It is pertinent to maintain the voltage and frequency

Transcription

1 Design of FNN VR for Enhancement of Power System Stability Using Matlab/Simulink SLM PERVEZ MEMON*, MOHMMD SLM UQILI **, ND ZUBIR HMED MEMON *** RECIEVE ON CCEPTED ON BSTRCT simple technique of excitation voltage control with NNVR (Neural Network utomatic Voltage Regulator) is proposed in this paper. Popular type of NN (rtificial Neural Networks) known as RBF (Radial Basis Function) architectures with OLS (Orthogonal Least Square) algorithm is suggested to design VR in order to prove its applicability and suitability. This proposed technique is implemented considering as SMIB (Single Machine Connected to Infinite Bus) system with linearized model of synchronous machine and its excitation system using Matlab/Simulink. The simulation results of RBF VR, when compared with conventional VR controllers show better performance, improve the transient and small signal stability of the system and above all its response is more suitable in case of load changing conditions. ey Words: Excitation System, utomatic Voltage Regulator, Synchronous Machine, Stability, Radial Basis Function, Matlab/Simulink.. INTRODUCTION It is pertinent to maintain the voltage and frequency of the system within permissible boundaries in order to keep the reliability of the system. Excitation control system is defined as the field current to maintain excitation of synchronous machine and include exciter and VR. When the changes in rotor angle () or frequency (f) occur, real power (P) is affected which is controlled by turbine-governor system. Voltage magnitude disturbs reactive power (Q) which is controlled by exciter- VR system. Therefore LFC (Load Frequency Control) system controls active power and reactive power is controlled by VR and both (LFC & VR) are installed separately for every generator. The better performance of VR can produce quick response, simple maintenance and high current facilities to the system thus the Q and generated voltage can be controlled efficiently. Excitation system contributes to the effective voltage control and enhances the system stability. Its quick response can improve transient and small signal stability of the system. [-4,7]. Conventional controllers are mostly fixed gain controllers, they are settled at particular timings with particular load conditions, they become failure when load conditions change from light to heavy loading. Secondly due to fixed gain parameters, linear modeling techniques are used. Most popularly PID (Proportional * ssistant Professor, Department of Electrical Engineering, Quaid-e-wam University of Engineering, Science & Technology, Nawabshah. ** Meritorious Professor, Department of Electical Engineering, Mehran University of Engineering & Technology, Jamshoro. ** ssociate Professor, Department of Electrical Engineering, Mehran University of Engineering & Technology, Jamshoro. Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 529

2 Integral and Derivative) controllers implemented which are linear and time invariant. They need re-tuned (which very difficult process) when time varying conditions occurs. Most importantly, if the PID controller is unable to deal with the complex process, no matter how you tune it, the system will not work. Power system is non linear, complex and subected to different kind of disturbances. [6-]. In order to have high gains, fast acting, automatic settlings, adaptive to load changing, tackling the nonlinearity and complexity, the implementation of neural network based RVR is proposed in order to show the suitability and enhancement in the stability of the system by controlling the terminal voltage with an efficient manner. 2. RTIFICIL NEURL NETWORS NNs and its applications in power system problems is not a new topic of research, because it has been suggested in many research areas with fast growing interest. Literatures indicate that NN is swiftly drawing the attentions and recognition amongst the power system researchers. They are enormously useful in the area of electrical engineering within few years [-2]. They have the capability of modeling the complex relationships which makes NN better to traditional controllers. Traditional controllers always require a comprehensive knowledge and skills about mathematical model of the controlled system. But neural networks controllers do not require such knowledge and skills and they can handle such complex systems very simply and efficiently. Training process teach them to map inputoutput relationships of the system. NNs are universal function approximators, having the capability of approximating any continuous nonlinear functions to arbitrary accuracy []. They have also robustness, parallel architecture and fault tolerant capability [4], furthermore NNs have great flexibility because they have been built on the actual mathematical formulations consisting a great versatility and logical mathematical techniques [5-6]. NN architectures have been divided into feedback NNs, cellular NNs & feedforward NNs the most popular and known as multilayer NNs and further sub divided into two categories as: multilayer perceptron NNs and radial basis function NNs [7-8]. The RBF network possesses a universal approximation and best approximation properties which have no botheration of selecting required number of hidden layer neurons. The learning properties of radial basis networks are quicker than that of multilayer perceptron networks; however, RBF usually take more number of hidden layer neurons as compared to MLP [9-2].. PROPOSED SCHEME ND METHODOLOGY NNs are competent of learning from off-line simulation data and can then be trained to reproduce the behaviour of the system under various loading conditions. This work studies the off-line simulations using a conventional controller like PID to control the system for normal and heavy loading conditions to obtain the input/ output data of the synchronous machine. This data will be utilized for training FFNN (RBF).. Model For FFNN pplications The proposed model for the application is considered as SMIB as shown in Fig.. The simulation model will be developed from the block diagram (Fig. 2) of governor (LFC) and VR excitation system of synchronous generator with their linearized equations and transfer functions [-5]. The state space equations for the complete simulation linearized model of synchronous generator with LFC (governor) and VR excitation controller system (with proper assumptions [-4] and ppendix-b) are given below: Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 5

