Differential game model with discretized solution for distributing heat produced by solar heating systems

Abstract

It is indispensable for the sustainable energy supply of our society to increase the proportion of the renewables in the energy production. For this purpose, it is important to distribute the renewables, like solar heat, with maximal efficiency among the consumers. The theoretically established, effective tool for the solution of this problem is the mathematical (and especially, the game theoretical) modelling.In the paper, a new differential game is proposed for solar heating systems with several consumers (players) to describe the temperature change of the solar storage and the change of the players’ payoffs over time, taking into account the heat recharge and the heat loss of the storage as well. After discretizing the players’ strategy sets, the general course of the solution of the solar heat distribution problem (among the consumers) is given assuring maximal yields for the players. For two consumers, the solution is given in details along with several practical examples, where the Pareto optimality of the non-cooperative solution (Nash equilibrium) is checked and a more advantageous cooperative solution is suggested (which is also Pareto optimal if possible) underlying that cooperation generally provides higher payoff for each player than if they consumed according to conflicting non-cooperative behaviour.