Energy storage systems (ESSs) have experienced a very rapid growth in recent years and are expected to be a promising tool in order to improving power system reliability and being economically efficient. The ESSs possess many potential benefits in various areas in the electric power systems. One of the main benefits of an ESS, especially a bulk unit, relies on smoothing the load pattern by decreasing on-peak and increasing off-peak loads, known as load leveling. These devices require new methods and tools in order to model and optimize their effects in the power system studies. In this respect, this paper will model bulk ESSs based on the several technical characteristics, introduce the proposed model in the thermal unit commitment (UC) problem, and analyze it with respect to the various sensitive parameters. The technical limitations of the thermal units and transmission network constraints are also considered in the model. The proposed model is a Mixed Integer Linear Programming (MILP) which can be easily solved by strong commercial solvers (for instance CPLEX) and it is appropriate to be used in the practical large scale networks. The results of implementing the proposed model on a test system reveal that proper load leveling through optimum storage scheduling leads to considerable operation cost reduction with respect to the storage system characteristics.