3 The linearized equations for the synchronous machine are given by []. E FDΔ 4 Δ = + d s + d s nd from definition of [PM nderson]. & = ω The complete state-space description of the system is given by: T eδ = Δ + 2 V tδ = 5 Δ + 6 nd E& q = d q 4 d + From the torque equation we have: d E FD E& q ω& & V& = V& V& R E& FD d 2 6 R R 4 d J 5 R R R F F F E E d ( S E + E ) F E ( S + ) E E E F q ω V V V R E FD + T m V REF ω& = T m 2 D q ω FIG.. SMIB SYSTEM Here the system is described with excitation system. The state variables are: t x = q [ ω V V V E ] R FD The driving functions are V REF and T m assuming that is zero. ll the parameters of the system are described in per unit system and their numerical values are mentioned in [-5,22-2]. Excitation System utomatic Voltage Regulator Con. Field Voltage Sector Steam Tarbine G ΔP v Valve Control Machines Δp ic Δp, ΔQ a c ΔP i Load Frequency Control Frequency Sector FIG. 2. BLOC DIGRM WHICH IS USED FOR LINER MODEL WITH GOVERNOR ND VR SYSTEM Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 5

4 .2 Methodology of RBF Network The potentiality and applicability of radial basis networks for this application is being investigated, because they have distinctive properties of simple network structure, efficient learning way, and best approximation, which make radial basis networks more powerful tool than the other types of neural networks. The radial basis networks consist of three utterly different layers. The input layer or first layer consists of a number of units fastened to the input vector. The units constituted by hidden layer or second layer have an overall response function, mostly a Gaussian function. The function of each class is computed by third layer. Diversity of different algorithms has been proposed in the latest literature for choosing the proper radial basis network centres. We prefer the universal approximator OLS algorithm for this research work [2]. OLS learning algorithm generates radial basis network, which have a hidden layer, smaller than that of radial basis network with arbitrarily chosen centres. Radial basis networks are used to fairly accurate function. They include neurons to the second or hidden layer awaiting it meets the precise MSEGF (Mean Square Error Goal [2-2]. For this application two-layer network has been created. The input or first layer takes radial basis transfer function neurons which calculates its weighted inputs and its net input with net product. The second layer takes linear transfer function neurons and calculates its weighted inputs with dot product and its net inputs with net sum. First and second both layers have biases. t first no neuron is available in radial basis transfer function and FF network architectures with two-layer structures are generated. In first hidden layer 9 neurons with radial basis transfer function as activation function are chosen. One neuron with linear transfer function having.7 spread constant and. error goal are trained for this research work. 4. SIMULTIONS RESULTS For the simulation results, MTLB 7., Simulink Version 7.8 and Neural Network Toolbox 7..2 (R2b) have been utilized. 4. Terminal Voltage response Terminal voltage (Vt) and frequency/speed deviation () responses are shown in Figs. -6 respectively. Time settling for terminal voltage and frequency deviations are fixed at.4 and 2 seconds till the responses passes their oscillations and become stable. Simulations results indicate the responses of RBF VR and PID LFC controllers in order to see the enhancement in stability of power system. Fig. (a-b) shows the Vt response (a) without controller and (b) with conventional PID VR controller. Fig. (c-d) shows Vt responses (c) with RBF VR (d) with RBF VR and PID LFC controllers. Fig. (d), clearly indicates that there is no change in Vt response having PID LFC controller. Because in Fig. (c), RBF VR is showing and excellent improvement which is exactly same in Fig (d). It means there is no impact of LFC controller on VR excitation system of synchronous machine. These all responses have been combined in Fig. (e) and Fig. 4 in large. 4.2 Frequency/Speed Deviation Responses Frequency deviation responses without LFC controller (a), with PID VR (b), PID-LFC and RBF-VR (c) and RBF- LFC and RBF-VR (d) are shown in Fig. 5(a-d) and combined responses are illustrated in Fig. 5(e) respectively. Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 52

