VIEWS: 58 PAGES: 5 CATEGORY: Computers & Internet POSTED ON: 6/12/2010 Public Domain
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 PSS Design Based on RNN and the MFA\FEP Control Strategy Rebiha Metidji and Boubekeur Mendil Electronic Engineering Department University of A. Mira, Targua Ouzemour, Bejaia, 06000, Algeria. Zeblah80@yahoo.fr The main problem in control systems is to Abstract – The conventional design of PSS (power system stabilizers) was carried out using a linearized design a controller that can provide the appropriate model around the nominal operating point of the control signal to meet some specifications plant, which is naturally nonlinear. This limits the constituting the subject of the control action. Often, PSS performance and robustness. In this paper, we propose a new design using RNN these specifications are expressed in terms of speed, (recurrent neural networks) and the model free accuracy and stability. In the case of neuronal approach (MFA) based on the FEP (feed-forward control, the problem is to find a better way to adjust error propagation) training algorithm [15]. the weights of the network. The main difficulty is The results show the effectiveness of the proposed how to use the system output error to change the approach. The system response is less oscillatory with controller parameters, since the physical plant is a shorter transient time. The study was extended to interposed between the controller output and the faulty power plants. scored output. Keywords-Power Network; Synchronous Generator; Neural Network; Power System Stabilizer; MFA/FEP Several learning strategies have been proposed control. to overcome this problem such as the supervised learning, the learning generalized inverse modeling, I. INTODUCTION the direct modeling based on specialized learning, and so on [14]. In this work, we used our MFA/FEP Power system stabilizers are used to generate approach because of its simplicity and efficiency supplementary control signals for the excitation [15]. The aim is to ensure a good damping of the system, in order to damp the low frequency power power network transport oscillations. This can be system oscillations. Conventional power system done by providing an adequate control signal that stabilizers are widely used in existing power affects the reference input of the AVR (automatic systems and have made a contribution in enhancing voltage regulator). The stabilization signal is power system dynamic stability [1]. The parameters developed from the rotor speed or electric power of a classical PSS (CPSS) are determined based on variations. a linearized model of the power system around its nominal operating point. Since power systems are The section II presents the power plant model. highly nonlinear with time varying configurations The design of the neural PSS is described in section and parameters, the CPSS design cannot guarantee III. Some simulation results are provided in section good performance in many practical situations. IV. To improve the performance of CPSSs, II. THE POWER PLANT MODEL numerous techniques have been proposed for their design, such as the intelligent optimization methods The standard model of a power plant consists of a synchronous generator, turbine, a governor, an [2], fuzzy logic [3,4,5], neural networks [7,8,9] and excitation system and a transmission line connected many other nonlinear control techniques [11,12]. to an infinite network (Fig.1). The model is built in The fuzzy reasoning using qualitative data and MATLAB/SIMULINK environment using the empirical information make the fuzzy PSS (FPSS) power system Blockset. In Fig.1, PREF is the less optimizing compared with the neural PSS mechanical power reference, PSR is the feedback (NPSS) performance. This is our motivation. through the governor, TM is the turbine output 217 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 torque, Vinf is the infinite bus voltage, VTREF is terminal voltage reference, Vt is terminal voltage, VA is the voltage regulator output, VF is field voltage, VE is the excitation system stabilizing signal, ∆w is the speed deviation, VPSS is the PSS output signal, P is the active power, and Q is the reactive power at the generator terminal. Figure 4. Block diagram of DTRNN. The switch S is used to carry out tests on the power system with NPSS, CPSS and without PSS (with switch S in position 1, 2, and 3, respectively). The synchronous generator is described by a seventh order d-q axis of equations with the machine current, speed and rotor angle as the state variables. The turbine is used to drive the generator Figure 5. Illustration of the state feedback. and the governor is used to control the speed and the real power. The excitation system for the III. THE NPSS DESIGN generator is shown in Fig.2 [4]. In this work, we used a neural architecture used primarily in the field of modeling and systems The CPSS consists of two phase-lead dynamic