Rising wind penetrations can suppress wholesale energy prices by displacing higher-cost conventional generation from the merit order. Wind suffers disproportionately from this price suppression, because the price is most suppressed when wind availability is high, hindering wind-investment incentives. One way to mitigate this price suppression is by wind exercising market power, which introduces efficiency losses. An alternative is to use energy storage, which allows energy to be stored when wind availability is high. This stored energy is later discharged when wind availability is lower and prices are higher. This paper proposes a bilevel equilibrium model to study market equilibrium interactions between energy storage and wind and conventional generators. We represent the market interaction using an equilibrium problem with equilibrium constraints. An illustrative case study is used to demonstrate the social welfare and profit benefits of using energy storage in this manner.