Quasi Monte Carlo method for reliability evaluation of power system based on Dimension Importance Sorting

Quasi Monte Carlo (QMC) is a type of improved Monte Carlo (MC) method, although its improvement over MC is known to degrade with large-dimension problems. This study proposes a Dimension Importance Sorting (DIS) method to solve this degradation problem, so QMC becomes feasible for large-dimension reliability evaluation of power systems. First, the error estimation principle of QMC is presented, and the uniformity degradation of low discrepancy sequence on high dimension is analyzed. The concept of analysis of variance is then employed to derive the decomposition term of error bounds for QMC, and a sampling method that uses Spearman correlation coefficient to sort the dimension importance is proposed to reduce the error bounds. Finally, 2 methods of reliability evaluation, QMC based on DIS (QMC-DIS) and cross entropy QMC-DIS (CE-QMC-DIS), are built to improve the conventional MC and CE, respectively, on the accuracy of reliability indices. The effectiveness of proposed methods is demonstrated on the Reliability Test System-79 generation system, a 292-unit generation system, and the Roy Billinton Test System generation and transmission system.