This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Be...This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Besides,generating equipment is divided into components depending on the types of energy resources used.The mathematical model is presented by a system of nonclassical Volterra integral equations of the first kind.One of the equations describes the balance between the total available capacity of the electric power system,commissioning of new equipment,and dismantling of obsolete one.The other equations define the shares of different types of power plants in the total composition of the electric power system equipment.Based on the considered model,we set a problem that searches the optimal lifetimes of electric power system capacities for a given demand for electricity.The optimality criterion is a functional reflecting cost of commissioning and operating the capacities.The specifics of the optimization problem are that the optimization parameter is in the lower limit of integration.An algorithm for solving of this optimal control problem numerically is developed.The influence of economic indices on the solution to the optimal control problem is studied.Calculations of the optimal development of the Unified Energy System of Russia until 2050 are carried out using real-life data.展开更多
基金The research was carried out under State Assignment,Project 17.3.1(Reg.No.AAAA-A17-117030310442-8)Project 17.4.2(Reg.No.AAAA-A17-117030310438-1)of the Fundamental Research of Siberian Branch of the Russian Academy of Sciences.
文摘This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Besides,generating equipment is divided into components depending on the types of energy resources used.The mathematical model is presented by a system of nonclassical Volterra integral equations of the first kind.One of the equations describes the balance between the total available capacity of the electric power system,commissioning of new equipment,and dismantling of obsolete one.The other equations define the shares of different types of power plants in the total composition of the electric power system equipment.Based on the considered model,we set a problem that searches the optimal lifetimes of electric power system capacities for a given demand for electricity.The optimality criterion is a functional reflecting cost of commissioning and operating the capacities.The specifics of the optimization problem are that the optimization parameter is in the lower limit of integration.An algorithm for solving of this optimal control problem numerically is developed.The influence of economic indices on the solution to the optimal control problem is studied.Calculations of the optimal development of the Unified Energy System of Russia until 2050 are carried out using real-life data.
