Study of Sampled Data Analysis of Dynamic Responses of an Interconnected Hydro Thermal System

Transcription

1 IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 ISSN : (Online) ISSN : (Print) Study of Sampled Data Analysis of Dynamic Responses of an Interconnected Hydro Thermal System 1 Dipayan Guha, 2 T. K. Sengupta, 3 A. Das 1 Dept. of Electrical Engineering, Asansol Engineering College, West Bengal, India 2 Supreme Knowledge Foundation Group of Institution, Mankundu, Hooghly, India 3 Dept. of Electrical Engineering, Jadavpur University, Kolkata, India Abstract This paper focused on study of dynamic responses of an interconnected power system. Two area interconnected system is considered with one thermal and another hydel unit. This work focused on modeling of the same in sampled data fashion. The concerned system was modeled in discrete state-space form. The studies of dynamic responses are carried out in MATLAB SIMULINK environment with 10% load changes in any control area. Keywords Automatic Generation Control, Modeling of Interconnected system, MATLAB SIMULINK I. Introduction Maximum pre-occupation and concern of power engineers was and still to control the MW power since it is the basic governing elements of revenue and requirement to industrial load. Earlier days power system networks, transmission systems, utilities were not so complicated, and therefore there was no obvious great concern on controlling these systems. Due to advent of new technology modern power system networks are more and more extensive, uses long transmission system, more load demands, frequent load fluctuations etc. Therefore, more attention is paid on control strategy which not only controls the disturbances occur in the system but also maintains other system constraints such as reliability, security and stability. In this aspect Automatic Generation Control (AGC) plays an important role. Modern power system networks are divided into number of grids and they are interconnected through transmission line, called as tie-line. A large interconnected power system comprises a suitable mix of hydro, thermal & nuclear power components. Since the nuclear unit is the high efficient unit, and it always operated in its base load close to maximum rating, hence it has no participation on AGC. Thus AGC falls on either thermal or hydro system. [4] Elgerds has presented AGC theory, commonly used in industry, where measurement of frequency and tie line power deviation is measured at continuous environment. But in actual practice, these measurements are done at a fixed interval of time, i.e., sampled data fashion. Even, it is well known that discrete system are more reliable, compact in size, less prior to environmental noise etc. compare to continuous system [2]. Indulkar has presented discrete theory of an interconnected system in his paper but assumption was made that the governor & turbine has unity gain transfer function. This paper focused on study of sampled data analysis of hydro thermal system in sampled data fashion taking the actual transfer function of governor & turbine system. Conventional PI controller is used in this paper, which is working as discrete form by placing a sample & hold circuit between controller and system. The aim of the proposed controller is to restore the frequency to its nominal value in the shortest possible time during load demand changes. The system is studied with three sampling time constant as T = 0.01 sec, 0.02 sec, 1 sec. MATLAB/SIMULINK simulation model was built to study the dynamic behavior of synchronous machine and the proposed controller taking 10% (sever case) load changes in any control area. II. System Investigated This paper modeled MW frequency control system assuming small signal assumption. MW frequency control system and MVAR frequency control system is isolated and liner perturbation system is modeled. This paper also considers two area interconnected power system with one thermal & one hydel unit. For simplicity we discarded different non linear elements & other parametric uncertainties such as dead zone of turbines, GRC of governor etc. Literature survey shows that in practice measurement of frequency or tie line power errors are done at a fixed interval of time, i.e. sampled data fashion. Based on the above knowledge and assumption, this paper modeled the two area hydro- thermal system in discrete data form. Fig. 1 shows the proposed model of an interconnected hydro thermal 170 International Journal of Electronics & Communication Technology

2 ISSN : (Online) ISSN : (Print) IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 Fig. 1: system where controller signal is discretized by placing a sample and hold circuit between controller & plant. Nominal s values of all parameters are defined in appendix 1. III. Modeling of Interconnected System (1) Equation (1) gives a differential equation which defines the dynamic behavior of continuous time system. Where, A, B and G are called as system matrix, input matrix and disturbance matrix, respectively, which depend on different system parameters and operating conditions of the system. Whereas, x, u and w are known as state variables, controlled input & disturbance input, respectively, these are defined as, x = [ f 1 f 2 P c1 P c2 P t1 P t2 X G1 X G2 P r P hw P tie ] u = [ u 1 u 2 ] T & w = [ P D1 P D2 ] T interval of time, therefore, the discrete dynamics of same system is defined by following difference equation, (2) Where, A d, B d and G d matrices are defined as, Ad = [I + A*T], where, I and T are identity matrix & sampling time period. B d = B*T and G d = G*T Matrices with nominal values of all parameters are defined as, Detail calculation of state space model of concerned two area hydro thermal system given in appendix 2. Since, in actual practice, frequency and tie line power are measured at discrete International Journal of Electronics & Communication Technology 171

