Eigenvalue Assignments in Multimachine Power Systems using Multi-Objective PSO Algorithm

Eigenvalue Assignments in Multimachine Power Systems using Multi-Objective PSO Algorithm

Yosra Welhazi (CEM Laboratory, National Engineering School of Sfax, University of Sfax, Sfax, Tunisia), Tawfik Guesmi (CEM Laboratory, National Engineering School of Sfax, University of Sfax, Sfax, Tunisia) and Hsan Hadj Abdallah (CEM Laboratory, National Engineering School of Sfax, University of Sfax, Sfax, Tunisia)
Copyright: © 2015 |Pages: 16
DOI: 10.4018/IJEOE.2015070103
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Applying multi-objective particle swarm optimization (MOPSO) algorithm to multi-objective design of multimachine power system stabilizers (PSSs) is presented in this paper. The proposed approach is based on MOPSO algorithm to search for optimal parameter settings of PSS for a wide range of operating conditions. Moreover, a fuzzy set theory is developed to extract the best compromise solution. The stabilizers are selected using MOPSO to shift the lightly damped and undamped electromechanical modes to a prescribed zone in the s-plane. The problem of tuning the stabilizer parameters is converted to an optimization problem with eigenvalue-based multi-objective function. The performance of the proposed approach is investigated for a three-machine nine-bus system under different operating conditions. The effectiveness of the proposed approach in damping the electromechanical modes and enhancing greatly the dynamic stability is confirmed through eigenvalue analysis, nonlinear simulation results and some performance indices over a wide range of loading conditions.
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1. Introduction

Power system stability has been considered as an exciting problem for secure system operation for many years. In recent decades, with the rapid growth of electric power system, some of areas of large power systems are interconnected by weak tie lines. Consequently, low frequency oscillations have been observed. If these oscillations are not damped and restrained, they may sustain, grow and limit the capacity to transmit power which leads to system separation (Sauer & Pai, 1998; Ali & Abd-Elazim, 2012).

To improve the dynamic stability of power systems, power system stabilizers (PSSs) are installed in generators. PSSs are widely used by power system utilities to generate a supplementary excitation control signal in phase with the rotor speed deviation (Shayeghi et al., 2009; Welhazi et al., 2014). PSSs are used to improve the damping of the power system oscillations and the general stability of the power generation including transmission system. By means of power system oscillations, two modes of oscillations are to be deemed; “Local plant oscillations” with typical range of oscillations from 0.8 to 2.0 Hz and “Inter-area oscillations” with typical range of oscillations from 0.1 to 0.7 Hz (Elmenfy, 2013). External disturbances such as variation of the mechanical power and a sudden increase in the load limit the effectiveness of the PSSs. Generally, optimal performance of such stabilizer is achieved at its nominal operating condition. Accordingly, the performance of PSS should be tested under different configurations of power system in order to assess the robustness properties.

Several techniques have been reported in the literature in order to solve the PSS design problem. Recently, several approaches based on modern control theory have been applied to search for optimal parameters of PSSs. These include variable structure control (Singh et al., 2012), optimal control (Ganjefar & Judi, 2010), adaptive control (Zhang & Lin Luo, 2009) and intelligent control (Abido & Abdel-Magid, 1999). Unfortunately, modern control techniques present some adaptive or variable structure techniques which may cause the instability of the power system. For this reason, the conventional lead-lag PSS (CPSS) is the widely used structure by power system utilities.

Different techniques of sequential design of PSSs are presented (Mahabuba & Khan, 2012; Jabr et al., 2010) in order to damp out one of the electromechanical modes at a time. Despite the potential of this approach, it may not finally lead to the optimal choice of PSS parameters. On the other hand, the stabilizers designed to damp one mode can produce adverse effects in other modes. The problem of tuning PSSs can be also solved by applying mathematical programming (Zanetta & da Cruz, 2005). The problem is formulated as both a quadratic and a linear programming problem. However, the number of constraints becomes unduly large. A gradient procedure (Yuan & Fang, 2009) can be applied to search for optimal parameters of PSSs. However, this technique presents several problems such as the heavy computational burden and slow convergence since the optimization process requires the computation of eigenvectors and sensitivity factors at each iteration. In addition, the search process can be trapped in local minima and the solution obtained will not be optimal.

Recently, genetic algorithm (GA) has been successfully applied to PSS design problem (Abedinia et al., 2010; Talaat et al., 2010; Ahmad & Abdelqader, 2011). Despite the fact that several successful applications have been reported, some inefficiencies in GA performance have been identified in applications with highly epistatic objective functions, i.e., where the parameters being optimized are highly correlated. Moreover, the processes of encoding and decoding of each solution require a lot of computing time. In addition, the application of GA presents a major problem which consists in the premature convergence. At this stage, we are interested in applying hill-climbing heuristics in order to overcome the different problems of the previous methods and to search for improvement (Lee & El-Sharkawi, 2007).

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