Contract design for frequency regulation by aggregations of commercial buildings

We investigate the contract design problem that an energy aggregator who participates in the wholesale market for Ancillary Services faces. Specifically, we consider a situation in which commercial buildings agree to adjust their heating, ventilation and air conditioning power consumption with respect to a nominal schedule, according to a signal sent by the aggregator. This signal may vary arbitrarily within a certain band, whose (time-varying) width is part of the agreed-upon contract between aggregator and building. In return, the aggregator offers monetary rewards to incentivize the individual buildings. This allows the aggregator to bundle the resulting capacities from different buildings and sell the total capacity in the spot market for frequency regulation. The aggregator's problem is to jointly determine nominal schedules, regulation capacities and monetary rewards to maximize its profit, while ensuring that the individual buildings have an incentive to participate. Assuming that there is no private information, we cast the contract design problem as a bilevel optimization problem, which we in turn reformulate as a mixed-integer program. We further show that if the building does not impose negative externalities on the aggregator, the problem reduces to a Linear Program.