3 IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 ISSN : (Online) ISSN : (Print) IV. Simulink Results Fig. 2: Frequency Error in Thermal Area of a Hydro Thermal System in CT Domain 172 International Journal of Electronics & Communication Technology

4 ISSN : (Online) ISSN : (Print) IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 Fig. 3: Frequency Error in Hydro Area of a Hydro-Thermal System in CT Domain Fig. 6: Frequency Deviation of Thermal Thermal System in Sampled Data Form Fig. 4: Tie-Line Power Deviation of a Hydro Thermal System in CT Domain Fig. 7: Tie Line Power Error in Two Area Hydro Thermal System in sampled data form Fig. 5: Frequency Error in Hydro Thermal Area in Sample Data form Fig. 8: Tie-Line Power Deviation of Two Area System Thermal Thermal System in Sampled Data Form International Journal of Electronics & Communication Technology 173

5 IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 ISSN : (Online) ISSN : (Print) [3] Prof. Prabhat Kumar, Ibraheem, Dynamic performance evaluation of 2-area interconnected power system a comparative study, IEEE-trans, August 14, [4] K.S.S Ramakrishnan, Pawan Sharma, T.S.Bhatti, Automatic generation control of interconnected power system with diverse source of power generation, IJEST, Vol. 2, No. 5, 2010, pp [5] Dipayan Guha, Prof.(Dr.) T.K.sengupta, Dynamic response analysis of automatic generation control in a 2 area (Reheat and Non-reheat) interconnected power system and a scheme for improvement of response for the same, IJMER, Vol. 3, Issue 1, Jan Feb [6] Elegerd, O.l., Eletric energy system theory: An introduction, second edition, Tata McGraw Hill. [7] Grainger, J, William,J, Stevenson, Jr, Power system analysis, edition 2003, Tata McGraw Hill. [8] Kothari, D.P, Nagrath, I.J., Power system engineering, second edition, Tata McGraw Hill. Fig. 9: Frequency Error in Two Area Hydro Thermal System in Sampled Data Form V. Observation Following points are observed from the SIMULINK results, Peak of undershoots of hydel unit is less compare to thermal unit, see fig. (2) & (3). Frequency error in hydel unit gets damped faster than thermal area, see fig. (3). System gets unstable with increase of sampling period, see fig (9). Tie-line power error gets die out within 30 to 35 sec. Appendix 1 Nominal parameters of hydro-thermal system investigated f = 50 Hz Tsg = 0.08 sec Tt = 0.3 sec Tr = 10 sec Kr = 0.5 Kps= 120 Tps= 20 sec Tw = 1.0 sec TR = 5 sec T1 = 48.7 sec T2 = sec R1 = R2 = 2.4 Hz/p.u Mw B1 = B2 = T12 = a12 = 1 Ki = 0.55 sec Appendix 2 VI. Conclusion In practice large power system network comprises of different power generating sources such as hydro, thermal, gas and nuclear. The frequency deviation in hydro-thermal case is within sec (fig.5) and tie line power is within sec (fig.7) and also the values are sec (fig.6) and sec (fig.8) with the same type of controller and sampling time in case of thermal thermal unit [5]. In practical situation, where hydro thermal coordination is required, the controller performance is a major criterion. Comparing fig. (5) and (6), and fig.(7) and (8), the analysis shows the performance of the controller for controlling frequency deviation and also tie-line power is much better in case of hydrothermal generation. From the study it is concluded that dynamic performances of hydro thermal situation is better. (3) VII. Recommendation This modeling and discritized control is recommended for hydrothermal coordinated generation for better performance. References [1] Prof J Nanda, Dr. M L Kothari, Sample data AGC of Hydro- Thermal system considering GRC, IEEE-trans., September 25, 1989 [2] Prof. C S Indulkar, Analysis of MW frequency control problem using sampled data theory, IEEE trans., January 1, (4) 174 International Journal of Electronics & Communication Technology

6 ISSN : (Online) ISSN : (Print) IJECT Vo l. 4, Is s u e Sp l - 1, Ja n - Ma r c h 2013 (5) (6) (9) (7) (10) (11) (12) (13) (8) International Journal of Electronics & Communication Technology 175