Due to the high integration of renewable energy, the power systems may become more susceptible to unbalanced grid voltages, grid frequency disturbances, harmonic resonances and others. Therefore, several works have pointed out that the ancillary services provided by the energy storage systems can minimize these issues. The combination of energy storage and static synchronous compensators (ES-STATCOM) has been proposed to reduce the cost. Modular multilevel converters (MMC) are featured as a good solution for ES-STATCOM realization, due to their high efficiency, modularity and inherent fault-tolerant structure. However, the study of the integration of the MMC based ES-STATCOM in a complex power system composed of power electronic converters, transmission system, renewable plants, transformers, etc, leads to a high computational burden. Therefore, this work presents a detailed design and implementation of three efficient simulation models of the MMC ES-STATCOM. The performance of these models compared during a grid frequency support case study by a 100 MVA/33 kV ES-STATCOM. In addition, the performance of these models is evaluated during a battery charging process and a grid symmetrical fault. The models are compared through the following aspects: processing time, normalized integral of absolute error, state-of-charge estimation and active and reactive power dynamic response.