control; namely the DTRNN (Discrete compensation blocks, a signal washout block, and a Time Recurrent Neural Network). This is analogous gain block. The input signal is the rotor speed to the Hopfield network (Fig.4). deviation ∆ω [16]. The block diagram of the CPSS is shown in Fig.3. W : global synaptic weight vector. S : weighted sum, called potential. U : output or neuron response. f : activation function. υ: external input. This is a neural network with state feedback. It has a single layer network with the output of each neuron is feed back to all other neurons. Each neuron may receive an external input [14]. This is well shown in Fig.5. Figure 1. The control system configuration. A. DTRNN network Equations Originally, the equations governing this network type are the form: U k 1 f∑ W U k ν k If we consider that the inputs ν are weighted as in (1) Fig.4, (1) can be rewritten as follows: U k 1 f∑ W U k (2) Figure 2. Block diagram of the excitation system. With 1 j 0 U k U k j 1, … , n ν k j n 1, … , n m (3) Where: Figure 3. Block diagram of CPSS. U k 1 : i Network state variable ν k : j External input (j=1… m). (i=1… n). 218 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 n : number of neurons in the network. U k =1 : inner threshold. m : dimension of the input vector, V. The outputs are chosen among the state variables. Learning is done using dynamic training algorithms that adjust the synaptic coefficients based on presented examples (corresponding desired inputs \ outputs) and taking into account the feedback information flow [17]. Figure 6. MFA/FEP control structure. In this work, we used the MFA training Y(k) = [y1(k), y2(k),…,yr(k)]T structure of Fig.6. The idea is to evaluate the output error (i.e. the gap between the system output and its = [U1(k), U2(k),… Ur(k)]T (5) desired value) to the controller input and to spread them directly from input to output, to get the hidden The standard quadratic error over the pth layers and the output layer errors. This can be sequence is given by realized by the feed forward error propagation J (W) = ∑ ∑ y (k) y (k) (6) algorithm (FEP) crafted specifically for this purpose. This allows direct and fast errors Where calculation of consecutive layers, required for the : is the length of the pth training sequence, controller parameters adjustment. r : is the number of the network outputs, B. Training the DTRNN controller based on the y (k) : is the jth network output, algorithm FEP y (k) : is the desired value corresponding to y (k). The weights are updated iteratively according to The approach MFA / FEP is an effective alternative for training controllers. Direct injection ( ) W (k 1) = W (k) μ ( ) (7) of the input error can provide error vector components required to the network weight update. The FEP formulation is given in the following where µ is the learning rate. The gradient in (7) is paragraph. calculated using the chain rule: Let consider a DTRNN given by (2) and (3). ( ) ( ) The global input vector, X (k), of the network = (8) ( ) ( ) ( ) consists of the threshold input, d=1, the external inputs, xi (k), and network state feedback variables, Ui (k). Where ∂U ∂f s (k) ∂s (k) = ∂W (k) ∂s (k) ∂W (k) 1 X (k) = f s (k) . x (k) (9) X (k) X (k) U (k) . . U (k) ( ) . . . The term in (8) is the sensitivity of Jp(w) to X (k) = ( ) X (k) = . and U (k) = . u (k 1) the node output, Ui(k). Let the error, calculated . . . . . between the network output and desired output, be . . U (k) u (k 1) X (k) (k) = Y(k) Y (k) = ∆Y(k) (10) As in the back-propagation algorithm, the term ( ) can be interpreted as the equivalent Then, we can write ( ) error, ε (k), with (i=1,2,…,n). Hence, we write U (k 1) = f S (k) = f ∑ W . X (k) (4) ( ) ( ) The outputs are chosen among the state variables. = ε (k) = ∑ ( ) ∆y (k) (11) ( ) For the simplicity of notation, let consider the first r state variables as outputs. The error vector, E0(k), can be calculated at the input ; since the network receives the output vector, Y(k), as input through the state feedback. The 219 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 equivalent error vector components, ε k , are -The nominal Power : Pn = 3.125×106 (VA). computed using (11), through the forward propagation of E0(k). -The nominal voltage : Vn =2400 (V). C. NPSS design using the MFA / FEP approach -The nominal frequency : fn = 50 (Hz). To evaluate the performance of the The aim is to ensure an optimal control of NPSS, the system response of the NPSS is power system output voltage. The MFA / FEP compared with the cases where there is no PSS and learning structure is illustrated by Fig.7. with a CPSS in the system. The adequate structure of the NPSS network consists of 3 neurons. The input vector X= [d=1,dw, w, UT]T , where U(3x1) is its own state vector, d is the threshold input, w is the angular velocity, and dw is its variation. The NPSS output, VNPSS, chosen as the first state variable, is applied to the