A Bi-level optimizer for reliability and security assessment of a radial distribution system supported by wind turbine generators and superconducting magnetic energy storages

Abstract

This paper is aimed at improving the reliability and security of radial distribution system supported by wind turbine generators (WTGs) and superconducting magnetic energy storages (SMESs). For reliability indices assessment, the load-oriented indices including energy not supplied (ENS) and average energy not supplied (AENS) as well as the customers-oriented indices including system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), customer average interruption duration index (CAIDI), and average service unavailability index (ASUI) are evaluated. Network security index (NSI) is also addressed, which refers to the risk level for current flow in the lines prior reaching to extremis. A multi-objective function is composed and formulated in order to simultaneously minimize ENS, SAIFI, SAIDI, ASUI, and NSI as indices which characterize the performance of distribution system using a hybrid approach based on equilibrium optimizer (EO) along with the loss sensitivity factors. A bi-level optimizer based on the hybrid approach addressing all constraints is applied for simultaneous minimization of reliability and security indices of distribution system. The outer level looks for an optimal sizing and sitting of WTGs and SMESs as well as optimal weighting coefficients whose evaluation is no longer assumed arbitrarily or left to the preferences of the decision maker. The inner level optimizes charging and discharging powers as well as initial state of charge of SMESs. Modeling of feeder's failure rate applying several mathematical functions is considered. The effectiveness of proposed approach is validated on the IEEE 33-bus test system considering commercial, industrial, residential, and mixed time-varying voltage-dependent load models. The performance of the distribution system is also checked as regards the energy loss in feeders, the bus voltage deviation from rated value as well as the voltage stability of the system. For validating the effectiveness of the EO algorithm, the obtained results using the EO algorithm are compared with those predicted by particle swarm optimization (PSO) and genetic algorithm (GA). Moreover, the obtained results display that the bi-level optimization can successfully achieve satisfactory improvement of the reliability and security indices of the distribution system.