A differential game model of power exchange between interconnected utilities

A qualitative model is proposed for the economic analysis of the power exchange between two utilities. The model combines an infinite horizon optimal control formulation with a cooperative game approach. The power exchange problem is decomposed into two subproblems, the first one dealing with the determination of an efficient exchange schedule, and the other dealing with the determination of an appropriate side payment in order to equalize the gains derived by the utilities from the exchange program. It is shown that the power exchanged is determined by a comparison at each instant of time of the marginal production costs, while its price is determined by a comparison between the two cost schedules obtained in autarky, and in cooperation respectively. Several pricing schemes realizing the desired side payment are discussed.