In this paper, based on stochastic optimization methods, a technique for optimal sizing of battery energy storage systems (BESSs) under wind uncertainties is provided. Due to considerably greater penetration of renewable energy sources, BESSs are becoming vital elements in microgrids. Integrating renewable energy sources in a power system together with a BESS enhances the efficiency of the power system by enhancing its accessibility and decreasing its operating and maintenance costs. Furthermore, the microgrid-connected BESS should be optimally sized to provide the required energy and minimize total investment and operation expenses. A constrained optimization problem is solved using an optimization technique to optimize a storage system. This problem of optimization may be deterministic or probabilistic. In case of optimizing the size of a BESS connected to a system containing renewable energy sources, solving a probabilistic optimization problem is more effective because it is not possible to accurately determine the forecast of their output power. In this paper, using the stochastic programming technique to discover the optimum size of a BESS to connect to a grid-connected microgrid comprising wind power generation, a probabilistic optimization problem is solved. A comparison is then produced to demonstrate that solving the problem using stochastic programming provides better outcomes and to demonstrate that the reliability of the microgrid improves after it is connected to a storage system. The simulation findings demonstrate the efficacy of the optimum sizing methodology proposed.