This paper studies operation decisions of energy storage facilities in perfectly and imperfectly competitive markets. In a perfectly competitive market, the storage facility is operated to maximize the social welfare. However, in a imperfectly competitive market, the storage facility operates to maximize its profit, while the market operator aims at maximizing the social welfare. In this case, the storage facility adapts its strategic behavior to take advantage of market conditions. To model the imperfectly competitive market, a bi-level optimization model is implemented to present the interactions between the storage facility and the market operator. In an illustrative test system, operation of the storage facility in these two market structures is compared and discussed.