Noncooperative Games for Autonomous Consumer Load Balancing over Smart Grid

Abstract

Traditionally, most consumers of electricity pay for their consumptions according to a fixed rate. With the advancement of Smart Grid technologies, large-scale implementation of variable-rate metering becomes more practical. As a result, consumers will be able to control their electricity consumption in an automated fashion, where one possible scheme is to have each individual maximize its own utility as a noncooperative game. In this paper, noncooperative games are formulated among the electricity consumers in Smart Grid with two real-time pricing schemes, where the Nash equilibrium operation points are investigated for their uniqueness and load balancing properties. The first pricing scheme charges a price according to the average cost of electricity borne by the retailer and the second one charges according to a time-variant increasing-block price, where for each scheme, a zero-revenue model and a constant-rate revenue model are considered. In addition, the relationship between the studied games and certain competitive routing games from the computer networking community, known as atomic flow games, is established, for which it is shown that the proposed noncooperative game formulation falls under the class of atomic splittable flow games. The Nash equilibrium is shown to exist for four different combined cases corresponding to the two pricing schemes and the two revenue models, and is unique for three of the cases under certain conditions. It is further shown that both pricing schemes lead to similar electricity loading patterns when consumers are only interested in minimizing the electricity costs without any other profit considerations. Finally, the conditions under which the increasing-block pricing scheme is preferred over the average-cost based pricing scheme are discussed.