Multi-machine optimal power system stabilizers design based on system stability and nonlinearity indices using Hyper-Spherical Search method

Design of power system stabilizer (PSS) withstanding critical situations is a challenging task. In this paper, an effective method for the design of a coordinated multiple PSS in power systems are offered and weaknesses of the existing methods are disclosed. The setup includes the nonlinear model of the system, a specific multi-objective function and a newly developed meta-heuristic Hyper-Spherical Search (HSS) optimization algorithm. The objective function includes both eigenvalue stability index (SI) and nonlinearity index (NI). The employed new NI is the second order modal interaction of the lightly damped electromechanical modes. The performance of the proposed Stability-Nonlinearity index (SN) based PSS design by HSS (SNPSS-HSS) is compared with SNPSS-GA, SI based PSS (SPSS) and the conventional design method (CPSS) under various operating conditions and disturbances. The investigations are conducted over both a single lead PSS and PSS2B. The performance is detailed using time domain simulations, SI and NI analysis. A four-machine two-area system and the IEEE 39-bus system are utilized for test purpose. The results of extensive simulations indicate the superiority of SNPSS-HSS design with respect to the others. The obtained relative stability is higher and the nonlinearity index is lower than the product of the other designs. Besides, as it is expected, using a high degree of freedom PSS2B improves the performance of the aforementioned algorithms.