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In the near future, a smart grid will accommodate customers who are prepared to invest in generation-battery systems and employ energy management systems in order to cut down on their electricity bills. The main objective of this paper is to determine the optimum capacity of a customer's distributed-generation system (such as a wind turbine) and battery within the framework of a smart grid. The proposed approach involves developing an electricity management system based on stochastic variables, such as wind speed, electricity rates, and load. Then, a hybrid stochastic method based on Monte Carlo simulation and particle swarm optimization is proposed to determine the optimum size of the wind generation-battery system. Several sensitivity analyses demonstrate the proper performance of the proposed method in different conditions.