This paper proposes an approach for determining the optimal location and size of an energy storage system (ESS) in a power system network integrated with uncertain wind power generation. The uncertainty of wind power output is represented by a scenario tree model, so that the nonanticipative behavior of operating decisions under system uncertainties can be properly addressed. The proposed formulation is too huge to be solved directly, so a Benders decomposition algorithm is applied to reduce the computational burden. Case studies are conducted to illustrate the influence of ESS on power system operation. It is shown that increasing the capital investment on ESS can reduce the daily operating cost of the power system. A capital/operating cost frontier is presented in this paper to demonstrate the tradeoff between ESS capital investment and daily operating cost, and to show how ESS planning decisions are affected by the budget for investment.