Renewable energy sources are an attractive alternative option for augmenting the supply that comes from the utility Grid. This is because they are environmentally friendly. However Photovoltaic power generation is intermittent in nature. Hence, it is usually combined with energy storage systems such as batteries. In this study, pumped hydroelectric energy storage is used for supplementing the power produced from the Solar Photovoltaic system especially during peak demands and when the solar irradiance is low especially at night. Thus, the objective of this study is to model and simulate a pumped energy storage hydro system that can provide power supply of up to approximately 100 kW for a 10 hour period to service the night time. The proposed system is modeled using MATLAB Simulink. A total volume of 91836.7 m3 of storage water was calculated to achieve this purpose. Maximum torque of about 90 N/m was attainable when the angular speed of the water turbine was between 1100 and 1200 rpm. Recommendation for further works can be considered to maintain the angular speed of the turbine within this range.