CALCULATION OF AVR PARAMETERS USING NEURAL NETWORK TO ENHANCE THE POWER SYSTEM STABILITY

In this paper a parameter optimization method using a neural network is suggested for finding the optimum control gains of a proportional deferential (PD) controller which it is used to control the excitation of the synchronous generator. In this work one PD controller and three D controllers has been used which it is mean five gains to be found which it is a very hard work to find it manually. The neural network has been used to automate the way in inding this gains which it was manually calculated until the desired plant output has been obtained. The controller gains which it is manually calculated has been compared with that calculated with neural network with MATLAB program and the performance has been simulated and compared


Introduction
A need for reliable and economic operation of power system led to interconnect the synchronous generator in the same plant or among plants in a wide area. The oscillation existed as soon as the synchronous generator has been connected together in the electrical network. The oscillation of small frequency topically of (1-3) Hz is described as hunting of synchronous machine (Bikash Pal & Balarko Chaudhuri 2005). The oscillation of the electromechanical coupling between the rotor and the rest of the system can be described as the pendulum motion which it is suffers from oscillatory acting following any disturbance from its nominal state (John J. Grainger & W.D. Stevenson 1994). The oscillations were found to be due to lack of damping of mechanical mode of the interconnected systems (Bikash Pal & Balarko Chaudhuri 2005). The additional damping can be provided by controlling the excitation system by adding an automatic voltage regulator (AVR).The fast evolution in the excitation techniques (like static excitation with power electronic devices) and its control ways (like P, PD, PID, and etc) helps the power system to enhance its stability (Dr. J. Kumar, P. Pavan Kumar, A. Mahesh & A. shrivastava 2011). The new excitation systems and controllers still suffer from the need to specify its gains by an efficient way because the deviations in these gains from the optimum value by a specific range may make the AVR to enhance the system instability (IEEE guide 1990). So the gains of the AVR should be specified by an automatic way rather than manual or mathematical calculation ways like Ziegler and Nichols method for tuning the control gains of PID controller (K. Ogata 1997).many researches have been made to automate the gain selection problem and many algorithms have been proposed. In T. Jayabarathi 2011) but first one still suffers from the problems of fuzzy controller and in second one only one PID controller has been tuned. The finding of a set (5 gains here) of control gains of many controllers acts together and gives acceptable results may be impossible by the manual methods. A neural network has been used here to automate this process. The paper is ordered as follows: Section 2 describes the system model and the study objective, Section 3 gives a brief introduction to the neural network, the design procedures are given in section 4 and section 5 is dedicated to the evaluation of controller performance.

System Model and Study Objective:
When generating station transmitting power over long distance to a load center then the system can be simplified in to a single machine connected to an infinite bus throw transformer and transmission line (SMIB) as shown in The synchronous machine considered her has three windings as stator windings and has one field winding and two damper windings. The excitation considered her is extracted from IEEE STA1 type and provided with an AVR known as strong action regulator as shown in following block diagram ( Figure 2). The objective of the work is to design a multilayer neural network to give the gains (K ou , K 1u , K ow , K 1w & K if ) of the excitation PD controllers to enhance the static and dynamic stability of the power system. Note that Figure 2 contains another variable (K w ) which it is constant and equal 1(K w =1).

Fig.2: A block Diagram of AVR and Excitation Systems.
Where are a time constants and are the change in voltage, frequency and excitation current respectively. The power system is highly nonlinear system but it can be linearized around an operating point which it is called the nominal operating point (Li Yan 2011). And the linearized system of equations will be expressed in state-space (SS) representation as (A 0 , B 0 , C 0 and D 0 ) with the following two equations: ). For more information about the driving of SS form of power system the reader referred to one of the very good references on this objective ((P.

