In the view that the energy sector involves several agents that are either non cooperating or partially cooperating, it is natural to analyze their interactions within the framework of game theory. In this presentation, we consider two such situations that can be modelled as bi-level mathematical programs. Both of them involve a smart grid that allocates energy in some 'optimal' fashion.
The first application is concerned with the issue of peak load management through price signals. Acting as a monopolist, an electricity provider sets hourly prices, aiming at simultaneously generating profit and minimizing peak load. At the lower level, a smart grid composed of interconnected meters, owned by consumers, optimally schedules the operation of household appliances, taking into account user preferences with respect to operating times, and various technical constraints. Three models are actually considered. The first involves preemptive tasks that can be interrupted and re-started at will within a time window centered around the 'ideal' interval specified by the user. Whenever the schedule does not match the wish of the customer, a penalty is incurred. The second model addresses the issue of non-preemptive appliances, while the third considers a mixed situation that involves both types.
The second application is motivated by the technology of bi-directional energy transfer (grid-to-vehicle G2V and vehicle-to-grid V2G), whose impact will grow with the massive deployment of electric vehicles.
Specifically, we consider the operator of a fleet of electric vehicles within a day-ahead wholesale energy market monitored by a smart grid. In this context, the operator plays the roles of both a consumer and a producer. It maximizes its revenue by determining optimal bidding and offer strategies, taking into account competing producers on the one hand and, on the other hand, the behaviour of the smart grid that strives for welfare maximization when allocating power to fulfill time-varying demand.
Economic and operational interpretations are drawn from a case study based on the power system of the province of Ontario, Canada.