This paper explores a method to obtain optimal energy storage system (ESS) operation strategy in distribution system with wind power. Considering main applications of ESS in distribution system, the optimization model for proposed problem includes three objectives: 1) minimize the cost for purchasing electricity; 2) minimize the deviation and fluctuation of distribution system's main substation's power; 3) minimize the amount of spilled wind power energy. A multi-objective genetic algorithm (GA) with matrix real-coded method is designed to solve the proposed problem. Numerical simulations with two case studies based on high and low penetration level of wind power energy, are analysed to understand the operation character of ESS with different scenarios.