Both the lack of the downward regulation capacity and the transmission capacity limit have led to considerable wind power curtailments in China. The battery energy storage system (BESS) provides a new solution to reduce the wind power curtailments due to its relatively high energy density and flexible installed location. In this paper, a new bi-level programming model is proposed to optimize the size and location of BESS for reducing the wind curtailments. The revenues of BESS, when it is located either at the wind farm or the load center, are considered comprehensively. Moreover, a numerical optimization algorithm is developed to solve the proposed model. Simulation results demonstrate the validity of the proposed model and developed algorithm. They also reveal that the BESS located at the load center offers more net profit compared to the one located at the wind farm. Subsequently, sensitivity analysis is performed to assess the effect of key parameters on the optimal values of BESS.