Automatic Generation Control Using LQR based PI Controller for Multi Area Interconnected Power System

Transcription

1 Advance in Electronic and Electric Engineering. ISSN , Volume 4, Number 2 (2014), pp Research India Publications Automatic Generation Control Using LQR based PI Controller for Multi Area Interconnected Power System Naresh Kumari and A.N. Jha Department of Electrical, Electronics and Communication Engineering, ITM University, Gurgaon, Haryana, INDIA. 1 nareshkumari@itmindia.edu, 2 anjha@itmindia.edu Abstract The continuous time Linear Quadratic Regulator (LQR) theory has been implemented in the present work for the design of optimal Proportional Integral(PI) controller for the frequency response enhancement of multi area interconnected power system. The PI controller gains as proportional gain (Kp) and integral gain (Ki) are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function known as integral of time multiplied squared error (ITSE).The two area network comprising of thermal power systems is considered without the reheat and generation rate constraint (GRC). The automatic generation control has been developed for two area thermal network using LQR based PI controller. In the present work firstly the block diagram of the system is designed. Then states of the system are identified which help to develop the state apace model of the system. The proposed model has nine states of the system for which the state feedback is given to LQR for keeping the Performance Index (PI) to minimum. The system state equation and output equation have been formulated with state matrix A, Input matrix B and Output matrix C. These matrices are developed on the basis of system parameters. The weighing matrices Q and R of LQ regulator are optimally designed to keep the frequency deviation with load changes within the desired limits. The two control signals are thus developed by LQ regulator which are fed one to each area for frequency response enhancement..the proposed load frequency control of two area electric power system has been developed by using MATLAB/SIMULINK. The thermal systems of two area network are

2 150 Naresh Kumari & A.N. Jha 2000 MW each.the active power control of the system with LQ regulator based PI controller help to achieve the frequency at the scheduled value with variation in the load. Keywords: Linear Quadratic Regulator; Automatic generation control; state space model; PI controller; Integral of time multiplied squared error (ITSE). 1. Introduction The linear quadratic regulator can realize closed loop optimal control through the state feedback so it has become one of the important design methods in the field of control engineering [J Longguo et al.]. This control method applies LQR theory to determine appropriate feedback gain along with the minimum variance method to design the automatic generation control of two area thermal power system. With the LQR optimal control the system can achieve better performance with reduced cost, can be easily realized using simple method, and also it can greatly reduce the excessive mathematical workload with the powerful matrix s handling ability of MATLAB/SIMULINK [ B Wang et al.]. The high quality and reliable electric power can be generated by keeping the balance between power demand and power generation of any system. The system frequency can be maintained at the desired value by regulating the various generator units with continuous adjustment of active power [O.I. Elgerd]-[R N Patel et al.].the variable parameters of the system can be changed under the varying load conditions for the frequency response enhancement. The LQ regulator has been used by the control designers for the tuning of PI controllers [J B He et al.].the LQR help to keep the state deviations to minimum level along with keeping the Performance Index to minimum. The mathematical model is established for two area interconnected thermal systems. The reheat and generation rate constraint have not been considered in the present work to keep the model simple and to have the less number of states for the feedback to LQR. The automatic generation control require the appropriate modeling of interconnected power system to enable the frequency regulation of the system. Firstly the block diagram of the two area thermal power system is designed then the state space model is developed. The tuning strategy of PI controllers with the optimal control technique of LQR allows the designer to achieve both optimal set-point tracking and optimal cost of control of the system [S Das et al.]. 2. Mathematical Modelling of Two Area Power System The system considered in this work comprises of two thermal power plants which are interconnected through tie line for sharing the power to maintain the generation load balance. The areas taken for investigation are of 2000 MW each. The important parameters according to the rating of the system are given in Table-1. The transfer function model using MATLAB/ SIMULINK has been designed. The generation rate constraint and reheat are not taken into account for the simplicity of the system.

3 Automatic Generation Control Using LQR based PI Controller for Multi Area 151 The block diagram for the automatic generation control of two area power system is developed and the nine variable parameters which are the states of the system are indentified. The state space model of two area thermal thermal (non-reheat) power system of 2000 MW for each plant, with full state feedback (9 state feedback) has been developed as per the scheme shown in Fig. 1[C B Bangal] and simulated in MATLAB /SIMULINK environment. Total nine State Variables for the system of as per the Fig 1. are as below: x 1 = f 1, x 2 = Pt 1, x 3 = Pg 1 x 4= f 2, x 5 = Pt2, x 6= Pg 2 x7 = Pt tie(1,2), x8 = ʃ (ACE 1) dt x9 =ʃ (ACE 2) dt Control inputs: u1 and u2 State equations for the different blocks of the system shown in Fig 1 have been developed. Fig. 1: Transfer function model of two area interconnected reheat thermal system. The state vector and control vector for the above system are given as: State Vector (X) = [ X1 X2 X3 X4 X5 X6 X7 X8 X9 ] The system state and output equations of the system are given by: The The state matrix A,Input matrix B and Output matrix C for the system in general form can be given as:

4 152 Naresh Kumari & A.N. Jha The optimal control system for the two area power system can be given as below: u(t) = Kx(t) where K= R B T P P can be calculated by the solution of the Continuous Algebraic Riccati Equation as below: A T P PA P BR -1 B T P Q 0 The Performance Index (PI) for the system can be given as PI = 1/2 ( x Q x + u R u) dt Q and R are the weighting matrices [M Saif] and they are designed by the proper understanding of the system.these are generally diagonal matrices as shown below: 3. Result and Discussion The state matrix A, Input matrix B and Output matrix C for the system are determined as per the variable parameters given in Table I.The state space model is developed for the system in MATLAB as sys = ss(a,b,c,d); The weighting matrices Q and R are chosen with trial and error so that the Performance Index of the system is minimum along with the minimum state deviations from their state trajectories. Then with those values of Q and R, the feedback gain matrix K is determined by equation [K,S,e] = lqr(sys,q,r,n) The two control vectors are generated which are given to the two thermal systems for the frequency response enhancement. The 0.5% load variation on one area at a time has been used for the study of load frequency control of two area power system in MATLAB/SIMULINK.The load variation in one area causes the frequency deviation in both the areas as shown in Fig. 2 to Fig. 5.

5 Automatic Generation Control Using LQR based PI Controller for Multi Area 153 Fig. 2: ΔF1 VS T for Area 1 When 0.5% Load Change in Area1. Fig. 3: ΔF2 VS T for Area 2 When 0.5% Load Change in Area1. Fig. 4: ΔF2 VS T for Area 2 When 0.5% Load Change IN Area 2. Fig. 5: ΔF1 VS T for AREA 1 When 0.5% Load Change in area Conclusion In this paper, the LQ regulator is used to control the various states of the two area power system and enhance the system performance under the changes in the power system parameters and load conditions. The PI controller is also tuned with LQR method. The power generation and load demand balance is maintained so that frequency change is within the desirable limits with the variation of load. This optimal LQR PI controller is more robust to changes occurring in the system. Table I: Parameters of two area power system investigated. f=60 Hz Kr =0.5 Tg =0.08 s Tt =0.3 Ptie max=200mw Kp= 120 Hz/puMW Tr= 10s,T12=0.544 a12=-0.5 Tp=20 s

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