With the increase of wind power penetration in power system, the uncertainty caused by wind farm forecast error is enlarged which results in deterioration of wind power curtailment. In order to optimize the capacity of battery storage for mitigating forecast error, firstly it is necessary to improve the accuracy of forecast error model. This paper proposed a modeling method of forecast error time series in usage of beta distribution. Varying with forecast output, parameters of the beta distribution are estimated by maximum likelihood estimation. Autocorrelated forecast error obeying beta distribution is generated by correlated Monto-Carlo simulation. Based on the forecast error model, an optimization method is proposed to determine the optimum size of battery storage for mitigating forecast error. Through maximizing the total profit composed of electricity sales revenue, penalty and battery cost, the optimum size of battery storage is calculated. The results show that the forecast error model proposed in this paper is able to simulate both probability density function and autocorrelation correctly, which is beneficial to improving the accuracy and economy of battery storage sizing.