Probabilistic Analysis of Small Signal Stability for Power Systems With High Penetration of Wind Generation

Wind generation is growing fast worldwide. The stochastic variation of large-scale wind generation may impact the power systems in almost every aspect. Probabilistic analysis method is an effective tool to study power systems with random factors. In this paper, a systematic nonlinear analytical probabilistic method is proposed to evaluate the possible effect of random wind power generation on power system small signal stability. A second-order polynomial is proposed to approximate the nonlinear relationship between the wind generation and the damping of a particular dynamic mode, such as the dominant mode. Gaussian mixture model formulates wind uncertainty in a uniform way. Spectral theorem is adopted to reshape the second-order polynomial into a form without cross-product terms. Cholesky decomposition is used to eliminate correlations among outputs of different wind farms. Thereafter the cumulative distribution function (CDF) of the damping ratio with respect to random wind power is consequently constructed. Numerical simulations are carried out in the IEEE standard test system. The proposed method is verified with higher accuracy than the traditional linearized method. Meanwhile, it is much more time-saving in calculation than Monte Carlo simulation.