Performance Analysis of PSO Optimized Fuzzy PI/PID Controller for a Interconnected Power System
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1 Performance Analysis of PSO Optimized Fuzzy PI/PID Controller for a Interconnected Power System 1 Pogiri Ramu, Anusha M 2, Gayatri B 3 and *Halini Samalla 4 Department of Electrical & Electronics Engineering 1,2,3 Sri Sivani Institute of Technology, Srikakulam, Andhra Pradesh Sri Sivani College of Engineering, Srikakulam, Andhra Pradesh Ids: 1 sachin.ramu143@gmail.com, 2 anusha@gmail.com, 3 gayatri25@gmail.com, 4 halini.samalla@gmail.com Abstract In this paper, design and performance analysis of Particle Swarm Optimization (PSO) algorithm based hybrid fuzzy PI/PID for a two area interconnected power system is presented. A two area thermal system with governor dead-band nonlinearity is considered for the design and analysis purpose. The design problem is formulated as an optimization problem and PSO is employed to search for optimal controller parameters. From the simulation results it reveals PSO optimized Fuzzy PID controller is performs better than fuzzy PI controller based system. Finally, robustness of proposed fuzzy PID controller is investigated by varying step load perturbation without retuning the controller paramters. Keywords Particle Swarm Optimization (PSO); Fuzzy PI/PID controller; Governor Dead Band (GDB); Robustness. I Introduction The intelligent systems has necessitated for increase in power demand growth in size and complexity of modern electric power systems. A modern power system network consists of a number of utilities interconnected together and power is exchanged between utilities over tie-line by which they are interconnected. For the stable operation of power systems, it should be maintained both constant frequency and constant tie-line power exchange. In each area, a Load Frequency Controller (LFC) monitors the system frequency and tie-line flows, computes the net change in the generation required (generally referred to as Area Control Error-ACE) and changes the set position of the generators within the area so as to keep the time average of the ACE at a low value. Therefore ACE, which is defined as a linear combination of power net-interchange and frequency deviations, is generally taken as the controlled output of LFC. As the ACE is driven to zero by the LFC, both frequency and tie-line power errors will be forced to zeros. Literature survey shows that very little attention has been given to the study of AGC of multi-area systems [1-2]. In these studies of multi-area systems, the focus has been to optimize the supplementary controller gain and comparison study between Zero order Hold Integral controller technique and fuzzy logic based techniques [3-4]. AGC function is essentially a supervisory control function which attempts to match the generation trend within an area, to 469
2 the trend of the randomly changing load of the area, so as to keep the system frequency and tie line power flows close to the scheduled values. AGC acts at a much slower time scale as compared with the dynamics of the individual unit control systems whose set points are adjusted by the AGC. An AGC system monitors the system frequency and the tie line flows, computes the net change in the area generation required (generally referred to as area control error, ACE) and changes the set points of the generators within the area so as to keep the time average of the ACE at a low value [5-6]. The control philosophies adopted By different utilities appear to have significant differences. Implementation details are generally proprietary and there is very little open discussion regarding the relative merits of the different schemes in use. It is also widely believed that continued enhancements of the present schemes are possible via new control approaches [7-8]. In the recent past, the application of Zero Hold Integral control and Fuzzy Control has also been Zero order controller paper, we show how the AGC problem can be viewed as a stochastic multistage decision making problem or a Markov chain control problem. Here, we present two different controllers. The first controller monitors