Improved probabilistic method for power system dynamic stability studies

Abstract

An improved probabilistic method using moments and cumulants of random variables for power system dynamic stability studies is presented. The uncertainties considered are system multi-operating conditions derived from operating curves of load powers and generations. The generator state and nodal voltages are solved from a stochastic load flow calculation. By means of the first and second order eigenvalue sensitivity representation, moments and cumulants of eigenvalues are determined from the statistical characteristics of nodal voltages and nodal injections. Probabilistic densities and conditional probabilities of critical eigenvalues are calculated from the Gram–Charlier series. In this method, random variables can have an arbitrary distribution. Dependencies among random variables and the interaction between expectation and covariance are all considered. Examination on two test systems shows that the proposed method can relieve/improve the conflict between computing requirement and precision.