Most of the power outages experienced by the customers are due to the failures in the electric distribution systems. However, the ultimate goal of a distribution system is to meet customer electricity demand by maintaining a satisfactory level of reliability with less interruption frequency and duration as well as less outage costs. Quantitative evaluation of reliability is, therefore, a significant aspect of the decision-making process in planning and designing for future expansion of network or reinforcement. Simulation approach of reliability evaluation is generally based on sequential Monte Carlo (MC) method which can consider the random nature of system components. Use of MC method for obtaining accurate estimates of the reliability can be computationally costly particularly when dealing with rare events (i.e. when high accuracy is required). This thesis proposes a simple and effective methodology for accelerating MC simulation in distribution systems reliability evaluation. The proposed method is based on a novel Multilevel Monte Carlo (MLMC) simulation approach. MLMC approach is a variance reduction technique for MC simulation which can reduce the computational burden of the MC method dramatically while both sampling and discretisation errors are considered for converging to a controllable accuracy level. The idea of MLMC is to consider a hierarchy of computational meshes (levels) instead of using single time discretisation level in MC method. Most of the computational effort in MLMC method is transferred from the finest level to the coarsest one, leading to substantial computational saving. As the simulations are conducted using multiple approximations, therefore the less accurate estimate on the preceding coarse level can be sequentially corrected by averages of the differences of the estimations of two consecutive levels in the hierarchy. In this dissertation, we will find the answers to the following questions: can MLMC method be used for reliability evaluation? If so, how MLMC estimators for reliability evaluation are constructed? Finally, how much computational savings can we expect through MLMC method over MC method? MLMC approach is implemented through solving the stochastic differential equations of random variables related to the reliability indices. The differential equations are solved using different discretisation schemes. In this work, the performance of two different discretisation schemes, Euler-Maruyama and Milstein are investigated for this purpose. We use the benchmark Roy Billinton Test System as the test system. Based on the proposed MLMC method, a number of reliability studies of distribution systems have been carried out in this thesis including customer interruption frequency and duration based reliability assessment, cost/benefits estimation, reliability evaluation incorporating different time-varying factors such as weather-dependent failure rate and restoration time of components, time-varying load and cost models of supply points. The numerical results that demonstrate the computational performances of the proposed method are presented. The performances of the MLMC and MC methods are compared. The results prove that MLMC method is computationally efficient compared to those derived from standard MC method and it can retain an acceptable level of accuracy. The novel computational tool including examples presented in this thesis will help system planners and utility managers to provide useful information of reliability of distribution networks. With the help of such tool they can take necessary steps to speed up the decision-making process of reliability improvement.Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 201
