Optimum load distribution between heat sources based on the Cournot model

Abstract

One of the widespread models of the heat supply of consumers, which is represented in the “Single buyer” format, is considered. The methodological base proposed for its description and investigation presents the use of principles of the theory of games, basic propositions of microeconomics, and models and methods of the theory of hydraulic circuits. The original mathematical model of the heat supply system operating under conditions of the “Single buyer” organizational structure provides the derivation of a solution satisfying the market Nash equilibrium. The distinctive feature of the developed mathematical model is that, along with problems solved traditionally within the bounds of bilateral relations of heat energy sources-heat consumer, it considers a network component with its inherent physicotechnical properties of the heat network and business factors connected with costs of the production and transportation of heat energy. This approach gives the possibility to determine optimum levels of load of heat energy sources. These levels provide the given heat energy demand of consumers subject to the maximum profit earning of heat energy sources and the fulfillment of conditions for formation of minimum heat network costs for a specified time. The practical realization of the search of market equilibrium is considered by the example of a heat supply system with two heat energy sources operating on integrated heat networks. The mathematical approach to the solution search is represented in the graphical form and illustrates computations based on the stepwise iteration procedure for optimization of levels of loading of heat energy sources (groping procedure by Cournot) with the corresponding computation of the heat energy price for consumers.