A battery energy storage system (BESS) is usually integrated with a wind farm to smooth out its intermittent power in order to make it more dispatchable. This paper focuses on the development of a scheme to minimize the capacity of BESS in a distributed configuration using model predictive control theory and wind power prediction. The purpose to minimize the BESS capacity is to reduce the overall cost of the system as the capacity of BESS is the main cost driver. A new semi-distributed BESS scheme is proposed and the strategy is analyzed as a way of improving the suppression of the fluctuations in the wind farm power output. The scheme is tested for similar and dissimilar wind power profiles, where the turbines are geographically located closer and further from each other, respectively. These two power profiles are assessed under a variety of hard system constraints for both the proposed and conventional BESS configurations. Based on the simulation results validated with real-world wind farm data, it has been observed that the proposed semi-distributed BESS scheme results in the improved performance as compared with conventional configurations such as aggregated and distributed storage.