desired speed deviation at time step k , which is equal to zero in a regulatory setup, and h is a tuning parameter which is used to obtain desired dynamic characteristics of the plant output. By taking h greater than zero, a p5nalty factor is applied to the control action generated by the NAPSS which helps the tuning of the dynamic trajectory and optimizing the overshoot and the settling time of the response curve. To minimize the cost function J ( k ) employing the gradient descent method, the weight matris W ( k ) of the NAPSS is moved toward the negative gradient of J ( k ) which in mathematical form gives the following weight update rule: W ( k )= W ( k - 1) - r ] V W J ( k )

(3)

where r] is the learning rate and G w J ( k ) is the gradient of J ( k ) with respect to W ( k ) . This gradient can be calculated as:

The term $$# can be computed by the backpropagation method and no difficulty is involved in it. But the term which is the Jacobian of the plant, is not easy to compute. Several methods are proposed in the literature to evaluate the’ Jacobian among which the best three are mentioned here. The first approach is to compute the Jacobian using plant equations. This method is computationally extensive and requires the evaluation of the the Jacobian in each sampling period. Moreover, it is not applicable to unknown or partially known plants. The second way is to build a neuro-identifier which is a realtime plant tracker [6]. Using this identifier, the Jacobian of the plant is computed by back-propagation method. Again this method puts an estra burden on the computation process for it necessitates the introduction and training of the neuro-identifier. However, this method yields a precise and adaptive way to indirect!y obtain the Jacobian and control the plant. The third approach, which is computationally the simplest one, is to approximate the partial derivative by its sign which can be known a priori when some information is available about the orientation in which the controller output affects the plant output [7]. This approach is adopted here. Therefore, (4) can be approximately written as:

w,

or simply:

considering that the sign of the Jacobian of the generating unit is negative and e = - A u ( k ) . Therefore, (3) can be

simplified as: W ( k )1W ( k - 1) + v[Aw(k) - h u ( k ) ]W - k ) aw(k)

(7)

Having (7), the learning process is summarized as: 1) At time step k , Au(k) and A P , ( k ) are sampled.

2) The output of the controller, u ( k ) ,is computed.

3) The scalar value of [Aw(k)

- h u ( k ) ] is backpropagated through the controller updating W ( k )and minimizing J ( k ) .

The above steps are taken in each sampling period, resulting in an on-line learning algorithm. The use of a single element error vector simplifies the training a1gorit)hm in terms of computation time. The resulting controller enjoys two interesting properties. First , the controller is adapted directly based on the plant output error; i.e. there is no extra stage for learning the identifier and/or computing the Jacobian. Second, it is adaptive; i.e. it can track the plant variations and adjust its parameters accordingly. 111. SIMULATION STUDIES

A number of studies have been performed to investigate the performance of the proposed NAPSS and the results are compared with those of a CPSS. A detailed nonlinear seventh-order model is used to simulate the dynamical behavior of the synchronous generator connected to a constant voltage bus through two parallel transmission lines. The governor is modeled by a first-order system and the AVR and exciter combination used is Type STlA from IEEE Standard P421.5/D15 [ 8 ] . Speed deviation and electrical power deviation are sampled at the rate of 25 Hz for control signal computation. The number of time delays used for the input of the controller, i.e. m and n in (l),are set to 2 experientially. This means that the controller has six inputs. There is one hidden layer of 8 neurons with sigmoid nonlinearity and an output layer having one linear neuron. Initial weights of the controller lie between [-0.1,+0.1], chosen randomly at the beginning of the process. The learning rate and the tuning parameter h are set to 0.01 and 9.5 respectively. The response of the system with the NAPSS and the CPSS are compared for various disturbances and different operating conditions, namely: 1)Louded Generator Test: A 0.10 pu step increase in input torque reference is applied at 1 s and removed at 5 s in the operating point of 0.7 pu power, 0.85 pf lag. (Fig. 2) 2) Light Loud Test: A 0.20 pu step increase in input torque reference is applied at 1 s and removed at 5 s with generator operating at 0.2 pu power, 0.8.5 pf lag. (Fig. 3)

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IV. CONCLUSIONS

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A direct adaptive controller for the generator using online trained neural network is presented in this paper. The controller enjoys the general advantages of neural networks such as high speed, generalization capability and fault tolerance as well as adaptivity (learning) property. Moreover, it has the following interesting properties: The controller is adapted directly in an on-line mode to reduce the output error.

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The structure of the controller is very simple. (just a few neurons) The learning algorithm is simplified by making use of a single element error vector. There is no need for the states of the generator.

REFERENCES

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The simulation results for the various operating conditions and disturbances show that the proposed neural adaptive stabilizer can provide good damping over a wide operating range. It, also, significantly and adaptively improves the dynamic performance of the system.

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Fig. 4. System response t o a 0.05 p u step decrease in voltage reference and return t o initial condition in leading power factor test.

3) Leading Power Factor Operation Test: A 0.05 pu step decrease in voltage reference is applied at 1 s and removed at 5 s with generator operating at 0.3 pu power, 0.9 pf lead. (Fig. 4)

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Time, s

Fig. 2. System response t o a 0.10 pu step increase in torque and return t o original condition.

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Fig. 3. System response to a 0.20 p u step increase in torque and return to original condition in light load test.

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E. V.

Larsen and D.A. Swann, “Applying power system stabilizers: Part 1-3”, IEEE Trans. Power Apparatus a n d Systems. vol. PAS-100, no. 6 , pp. 3017-3046, Jun. 1981. K. S. Narendra a n d K. Parthasarathy, “Identification and control of dynamical systems using neural networks”. IEEE Trans. Neural Networks, vol. 1, pp. 4-27, Mar. 1990. S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan, 1994. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. 1: Foundations, chapter 8 , pp. 318-362, Cambridge, MA: MIT Press, 1986. G. Cybenko, “Approximation by superposition of a sigmoidal function”, Math. Control, Signals, Systems, vol. 2, pp. 303-314. 1989. D. Nguyen and B. Widrow, “The truck backer-upper: An esample of self-learning in neural networks”, in Proceedings o j the Int. Joint Conference on Neural Networks, Washington DC. June 1989, vol. 2, pp. 11357-11363. M. Saerens a n d A. Soquet, “Neural controller based on backpropagation algorithm”, IEE Proceedings-F, vol. 138, no. 1 . pp. 55-62, Feb. 1991. IEEE Excitation System Model Working Group, “Excitation system models for power system stability studies”, Draft 15 f o r ANSI/IEEE Standard, P421.5/D15, 1990.