Forecasting uncertainties limit the widespread adoption of wind power generation. Energy storage systems (ESSs) are essential for managing uncertainty, and ESS sizing determines the availability of uncertainty management. However, most ESS sizing studies utilize heuristic approaches. Therefore, research on the determination of ESS sizing related to uncertainty management performance is needed. This paper proposes a theoretical ESS sizing method that considers the stochastic properties of the uncertainty. In the proposed method, the power subsystem (PS) and energy subsystem (ES) capacities, which are related to the instantaneous and accumulated uncertainty characteristics of the ESS, respectively, are determined in terms of the confidence interval of the uncertainty statistic. They are presented as simple formulas by applying the extreme value theory. Furthermore, to demonstrate the uncertainty management performance of ESS sizing, the mean absolute error (MAE) is analyzed, as the variance and absolute errors of the uncertainty determine the MAE of the PS and ES, respectively. A numerical study using real wind power generation and its forecasting data verifies that the proposed method suitably reflects the characteristics of the uncertainty, with an analysis gap between the analyzed MAE and the actual measured value of less than 1%. This study can act as a reference for the expected performance when using ESS and can be extended to the theoretical economic evaluation of ESS usage. (C) 2020 Elsevier Ltd. All rights reserved.