Improved cross-entropy-based power system reliability evaluation using GMM with highly-efficient closed-form parameter updating

The reliability evaluation of composite generation and transmission systems (CSRE) is essential for power system planning and operation but often faces significant computational challenges. To accelerate CSRE, the Gaussian mixture model (GMM), known for its ability to model arbitrary probability densities, has been incorporated into the Cross-Entropy Method (CEM) to estimate the importance sampling probability density function (IS-PDF) of continuous random variables, such as correlated wind speeds and system load. However, the classical CEM produces a non-closed-form solution for the GMM-based IS-PDF, resulting in an alternating parameter updating procedure for the GMM parameter set and larger pre-simulation cost. To address this issue and enhance the simulation speed of CEM-based CSRE, an improved CEM with a highly efficient closed-form parameter updating mechanism is proposed. By developing an equivalent variant of the GMM that belongs to the exponential family, a closed-form solution is derived, eliminating the need for alternating updates. The improved CEM achieves higher efficiency and simplifies the modeling of the GMM-based IS-PDF. Numerical tests are conducted to validate the performance and advantages of the proposed method.