5 The in large view of Fig. 5(e) is shown in Fig. 6. These all responses show good improvement in stability but again prove that there is no coupling impact between VR and LFC controllers. Hence both RBF VR and RBF LFC controllers have their excellent own responses separately which is verified from their results because transient, small signal and dynamic stability improves efficiently. 5. CONCLUSIONS RBF VR controller with OLS algorithm, in SMIB with linearized model of SM and excitation system as model using Matlab/Simulink and neural network toolbox has been successfully demonstrated. The proposed technique controls terminal voltage and reactive power thereby improving transient stability of the system and eliminates the drawbacks of conventional VR control system. The suggested method of designing RBF VR is easy to implement with the help Matlab/simulink software. In order to validate the simulated results, the propose VR is compared with conventional VR. These results show that the RBF VR controller has promising satisfactory generalization applicability and suitability as well as accuracy. RBF VR is more suitable where various types of disturbances at different times occur as in case of power system. It also ensures superior responses at different load conditions. Due to fast acting and settling, proposed VR is more suitable for transient and small signal stability of the system. CNOWLEDGEMENTS uthors acknowledge with thanks the higher authorities and Department of Electrical Engineering, Quaid-e-wam University of Engineering, Science & Technology, Nawabshah, Sindh, Pakistan,and Mehran University of Engineering & Technology, Jamshoro, Sindh, Pakistan, for continuous encouragement and time to time facilities when required during this research work, which is an attempt for Ph.D work. FIG. (a-e). TERMINL VOLTGES RESPONSES FIG. 4. COMBINED LL TERMINL VOLTGES (IN LGER) Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 5

6 Frequency/Speed Deviation () WITHOUT CONTROLLERS (B) WITH PID-VR (C) PID-LFC & RBF-VR (D) RBF-LFC & RBF-VR Time (Seconds) (E) COMBINED RESPONSES WITH CONTROLLERS FIG. 5(a-e). FREQUENCY/SPEED RESPONSES FIG. 6. COMBINED LL FREQUENCY RESPONSES (IN LRGE) PPENDIX- List of Notations,B,C System polynomials D Damping coefficient E B or V Infinite bus bar voltage E d Direct axis voltage E fd or E FD Field voltage E q Quadrature axis voltage E t or V t Generator terminal voltage H Inertia constants I F Field current - 6 Constants of the linearized model Regulator amplifier gain D Damping factor E Exciter gain F Stabilizing transformer gain G Generator gain g Governor gain P,, D Proportional, integral and derivative (PID) controller gains R Sensor gain T Turbine gain L e or X e Transmission line inductance or reactance P or P e Generator real or electrical power P g Governor power P L Load real power P m Mechanical power input Q Reference real power Q L Generator reactive power r F Load reactive power Q L Field resistance R Speed regulation of governor R e Transmission line resistance (s) Shows Laplace transformation T e Electrical torque T m Mechanical torque V d,v q Direct and quadrature axis voltages V e Error voltage v F Field voltage V F Exciter voltage V L Load voltage V R Regulator amplifier voltage V refs Reference voltage V S Sensor voltage X d,x q Direct and quadrature axis reactances x d,z q Direct and quadrature transient axis reactances Generator rotor angle Α Regulator amplifier time constant E Exciter time constant F Stabilizing transformer time constant G Generator time constant g Governor time constant R Sensor time constant T Turbine time constant ω ngular speed ω R Rated angular speed ω ref Reference speed Δ Shows change λ d Direct axis flux linkages λ q Quadrature axis flux linkages [2-4] Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 54

