Improving distribution system reliability calculation efficiency using multilevel Monte Carlo method

Power distribution system reliability is generally evaluated by sequential Monte Carlo simulation (MCS). To obtain a high accuracy, we found that sequential MCS technique needs long execution time. In this paper, we show that reliability indices could be evaluated using a novel sequential multilevel Monte Carlo technique that improves the computational efficiency of MCS. The key idea behind the multilevel Monte Carlo method is to use computationally cheaper low-accuracy solutions of coarse grids as control variates for high-accuracy solutions of fine grids. Therefore, the proposed method can construct multilevel estimators of reliability indices with lower variance. Reliability indices are modelled based on stochastic differential equations and exponential probability distributions. The Milstein path discretisation is used to approximate the numerical solution of stochastic differential equations. Case studies are performed on a small distribution system. Numerical results are presented to demonstrate the computational cost-effectiveness of the proposed method in comparison with the sequential MCS.