This study is aimed at determining the optimal energy storage system (ESS) operation schedule to minimize the peak load on the feeder of a distribution network. To reduce the peak load, the feeder load profile needs to be predicted. A deterministic prediction is not reliable, however, because it may contain errors. This study proposes the use of prediction intervals (PIs) of estimated error based on prior predictions. The proposed algorithm is intended for the determination of an optimal ESS schedule using the PIs. To demonstrate the method's validity, a case study is presented where a proposed optimal ESS schedule determined from PIs reduces the peak load during network operations over a one-year period. The performance of the proposed method is superior to that of the conventional method which uses deterministic load prediction.