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Optimum location of power system stabilizers based on probabilistic analysis

This paper introduces the probabilistic approach for the optimum location of power system stabilizers (PSSs). When the variation of nodal injected powers representing various load levels is described by statistical attributes and considered in eigenvalue analysis. The probabilistic distribution of an eigenvalue is expressed by its expectation and variance under the assumption of normal distribution. The utilization of PSSs improves both of the expectations and the variances for the critical eigenvalues. This paper therefore calculated, not only the sensitivities for the expectations and variances of eigenvalues, but also the probabilistic distributions of these sensitivity coefficients which is accomplished by means of the second order sensitivity calculation of eigenvalues with respect to nodal injections and PSS gains. Probabilistic sensitivity indexes corresponding to conventional participation factors and residues are used for selecting the best PSS sites. The proposed probabilistic analysis approach is validated on a nine-bus testing system.