The goals of carbon peaking and carbon neutrality and the construction of new power system have promoted the continuous development of new energy resources, while bringing along higher demands for energy storage. When configuring energy storage for wind farms in the power system, the shared economic model is used to optimize the configuration of energy storage with consideration of the pricing mechanism, and the impact of wind generation uncertainty on the energy storage configuration scheme is discussed. Firstly, based on the Stackelberg game for determining the price, a shared energy storage optimal configuration model is proposed, in which the shared energy storage operator is the leader, wind farms are the followers, and the profit of each participant is maximized. Then, to address the fluctuations of wind power output, a moment information-based distributionally robust optimization method is introduced to construct chance constraints to describe uncertainties, where the moment information is used to complete the ambiguity set to reduce the conservatism. The wind farm model is reconstructed into a mixed integer second-order cone programming model through Chebyshev inequality for solution. Finally, case studies are conducted based on the actual wind farm data in Ningxia, and the results show that the proposed optimal configuration model can reduce redundant investment, promote energy storage to participate in configuration and address the actual wind power generation fluctuations.