7 PPENDIX-B The numerical values of various components as well as other constants required developing simulation model. For turbine and governing systems g =., g =.2, T =., T.5m R=.5 SMIB (Synchronous Generator and Constants of Linear Model) D=., H=5, =.5, T =.2, 4 =.4, 5 =-., 6 =.5, G =.8, G =.5 Values for excitation model E =.,, E =.4, =., =., R =., R =.5 is the change in electrical torque for a small change in rotor angle at constant d axis flux linkage; i.e.the synchronizing torque coefficient T eδ Δ = 2 is the change in electrical torque for small change in the d axis flux linkage at constant rotor angle T eδ 2 = = is the direct axis open circuit time constant of the machine. d is an impedance factor and E t lim Δ Δ = final value of unit step V F response = ()] t 4 is the demagnetizing effect of a change in the rotor angle (at steady state) ()] t =, u() t 4 = E Δ v F t lim Δ Δ = 5 is the change in the terminal voltage Vt for a small change in rotor angle at constant d axis flux linkage, or V tδ 5 q = q Δ = 6 is the change in terminal voltage V t for a small change in the d axis flux linkages at constant rotor angle, or [2-4] V tδ 6 = = q Δ REFERENCES [] Schleif, F.R., Hunkins, H.D., Martin, G.E., and Hattan, E.E., "Excitation Control to Improve Power Line Stability", IEEE Transactions on Power Systems, Volume 87, pp , 968. [2] demello, F.P., and Concordia, C., "Concepts of Synchronous Machine Stability as ffected by Excitation Control," IEEE Transactions on Power Systems, Volume 88, pp. 6-29, 969. [] nderson, P.M., and Fouad,.., "Power System Control and Stability", Iowa State University Press, Iowa, US, 977. [4] undur, P., Power System Stability and Control, 4th Edition, McGraw-Hill Inc., 994 [5] Saddat, H., Power System nalysis, st Edition, McGraw-Hill Inc., 999. [6] Hsu, Y.Y.S., Shyue, W., and Su, C.C., "Low Frequency Oscillations in Longitudinal Power Systems, Experience with Dynamic Stability of Taiwan Power System", IEEE/ PES, Winter Meeting, New York, 986. [7] Moussa, H..M., and Yu, Y.N., "Optimal Power System Stabilization Through Excitation and/or Governor Control", IEEE Transactions on Power Systems, Volume 9, pp , 972. [8] Chan, W.C., and Hsu, Y.Y., "n Optimal Variable Structure Power System Stabilizer for Power System Stabilization", IEEE Transactions PS, Volume 2, pp , 98. [9] Yu, Y.N., and Siggers, C., "Stabilization and Optimal Control Signals for a Power System", IEEE TP-5 Summer Power Meeting and EHV Conference, July, 97. [] NSI/IEEE Std 22 (985), IEEE Recommended Practice for Functional and Performance Characteristics of Control Systems for Steam Turbine-Generator Units, The Institute of Electrical and Electronics Engineers, US, 985. [] Neibur, D., "rtificial Neural Networks for Power Systems", Report by TF 8.6.6, Electra No. 59, pril, 995. Mehran University Research Journal of Engineering & Technology, Volume, No., July, 22 [ISSN ] 55

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