Neural Network Introduction
A neural network NN is a computational network taking from a biological model consisting of many computational units called neurons (Howard Demuth & Mark Beale 1998). The NN has many advantages like adapting itself, and learning with part of data and generalized it to all data ranges and other practical properties. The NN arranged in layer form first layer is called the input layer the last layer is called the output layer any layer in between these two layers is called hidden layer. Each neuron can perform a function like sigmoid and pure line. The experiment shows that a NN with one sigmoid function as a hidden layer and an output layer with pure line function can approximate any function (Howard Demuth & Mark Beale 1998). In this paper the work will be divided into three steps first train the NN to approximate the plant work second connect the controller with the trained NN and train the controller alone. At the end separate the controller and take its average output. Controller design: First step: As said above that the experiment shows that a NN with one sigmoid function as hidden layer and an output layer with pure line function can approximate any function (Howard Demuth & Mark Beale 1998). Here the same structure will be used with 5 neurons in the hidden layer and one neuron in the output layer to approximate the step response of the plant as can be seen in Figure 3. 5 3*1 Where IW & LW are the input and hidden layer weight matrix respectively and b1 & b2 are the input and hidden layer base vectors respectively. The neural network will be trained by Fletcher-Reeves method with hybrid bisection-cubic line search (for more details see reference (Howard Demuth & Mark Beale 1998)). Figure 4 shows the step response of the original plant function red line and its approximation by neural network the blue line.

Fig.4: the NN Tracking (Blue Line) to the Step Response of the Plant (Red Line).
In the above Figure (Figure 4) the blue line represents the output (y) of ( Figure 3) and shows the good tracking performance of the neural network.

Second step:
The previously trained NN will be connected with a new NN as shown in Figure 5. The new NN will be consisted of input layer, one hidden layer with sigmoid function and output layer with linear function as shown in Figure 5. Where the three inputs to the new neural network are assumed to be the range of change in the terminal voltage, frequency and excitation current which are defined by the following ranges.
Which they are decided from simulating the machine under normal and abnormal conditions. The new NN will be trained to perform the controller work. The same function will be used for training and line search function to train the network. The response of the overall NN can be seen in Figure 6 which shows good tracking performance for the step response of the real system. Some error can be seen in the first few epochs but after that the two lines can be considered identical to some extent tolerance as it clearly can be seen in Figure 6. Where the blue line in Figure 6 represents the output (y) of Figure 5.

Third step:
Disconnect the controller NN and gate its outputs. The outputs of this NN will be the gains of the PD controller of the synchronous generator exciter. The gains will be as can be seen in Table 1.

Results and Discussion
Here the static and dynamic stability will be studied. The static stability will be studied from the location of the Eigen values and the damping ratio (ζ) point of view. The damping ratio (ζ) is used to measure the rate of decay of the signal's oscillation. The damping ratio for the system with the PD gains calculated with the analytical method will be compared by that which it is gotten by NN.The comparison has been listed below in Table 2. Our concern is the eigen value with a frequency less than or equal (10 rad).
(For more information about the PD gains values see appendix of this paper). For the dynamic stability of the plant, the response of the plant to a 3 phase fault and a duration 0f (0.2 sec) in the machine terminal will be studied here.

Conclusion:
The design of a PD controller with a NN for gains calculation of the PD controller has been proposed here. The proposed controller has the same structure of the PD controller but with a NN to calculate the gains of the PD controller in off line mode. The structure of the NN has been proposed. The stability of a single machine infinite bus bar (SMIB) has been discussed and compared with the conventional PD controller (the parameters were selected by analytic calculation) from the point of view of damping ratio, the location of Eigen values and the dynamic simulation of the SMIB system. The NN parameter estimation was found to give optimal parameters to the PD controller which enhances the response of the PD controller which in turn enhances the static and dynamic stability of the system. id, iq = current in d & q stator winding. ir = current in excitation winding. Rs = stator windings resistance. Rsf = field winding resistance. R1d, R1q = damper winding resistance. x s = stator winding self reactance. x sf = field winding self reactance. X s1d , X s1q = damper windings self reactance. X t = transmission line reactance. v d , v q = stator windings voltages. E fd = field winding voltage. s = machine slip. δ = load angle. H = related inertia constant of the machine. ω = synchronous speed. T mech = mechanical torque. T em = electro mechanical torque.