Wind power generation has been attracting attention due to environmental issues such as fossil fuel depletion and global warming. However, the power output of wind power generation fluctuates depending on wind conditions, leading to a decrease in power quality in the grid. Since ESSs are expensive, they must be downsized to reduce the maximum output power in order to expand the use of wind power. The ESS is expensive, so it is necessary to downsize it to reduce its maximum output power in order to increase the adoption of wind power generation. The conventional control methods are based on historical data, which limits the downsizing of the ESS. In this paper, we propose a control method to determine the optimal power output to minimize the ESS output while satisfying the technical requirements, in order to further reduce the size of the ESS by using wind power output prediction. The effectiveness of the proposed method is demonstrated by simulation.