The energy storage system (ESS) is recently drawing an increasing attention as an efficient and affordable tool in energy systems. While most interest has been concerned with developing better ESS technology, attention should be given to constructing a rigorous decision-supporting framework for operating the ESS. Motivated by this need, a mathematical modeling framework for the operation of an ESS is proposed in this paper. The proposed framework allows us to prepare ESS operations such as when to charge or discharge by which amount over multiple time periods. Numerical examples are presented to illustrate the applicability of the proposed framework.