The economic independence of any nation depends largely on the supply of abundant and reliable electric power and the extension of electricity services to all towns and villages in the country. In this work, the mathematical study of an electric power generating system model was presented via optimal control theory, in an attempt to maximize the power generating output and minimize the cost of generation. The factors affecting power generation at minimum cost are operating efficiencies of generators, fuel cost and transmission losses, but the most efficient generator in the system may not guarantee minimum cost as it may be located in an area where fuel cost is high. We choose the generator capacity as our control ui(t), since we cannot neglect the operation limitation on the equipment because of its lifespan, the upper bound for ui(t) is choosing to be 1 to represent the total capability of the machine and 0 to be the lower bound. The model is analyzed, generation loss free equilibrium and stability is established, and finally applications using real life data is presented using one generator and three generator systems respectively.
