Optimal stochastic scheduling in microgrids under managed risk

Document Type : Original Article


1 Electrical Engineering Department, Razi University, Kermanshah, Iren

2 Electrical Engineering Department, Engineering Faculty, Razi University, Kermanshah, Iran



This paper addresses the stochastic optimal day-ahead microgrid (MG) energy resources scheduling, considering the uncertain load, price of electricity, and generated electrical power by wind and solar units. Moreover, the vehicle-to-grid (V2G) implementation, load curtailment cost, and spinning reserve requirements are modeled to make the results more practical and applicable. Furthermore, the price elasticity of supply is considered to explore the relation between V2G capability and the optimization process. The stochastic energy resources scheduling problem is formulated in a two-level optimization framework. The unit commitment of dispatchable resources is analyzed in the upper level, and the lower level is formulated as a scenario-based two-stage stochastic programming problem that minimizes the operation cost of MG considering all the constraints. The risk of attaining unfavorable high costs of MG scheduling is considered using the variance approach. The generated scenarios are reduced by using the backward reduction method for each uncertain variable at each hour, independently. The artificial intelligent-based methods, including differential evolution algorithm (DEA), particle swarm optimization (PSO), and covariance matrix adaptation evolution strategy (CMAES) are applied to solve the problem. The effectiveness of the proposed approaches is confirmed by simulations on a modified 13-bus IEEE test system, in two cases of neglecting the risk and including the managed risk by applying the real-world data. The results confirmed the better performance of CMAES for solving such optimization problems. 


Main Subjects

Volume 6, Issue 1
March 2022
Pages 33-43
  • Receive Date: 05 April 2021
  • Revise Date: 28 June 2021
  • Accept Date: 28 June 2021
  • First Publish Date: 28 June 2021