A Particle Swarm approach for the Design of Variable Structure Stabilizer for a Nonlinear Model of SMIB System NAJI A. AL-MUSABI**, ZAKARIYA M. AL-HAMOUZ*, HUSSAIN N. AL-DUWAISH* ** The Petroleum Institute, Electrical Engineering Program, Abu Dhabi, PO. BOX: 2533 UNITED ARAB EMIRATES, ABU DHABI * King Fahd University of Petroleum and Minerals, Electrical Engineering Department, Dhahran 31261, SAUDI ARABIA Abstract: - There is a vivid trend in engineering optimization problems towards the adoption of heuristic optimization algorithms to arrive at optimal solutions. This is mainly due to the simplicity of these algorithms and the great cut down of complicated mathematical manipulations that are required in other optimization theory methods. This paper demonstrates the application of an iterative heuristic optimization algorithm, namely, Particle Swarm Optimization (PSO), in the design of variable structure stabilizers for a nonlinear single machine infinite bus system (SMIB). Two versions of PSO, namely the inertia weight method of updating the velocities (PSO-iw) and constriction factor method (PSO-cf) are applied in the optimal design of the stabilizer. The success of the PSO approach is supported by simulation results that confirm the attainment of the stabilizer control objectives. Key-Words: - Variable Structure control, Power system stabilizer, Particle Swarm Optimization 1 Introduction An important problem in stability of power systems is the excitation control of synchronous machines. The significance of excitation control induced researchers to study and design new control methods for the problem such as Proportional-Integral-Derivative (PID) excitation control, Power System Stabilizers (PSS), Linear Optimal/Sub-Optimal Excitation Control (LOEC), Nonlinear Optimal Excitation Control (NOEC), Adaptive and Intelligent Control [1-5]. In recent years, Power System Stabilizers (PSS) were usually used to enhance the damping of power oscillations caused by several types of small disturbances in a power system. The conventional lead-lag compensation is adopted by most designers due to its simple structure and easy implementation [6]. LQR, Neural Networks, and Fuzzy logic are some of the other design methods proposed for PSS [7-9]. Furthermore, a PSS design based on Variable Structure law is reported in [10-13]. Robustness and good transient response are some of the attractive features of VSC. However, the switching feedback gains of the VSC were not previously chosen by a systematic way. Furthermore, a VSC that operates satisfactory over a wide range of operating point was proposed in [10].ca However, the feedback gains were again chosen by empirical experiments. In [11], a VS PSS was proposed, for linear model of synchronous machine, which operates over a wide range of operating points by using a neural network to adapt the feedback gains of the controller. For each operating point, the feedback gains were chosen by Genetic Algorithms. In this paper, a nonlinear model of synchronous machine has been studied and a VSC is designed for it. In conventional design methods, nonlinear transformation techniques are used before linear system theory is applied to the system. The new design method utilizes iterative heuristic optimization techniques (PSO) and provides a simpler and more systematic design. 2 Nonlinear SMIB Model The nonlinear model of a single machine infinite bus system is shown in Figure 1 [13]. The machine has an AC/DC converter, a silicon-controlled rectifier, for added control purposes. The dynamics of the system are described by the following equations: ω δ = . (1) [ ] ω ω ω . D KP P P H dc ac m B . − − − = 2 (2) d d c dc I ) I R ) (cos( P − = β (3) ) I R ) (cos( L / I d c . d − = β 1 (4) v P P m m . + − = α (5) Proc. of the 5th WSEAS/IASME Int. Conf. on Electric Power Systems, High Voltages, Electric Machines, Tenerife, Spain, December 16-18, 2005 (pp262-267)