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Currently the energy storage system (ESS) has become the development focus in the electric power systems (EPS) with the renewable energy power generation. At the same time, high penetration levels of ESS leads to a change the dynamic properties of the EPS. Accordingly, the analysis of the specifics of ESS operation becomes necessary for effective solution the problems of designing and operating EPS with ESS. Since mathematical simulation level is the main way to obtain the indicated information, the task of the adequacy of approaches and methods for modeling a processes in the ESS as part of the EPS becomes relevant. In the first part of the article, detailed mathematical models of the main elements of the ESS were considered. An analysis of mathematical models of ESS with different detailization level, depending on the type of energy storage device and a number of other factors, are presented within the framework of the second part of the article. The article also provides an overview of the approaches used to simplify the ESS models and their mathematical description. The areas of application of these models are considered. In addition, an analysis of the limitations and disadvantages associated with the simplification of models are presented. The article is an overview and can help in choosing an appropriate mathematical model of the ESS for solving a required designing and operating tasks.