With a rapid increase in capacity, independently-invested energy storage systems (ESSs) might take up a significant share in the generation mix, and would be required to participate in the electricity market. Considering the arbitrage capability of ESSs, their behaviors would be remarkably different from those of conventional generators, impacting the market equilibrium. These impacts would vary with the type of ESSs and the generation mix. Therefore, this paper formulates a multi-period market equilibrium problem with equilibrium constraints (EPEC) to study the strategic behaviors of different types of ESSs and their impacts on the market outcomes, assuming that ESSs behave as price-makers. The EPEC model is established within a general framework, which considers the individual profit-maximization behaviors of different ESSs and generators, including thermal units, hydro units and renewable units. Interactions between different generators and the market operator are also represented. Finally, numerical studies based on a modified IEEE 57-node system with different wind generation curves are performed for illustration and validation. (C) 2016 Elsevier Ltd. All rights reserved.