Probabilistic Small-Signal Stability Analysis of Power Systems With Renewable Energy: A Truncated GMM-Based Analytical Method

With the increasing penetration of renewable energy, the secure and stable operation of power systems faces the challenge brought by renewable generation uncertainties. This paper proposes a truncated Gaussian mixture model (TGMM)-based analytical method to quantify the impact of renewable generation uncertainty on power system small-signal stability. The renewable generation uncertainty based on probabilistic forecasting is accurately modelled as a Gaussian mixture model. Then a piecewise affine transformation is developed to obtain the analytical piecewise mapping relationship between renewable generation injection and small-signal stability index output. Besides, a discrete integral method is proposed to derive the conditional distributions of renewable generation with regard to each subregion in the analytical form of TGMM. It is proved that one-dimensional TGMM exhibits truncated invariance. Thus, the probability mapping from renewable generation to stability index in each subregion is obtained by the truncated invariance of TGMM. Finally, the overall probability distribution of stability index is constructed analytically based on the probability distribution weighted fusion from different dimensional projections. The superior performance of the proposed method is verified by comprehensive case studies in the modified IEEE 39-bus system.