Robust PSS design based on probabilistic approach

Abstract

Most existing techniques for power system dynamic stability studies are based on deterministic system conditions. To consider the effect of load variations, the probabilistic approach is applied to eigenvalue analysis and robust power system stabilizer (PSS) design in this thesis. An analytical representation of eigenvalue sensitivities is prerequisite for the in-depth analysis of the statistic nature of eigenvalues. First and second order eigenvalue sensitivities with respect to arbitrary parameters, such as nodal injections, transformer taps and line admittances, are systematically derived. Based on a highly versatile multimachine modeling technique, an algorithm for probabilistic eigenvalue analysis is developed under normal distribution. This algorithm is then much improved by considering the correction of covariances on expectations, retaining the second order terms and employing high order moments and cumulants. Random variables are thereby allowed to have any distributions. In robust PSS design, two types of probabilistic sensitivity indices (PSIs) are developed. The first type of PSI is used for the selection of best PSS locations, while another is more suitable for PSS parameter adjustment. With some initial values of PSS gains and time constants determined by PSI analysis, a PSI matrix is formed to represent the sensitivity relationship between concerned eigenvalues and all adjustable PSS parameters. PSS parameters are directly tuned using the PSI matrix to improve the probabilistic distributions of concerned eigenvalues. For more complex case with multiple PSSs, a nonlinear objective function is constructed from eigenvalue expectations and variances to take account the distribution nature of eigenvalues. With all damping constants and damping ratios considered,, this optimization problem is solved by the quasi-Newton method of the nonlinear programming technique. The convergence characteristic of the proposed approach is discussed on a test system with five PSSs.