the composite signal, ACE, to achieve the load enervation balance-an objective pursued by all AGC algorithms at present. Our second controller does not compute or use the ACE signal, but seeks to achieve satisfactory performance by monitoring only the deviations in the system frequency and the tie line flows [1]. II System Investigated The AGC provides the control only during normal changes in load which are small and slow. So the nonlinear equations which describe the dynamic behaviour of the system can be linearized around an operating point during these small load changes and a linear model can be used for the analysis thus making the analysis simpler. The system under investigation consists of two area interconnected power systems of reheat thermal plant with non-linear governor dead band as shown in Fig. 1. The system is widely used in literature is for the design and analysis of automatic load frequency control of interconnected areas. In Fig. 1, B 1 and B 2 are the frequency bias parameters; ACE ACE 1and 2 are area control errors; u 1 and u 2 are the control outputs from the controller; R 1 and R 2 are the governor speed regulation parameters in pu Hz; T G1 and T G2 are the speed governor time constants in sec; P G1and P G2 are the change in governor valve positions (pu); T T1and 2 T T are the turbine time constant in sec; K R 1 and K R 2 are reheat turbine constants; T R 1and T R 2 are reheat turbine time constants; P T 1 and P T 2 are the change in turbine output powers; P D 1 and P D 2 are the load demand changes; PTie is the incremental change in tie line power (p.u); K PS 1 and KPS2 are the power system gains; TPS1and T PS2 are the power system time constant in sec; T12 synchronizing coefficient and F1 and F2 given in appendix. is the are the system frequency deviations in Hz,. The relevant parameters are 47
3 B 1 1 R 1 a12 a12 B 2 AEC 1 AEC 2 u 1 Controller Output.2.8 s 1 st G 1 Governor with deadband P G1 P D1 1 P T1 K PS1 F 1 1 st T 1 1 stps1 Turbine P Power System 12 P Tie 2 T 12 s P 21.2 u 2.8 s P G2 1 P T 2 K PS 2 F 2 1 st T 2 1 st Controller PS 2 1 st G 1 Output Turbine Power System Governor with 1 P deadband D2 R 2 III Controller Structure In this present study we have designed PI/PID controllers with Fuzzy Knowledge Based Controller. The basic structure of the conventional PI and PID controllers are represented as follows u KP e K edt (1) I de u KPe KI edt KD (2) dt where K P, K I and K D are the proportional, integral and derivative gains respectively and e is the error signal (i.e. e=process set point process output variable). For the load frequency control problem The error inputs to the fuzzy PI/PID controllers are the respective area control errors (ACE) given by: e 1 ( t) ACE1 B1 F1 P Tie (3) e 2 ( t) ACE2 B2 F2 a12 P Tie (4) The inputs and outputs are transformed to seven linguistic variables NB, NM, NS, Z, PS, PM and PB which stand for Negative Big, Negative Medium, Negative small, Zero, Positive Small, Positive Medium and Positive Big respectively. Symmetrical triangular (expect of the two outermost ones which have a trapezoidal shape) membership functions [1] is considered here for all the three variables of ACE, ΔACE and Δu. The membership function of ACE over the operating range of minimum and maximum value of ACE is shown in Figure 2. The membership function 471
4 would perform a mapping from the crisp value to a fuzzified value. As shown in Figure 2, one particular crisp input ACE is converted to fuzzified value i.e..8.2 NS NM where.8 and.2 are membership grades corresponding to the linguistic variable NS and NM in FNN system. The membership grades are zero for all other linguistic values except NS and NM. The crisp value input to the system in this way will be converted to a fuzzified value consisting of several membership grades corresponding to each linguistic variable. In the same manner, the other input, ACE2, and the output, Δu is fuzzified. As each of the three fuzzy variables are quantized to seven fuzzy sets, so total 7 7 or 49 rules are required to generate an fuzzy output relating two input fuzzy sets as shown in Table 1. Fuzzy rules play a major role in FLCs and have been