Wind power producers (WPPs) that sell power in forward power markets would like to minimize their operating costs which increase with generation uncertainty. In this work, the value of energy storage for reducing such costs is studied. In particular, profit maximization is considered for a WPP who participates in a two-settlement (forward and real time) market and utilizes energy storage by charging/discharging it strategically. An infinite horizon discounted cost minimization problem for the optimal use of energy storage is formulated as a dynamic programming (DP) problem that includes the past unfulfilled forward contracts in the state space. The optimal storage operation policy is shown to have a structure with two thresholds: after delivering its contracted power, if a WPP's energy falls below a lower threshold, it buys energy and charges its storage up to this threshold; if its energy exceeds a higher threshold, it sells the excess energy and maintains its storage level at this threshold. Several heuristics for solving the DP are derived based on approximating the problem model: a) a discrete policy based on discretizing the state and action space, and b) affine and look ahead policies derived by solving a Linear Quadratic (LQ) controller whose parameters are fit from the DP. The heuristics are tested both with simulated and real world wind and price data. It is observed that while the discrete optimal policy performs better on simulated data than either the look ahead or the affine policies (except with a very high battery capacity), the look ahead policy performs much better with real world data. This suggests that the performance of look ahead approximate optimal policy is more robust to the modeling errors and mismatch between analytic models and real data traces. The appropriate heuristic to use thus depends on modeling fidelity, available computational resources and variability of wind and price forecasts.