Hydroelectric power is a renewable source of energy. By principle, hydroelectric power generation relies on the law of conservation of energy where kinetic energy that resulted from the movement of the mass of water from the river is translated into electricity, the quantum of which depends on systemic variables viz: plant efficiency, volumetric water flow through the turbine and the head of the water from the water surface to the turbine. Understanding the dynamics of these variables, and the correlation between them are core to proper planning and management of a hydroelectric power station. In this Study, simple mathematical methods that include linear programming and statistical analysis based on simulation techniques were used to evaluate vital parameters based on the data obtained from the Hydrologic units of the Shiroro Power Stations in Nigeria. The overall aim of the study is to idealize power generation at Shiroro dam in and out of raining season so as to ensure optimum generation of electricity all year round in order to achieve energy sufficiency in Nigeria. The result of the study is encouraging as it supports the viability of the pumped storage system for generating hydroelectric power all year round. The coupling of the hydroelectric power with pumped storage system if properly harnessed could be the needed panacea for the erratic power supply in Nigeria.