Energy storage systems (ESSs) are of great value to realize energy management and to support large-scale renewable generation. The combined operation of ESSs and renewables is one way to achieve output levelling and to improve the integration of sustainable energy. However, in a market-based environment, ESSs would make strategic decisions on self-schedules and arbitrage in energy and ancillary service markets, maximizing the overall profits. Will the strategic operation of ESSs promote renewable generation integration? To explicitly answer this question, this paper proposes a multi-period Nash-Cournot equilibrium model for joint energy and ancillary service markets to evaluate the contribution of the ESSs for supporting renewable generation. Then, a reformulation approach based on the potential function is proposed, which can transform the bi-level equilibrium model into an integrated single-level optimization problem to enhance the computation efficiency. Numerical examples are implemented to validate the effectiveness of the reformulation technique. The results of the case study indicate that the ESSs indirectly but substantially provide improved flexibilities while pursuing individual profit maximization.