The proportion of wind power in the regional power grid is increasing. To solve the problem of wind power output fluctuation during the black start process of wind farms, an energy storage configuration method with an energy storage operation strategy is proposed. First, the predicted power is obtained based on a wind power prediction algorithm, and the minimum black-start output probability density and the black-start executable probability inclination are defined by non-parametric kernel density estimation. Then the black-start period is determined. Secondly, the energy storage operation strategy is formulated with the role of energy storage in compensating for power shortage and suppressing fluctuations during the black start process. For the influence of energy storage operation strategy on capacity allocation, taking the rated power and capacity of energy storage as model independent variables, an energy storage optimal allocation model with the maximization of compensation power shortage as the objective function is established. The improved particle swarm optimization algorithm is used to analyze the model. Finally, the data of a 45 MW wind farm in Inner Mongolia verifies the feasibility of the energy storage operation strategy and optimal configuration model. This work is supported by the Youth Fund of Basic Research for Application in Shanxi Province (No. 20210302124553).