automatic voltage regulator input. The learning rate is fixed at µ = 0.2. The training procedure is summarized by the followed steps: Step1- Initialize the weights to small values in an interval [0, 0.1]. The synaptic weight matrix is of size 3 × 6 (3 outputs and 6 inputs). Step 2- Initialization the state variables. Figure 8. Terminal voltage response. Step 3- Compute NPSS output. Step 4- Application to the single-machine infinite bus (SMIB) process. Step 5- Compute the output error and update the NPSS weights. Step 6- Go to step 3 or stop if the learning is completed. Figure 9. Machine angular speed. From these results, we can see that the response of the system stabilizes at the reference value after 2 sec. But, the NPSS provide a better voltage response with reduced overshoot and rise time. Figure 7. The NPSS training structure based on MFA / FEP approach. In order to evaluate the performance of the different PSS in the presence of defects, let us consider, as an example, a temporary short circuit, at t = 5s, that lasts 0.1s (time required for switching IV. SIMULATION RESULTS the circuit breaker protection). The parameters of the machine model used hang the simulation are: 220 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 System Stabilizer with Learning Ability’’, IEEE Trans on Energy Conversion, Vol. 11, No. 4, pp. 721-727, Dec 1996. [4] M. Chetty, ‘’A Fuzzy Logic Based Discrete Mode Power System Stabilizer’’, Asian Journal of Cont, Vol. 4, No. 3, pp. 327-332, Sep 2002. [5] P. V. Etingov & N. I. Voropai,‘’ Application of Fuzzy Logic PSS to Enhance Transient Stability in Large Power Systems’’, Proc. Interna. Conf. on Power Electronics, Drives and Energy Systems, pp. 1 - 9, 2006. [6] A.A. Gharaveisi, S.M.R. Rafiei, & S.M. Barakati ‘’An Optimal Takagi-Sugeno Fuzzy PSS For Multi- Machine Power System‘’, Proc of the 40th North American Power Sympo, pp. 1- 9, 2008. [7] P. Shamsollahi & 0. P. Malik, ‘’An Adaptive Power System Stabilizer Using On-Line Trained Neural Networks‘’, IEEE Trans. on Energy Conversion, Vol. 12, No. 4, pp. 382 -287, Dec 1997. [8] C.-J. Chen, T.-C. Chen, & J.-C. Ou, ‘’Power System Stabilizer Using a New Recurrent Neural Network for Multi- Machine‘’, Proc. IEEE Interna. Power and Energy Conf, pp. 68 Figure 10. Terminal voltage response. – 72, 2006. [9] C.-J. Chen, T.-C. Chen, H.-J. Ho & J.-C. Ou‘’ PSS Design Using Adaptive Recurrent Neural Network Controller ‘’, Proc. Interna. Conf. on Natural Computation, 2009. ICNC '09. Fifth, Vol.2, pp. 277-281, 2009. [10] P. Tulpule & A. Feliachi, ‘’Online Learning Neural Network based PSS with Adaptive Training Parameters‘’, IEEE Power Eng. Society General Meeting, pp. 1-5, 2007. [11] S.-M. Baek & J.-W. Park, ‘’ Nonlinear Controller Optimization of a Power System Based on Reduced Multivariate Polynomial Model‘’, Proc. Interna. Joint Conf. on Neural Networks, pp. 221 -228, 2009. [12] H. Amano & T. Inoue, ‘’ A New PSS Parameter Design Using Nonlinear Stability Analysis‘’, IEEE Power Engineering Society General Meeting, pp. 1- 8, 2007. [13] S. Panda & C. Ardil, ‘’Robust Coordinated Design of Multiple Power System Stabilizers Using Particle Swarm Optimization Technique‘’, Interna. Journal of Electrical and Electronics Eng. 1:1 2008. [14] J. He, ‘’Adaptive Power System Stabilizer Based On Recurrent Neural Network ‘’, PhD thesis, Univ. of Calgary, 1998. Figure 11. Machine angular speed. [15] B. Mendil & K. Benmahammed, ‘’Model Free Approach for Learning Control Systems‘’, Interna. Journal of Computer The fault in the network has affected the output Research, Vol. 11, n° 2, pp 239-247, 2002. voltage and the angular speed. We also note that the [16] A. A. Gharaveisi, M. Kashki, S.M.A. Mohammadi, S.M.R. Rafiei, & S.M. Vaezi-Nejad, ‘’A Novel Automatic Designing system returns to steady state with less oscillations Technique for Tuning Power System Stabilizer ‘’, Proc. of the and with a shorter time using the control system World Congress on Eng. Vol III, 2008. (AVR) with the NPSS compared to CPSS and also [17] D. R. Hush & B.G. Horne, ‘’Progress in Supervised Learning with the system without PSS. Neural Networks‘’, IEEE signal proc. magazine, Vol.10, No.1, pp.8-39, Jan. 1993. V. CONCLUSION In this paper, we have developed another way to design PSS. The NPSS is a DTRNN trained using our MFA / FEP learning structure. The results show the effectiveness and the best performance of the resulting stabilizer. REFERENCES [1] S. M. Pérez, J. J. Mora, & G. Olguin, ‘’ Maintaining Voltage Profiles by using an Adaptive PSS‘’, Proc. IEEE PES Transmission and Distribution Conf. and Exposition Latin America, Venezuela, 2006. [2] L. H. Hassan, M. Moghavvemi, & H. A.F. Mohamed, ‘’Power System Stabilization Based on Artificial Intelligent Techniques: A review’’ , International Conference for Technical Postgraduates (TECHPOS), pp. 1-6, 2009. [3] A. Hariri & O.P. Malik, ‘’A Fuzzy Logic Based Power 221 http://sites.google.com/site/ijcsis/ ISSN 1947-5500