With worldwide growth of battery technologies in renewable energy production, the selection of battery model has become an important factor for a Battery Energy Storage System (BESS) to be deployed in a grid environment. It is essential to understand the battery type and the model, to achieve a coordinated control of the performance of BESS, Renewable Energy Sources (RES) and load management, including battery applications such as ramp control, frequency response, voltage response, emergency backup, transmission and distribution capacity utilization and peak load leveling, when connected to the grid. Recent studies showed that the battery capacity utilization is based on the battery discharge characteristics. In this paper, two types of battery models such as 'stacked cell model' and 'single cell model' of a 1 MWh Lithium Manganese Oxide (LMO) battery are taken into consideration to study the discharge characteristics. The approach is based on the use of the Dual Polarization Model (one of the Electrical Equivalent Circuit Models also called as Two Time Constant Model) in building the above mentioned battery models. The purpose of this paper is to build and simulate the battery models in Power Systems Computer Aided Design (PSCAD). Also the battery models are compared and analyzed on their performance during faults when connected to the resistive load at 1C discharge rate. The 'single cell model' is constructed using the electrical equivalent circuit to build the 1 MWh battery module. In an attempt to simulate the 'stacked cell model', initially one cell of the battery rated at 4.12 V, 60 Ah is modeled in PSCAD and then the cells are connected in series and parallel to build the model of 1 MWh battery module. The key results include the modeling of single cell and stacked cell models of the 1 MWh battery. The discharge characteristics of the battery models rated at 960V, 1200 Ah will be analyzed for the faults applied near the resistive load. The models will be tested for node compatibility, compilation issues and the response effectiveness when connected to the resistive load. Thus, the research paper will perform a comparative analysis of the simulation results of the two battery models in terms of discharge characteristics, speed, performance, stability and compatibility.