Design of a battery energy storage system (BESS) in a buffer scheme is examined for the purpose of attenuating the effects of unsteady input power from wind farms. The design problem is formulated as maximization of an objective function that measures the economic benefit obtainable from the dispatched power from the wind farm against the cost of the BESS. Solution to the problem results in the determination of the capacity of the BESS to ensure constant dispatched power to the connected grid, while the voltage level across the dc-link of the buffer is kept within preset limits. A computational procedure to determine the BESS capacity and the evaluation of the dc voltage is shown. Illustrative examples using the proposed design method are included.