By combining a wind turbine with an energy storage system (ESS), we are able to attenuate the intermittent wind power characteristic making the power derived from a wind farm dispatchable. This paper evaluates the influence of the phase delay of the low-pass filter in the conventional smoothing power control on the ESS capacity; longer phase delays require a larger ESS capacity. In order to eliminate the effect of the phase delay, we optimize the power dispatch using a zero-phase low-pass filter that results in a non-delayed response in the power dispatch. The proposed power dispatching method significantly minimizes the ESS capacity. In addition, the zero-phase low-pass filter, which is a symmetrical forward-reverse finite impulse response type, is designed simply with a small number of coefficients. Therefore, the proposed dispatching method is not only optimal, but can also be feasibly applied to real wind farms. The efficacy of the proposed dispatching method is verified by integrating a 3 MW wind turbine into the grid using wind data measured on Jeju Island.