## Accelerated distribution systems reliability evaluation by multilevel Monte Carlo simulation: implementation of two discretisation schemes

This study presents the performances of two discretisation schemes which are implemented in a novel multilevel Monte Carlo (MLMC) method for reliability calculation of power distribution systems. The motivation of using the proposed approach is to reduce the computational effort of standard Monte Carlo simulation (MCS) and accelerate the overall distribution system reliability evaluation process. The MLMC methods are implemented through solving the stochastic differential equations (SDEs) of random variables related to the reliability indices. The SDE can be solved using different discretisation schemes. Two different discretisation schemes, namely Euler–Maruyama (EM) and Milstein are utilised in this study. For this reason, the proposed MLMC methods are named as EM-MLMC and Milstein MLMC. The reliability evaluation efficiency of the methods is analysed and compared based on accuracy and computational time saving for basic reliability assessment of Roy Billinton test system. Numerical results show that both methods reduce the computational time required to estimate the reliability indices compared with the same discretisation schemes used in MCS and maintain satisfactory accuracy levels.