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

© The Institution of Engineering and Technology
Received 17/02/2017, Accepted 15/05/2017, Revised 20/04/2017, Published 06/06/2017

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.

Inspec keywords: power distribution reliability; stochastic processes; Monte Carlo methods; differential equations; random processes

Other keywords: SDE; standard MCS; computational time saving; Euler–Maruyama discretisation schemes; standard MC simulation; random variables; reliability indices; Milstein discretisation schemes; discretisation schemes; computational time reduction; accelerated distribution system reliability evaluation; EM-MLMC method; Milstein MLMC method; multilevel Monte Carlo simulation; reliability assessment; MLMC methods; power distribution system reliability calculation; stochastic differential equations; Roy Billinton test system

Subjects: Reliability; Monte Carlo methods; Differential equations (numerical analysis); Distribution networks

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