As a black-start power source, a wind power and energy storage system plays an important role in solving the problem of hydroelectric generation in regions with more wind and less water. However, because of the fluctuation of wind power and the high cost of energy storage, their development as a black-start source is restricted. In order to solve the problem of power fluctuation caused by wind power and the operating constraints of the battery energy storage system itself, an optimal energy storage capacity configuration strategy is proposed. First, based on the minimum wind speed of a black start, the probability density of the minimum wind speed and the probability inclination of optimal wind speed are defined. The wind farms involved in a black start are determined from the three aspects of numerical value, time and effective utilization of resources. Secondly, based on a wind power prediction method combined with a Self-Organizing Feature Mapping (SOFM) neural network and the Least Squares Support Vector Machine (LSSVM), the capacity and maximum charge-discharge power of the energy storage assisting wind power in a black start are determined. Finally, the effectiveness of the proposed model and method is verified in the Inner Mongolia power grid which is connected to 5 wind farms. This work is supported by the Joint Foundation of Natural Science Foundation of Jilin Province (No. 2020122352JC).