Electrical energy storage system (ESS) has been used worldwide as ancillary support to the grid, aiding in frequency regulation and grid stability. Intermittent renewable energy sources (RESs) can be effectively integrated into the grid by maintaining power balance using different types of energy storage. However, the power requirement during small frequent, and large persistent power variations in the load demand can be more effectively controllable with the combination of the different energy storage according to their operational characteristics. This paper evaluates the suitability of a dual energy storage system (DESS) integrated in a grid connected microgrid (MG) system for providing ancillary services to the utility grid. The DESS is a combination of battery bank storage (BBS) and pump hydro storage (PHS). The BBS is very fast responding and it can counter the immediate variations in the power whereas, the PHS system can counter the large variations of the power as needed in the MG system. Four different operating cases have been studied to obtain the optimal size of the DESS for optimizing not only the operational cost but also for the best combination size of the storage systems to counter the variability in power generations and the load demand in the power system. Day-ahead electricity market scheduling has been performed on the MG to control the net power demand variations on the distribution feeder of the utility grid. The simulation results show that the higher capacity of the DESS does not always provide the optimal operational cost of the MG system during the grid-connected mode. Therefore, optimal sizing of the storage system also plays an important role in providing the optimal solution. It has been found that the optimal size of the individual energy storage and the DESS is different for microgrids supporting or not supporting the grid. The study enables the system operator (SO) to choose the best combination of storage systems for the supportive and non-supportive operation of microgrid system.