Research on Power Grid Reliability Probability Distribution Calculation Based on Continuous Markov Chain Cross-Entropy Method

Abstract

The evaluation of large power grid reliability is crucial for quantifying the risk level and identifying weak links, offering valuable insights for power grid planning and operation. The sequential cross-entropy important sampling method has gained widespread application in large power grid reliability evaluation, significantly enhancing the efficiency of the sequential Monte Carlo method. Despite its ability to achieve unbiased estimations of power grid reliability index expected values, the method faces inherent limitations preventing the calculation of the probability density distribution of the reliability index. For a comprehensive characterization of power grid reliability, the probability density distribution of the reliability index is essential, with the expected value serving as a measure of the long-term reliability level. Comparative analysis reveals a 15% increase in the average fault interval and a 20% reduction in the average system repair time compared to traditional methods. These findings underscore the superior performance of the continuous Markov chain cross-entropy method, providing robust technical support for advancements in power grid reliability research. In view of the inherent defects of the traditional sequential cross-entropy important sampling method and the system state transfer law, how to construct the probability density distribution of the continuous time Markov chain path and solve the important sampling function is the primary problem in this paper. The Markov chain models the system's state transitions, representing the reliability states of various grid components. Continuous Markov chains are particularly suited for dynamic systems where the transitions occur over continuous time. Originally developed for rare-event probability estimation, the cross-entropy method optimizes the sampling process by iteratively adjusting the probability distribution to minimize divergence from the target distribution.