investigated extensively. However, fuzzy rules usually can be generated using knowledge and operation experience with the system or by understanding the system dynamics. Table 1 shows the 49 rules that are generated through the behaviour of the system response after a load change. error NB NM NS Z PS PM PB NB PB PB PM PM PS PS Z NM PB PM PS PS PS Z Z NS PM PS PS PS Z Z Z Z Z Z Z Z Z Z Z PS Z Z Z NS Z NS NS PM Z Z NS NS NM NM NB PB Z NS NS NM NM NB NB Table 1: Fuzzy rules IV Result Analysis A typical example of two area power system is considered for the simulation and the values of different parameters system are given in appendix. Two different controllers are considered. A step A small step load perturbation (SLP) of 1% is applied to area-1 for studying the transient response of the fuzzy PI/PID controlled AGC. The optimized PSO [9] based fuzzy PI/PID controller gains are given below: for FUZZY-PI: KP1=1.353; KP2=1.95; KI1=1.7978; KI2=.199; K1=.1819; K2=.685; K3=.6483;K4=.3321 for FUZZY-PID KP1=.394;KP2=.7155;KI1=.5719;KI2=.1793;KD1=.2488;KD2=.948;K1=1.463;K2=.6865; K3=1.1659;K4=.6829 where, KP1, KP2, KI1, KI2, KD1, KD2 are gains of PID controller and K1, K2, K3, K4 are input scaling factors of fuzzy controller. The Dynamic responses of fuzzy PI and fuzzy PID system are shown in Figs From, simulation results it shows that PSO optimized fuzzy PID system performs better than fuzzy PI system in terms of overshoot and settling times
5 In Figs. 2-4, blue colored line indicates for fuzzy PI and red colored line indicates for fuzzy PID controller. Finally, the robustness of Fuzzy PID controller are investigated by varying step load disturbance and the corresponding the change in frequency of area-1 is given in Fig.5. From Fig.5, it can be concluded that the proposed fuzzy PID controller is robust..1.5 Change in freq Fig. 2 Frequency deviation of area 1 for 1% disturbance in area 1 5 x 1-3 Change in freq Fig. 3 Frequency deviation of area 2 for 1% disturbance in area
6 .5 x Change in tie line power Fig. 4 Tie-line power deviation for 1% disturbance in area 1 Change in freq % SLP 5% SLP 1% SLP Fig. 5 Frequency deviation in area 1for different loading conditions V Conclusion In this paper design analysis of Fuzzy PI/PID controller is presented. In next step, a two area non thermal power system with GRC is considered. Bacterial Forging Optimization Algorithm (BFOA) is employed here to obtain the gain values of FOID controller. The performance of system comprising of FOPID controller is better. Finally, the robustness of proposed controller is observed. Appendix Frequency F=6Hz; B 1 = B 2 =.425 p.u. MW/Hz; R 1 = R 2 = 2.4 Hz/p.u.; T G1 = T G2 =.2 s; T T1= T T 2 =.3 s; K PS 1 = K PS2 =12; T PS1 = T PS2 = 2 s; T 12=.77 pu; a 12= -1, K r1 = K r2 =.5, T r1 = T r2 =
7 References [1] Elgerd, O.I. Electric energy systems theory. an introduction. 2 nd ed., Tata McGraw-Hill, 27. [2] Kundur, P. Power system stability and control. McGraw-Hill, New York [3] Mudi KR, Pal RN. A self-tuning fuzzy PI controller, Fuzzy sets and systems, 2; 115(2): [4] Yesil E, Guzelkaya M, Eksin I. Self tuning fuzzy PID type load and frequency controller, Energy Conversion and Management 24; 45(3): [5] Lee KA, Yee H, Teo CY. Self-tuning algorithm for automatic generation control in an interconnected power system. Elect Power Syst Res 2(2) (1991) [6] Talaq J, Al-Basri F. Adaptive fuzzy gain scheduling for load frequency control. IEEE Trans Power System 14(1) (1999) [7] H. Gozde, M. C. Taplamacioglu, Automatic generation control application with craziness based particle swarm optimization in a thermal power system, Electrical Power and Energy Systems 33 (211) [8] Jayant Kumar, Kah-Hoe Ng and Gerald Sheble: AGC simulator for price based operation, part-i, IEEE Trans. on Power Systems, 12 (2) (1997) [9] Particle Swarm Optimization. Kennedy, J. and Eberhart, R. Perth, Australia: IEEE International Conference on Neural Networks, [1] Ramesh, S., and Krishnan, A. Fuzzy rule based load frequency control in a parallel AC-DC interconnected power systems through HVDC Link, International Journal of Computer Applications, (3) (21);
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