Our paper addresses an integral model of the large electric power system optimal development. The model takes into account the age structure of the main equipment, which is divided into several types regarding its technical characteristics. This mathematical model is a system of Volterra type integral equations with variable integration limits. The system describes the balance between the given demand for electricity, the commissioning of new equipment and the dismantling of obsolete equipment, as well as the shares of different types of power plants in the total composition of the electric power system equipment. Based on the developed model, we got numerical solution to the problem of finding the optimal strategy for replacing equipment with a minimum of the cost functional. The case study is the Unified Electric Power System of Russia. Calculations of the forecast for development of the electric power system of Russia until 2050 were made using real-life data.