The need for secure and flexible operation of distribution power systems with renewable generation and the decline in battery prices have made energy storage projects a viable option. The storage characterization currently utilized for power system models relies on two significant assumptions: The storage efficiency and power limits are constant. This approach can lead to an overestimation of the available battery power and energy, thus, threatening the system reliability. We introduce a stochastic operating model for distribution systems with non-ideal energy storage, that allows the purchasing of energy and reserves from the electricity market through the interconnection with the transmission system. The model's objective is the centralized minimization of the operational costs derived from the energy and reserves purchase at the electricity market, as well as those incurred while operating the system's fuel-based and renewable generation, and energy storage system. The proposed energy storage model is computationally validated and compared on a modified IEEE 33-bus electric distribution system.