Energy storage system (ESS) is a key technology to accommodate the uncertainties of renewables. However, ESS at an improper size would result in no-reasonable installation, operation and maintenance costs. With concerns on these costs outweighing ESS operating profit, this paper establishes a stochastic model to size ESS for power grid planning with intermittent wind generation. In the model, the hourly based marginal distributions with covariance is first derived from historical data of wind generation, and a stochastic cost-benefit analysis model with consideration of the generation fuel cost expectation and ESS amortized daily capital cost is formed. Then a hybrid solution approach combining the Point Estimated method and the parallel Branch and Bound algorithm (PE-BB) is designed to solve the model. Finally, the stochastic model and PE-BB approach are thoroughly tested on the 10-unit and 26-unit systems with uncertain wind generation. Simulation results confirmed the proposed model and PE-BB approach are effective to optimize ESS size for power grid planning with intermittent wind generation. The cost-benefit investigations on four typical ESSs also indicated that the ESS capital cost, charging/discharging efficiency and lifetime are important properties for optimizing ESS size, and it is not always economically justifiable to install ESS in power system. (C) 2018 Elsevier Ltd. All rights reserved.