The integration of large-scale intermittent renewable energy generation into the power grid imposes challenges to the secure and economic operation of the system, and energy storage (ES) can effectively mitigate this problem as a flexible resource. However, the conventional ES allocation is mostly planned to meet the regulation demands of individual entities, which is likely to result in low utilization of ES and difficult to recover the investment cost. Therefore, a two-stage stochastic optimal allocation model for grid-side independent ES (IES) considering ES participating in the operation of multi-market trading, such as peak-valley arbitrage, frequency regulation, and leasing, is proposed in this paper to improve the comprehensive benefits and utilization rate of ES. The first stage aims to allocate IES and develop a systematic scheduling plan based on the forecast of wind power output and load demand, while the second stage responds to the uncertainty of wind power output by re-dispatching generating units and invoking ES power leased by wind farms. Then, a two-layer loop iterative solution algorithm based on the Benders decomposition is formed to effectively solve the proposed model. Finally, the approach developed in this paper is applied to a modified IEEE RTS-79 test system, and the results verify that it is both feasible and effective.