Reduced-Order Models for Load Management in the Power Grid

In recent years, considerable research efforts have been directed towards designing control schemes that can leverage the inherent flexibility of electricity demand that is not tapped into in today's electricity markets. It is expected that these control schemes will be carried out by for-profit entities referred to as aggregators that operate at the edge of the power grid network. While the aggregator control problem is receiving much attention, more high-level questions of how these aggregators should plan their market participation, interact with the main grid and with each other, remain rather understudied. Answering these questions requires a large-scale model for the aggregate flexibility that can be harnessed from the a population of customers, particularly for residences and small businesses. The contribution of this thesis towards this goal is divided into three parts: In Chapter 3, a reduced-order model for a large population of heterogeneous appliances is provided by clustering load profiles that share similar degrees of freedom together. The use of such reduced-order model for system planning and optimal market decision making requires a foresighted approximation of the number of appliances that will join each cluster. Thus, Chapter 4 provides a systematic framework to generate such forecasts for the case of Electric Vehicles, based on real-world battery charging data. While these two chapters set aside the economic side that is naturally involved with participation in demand response programs and mainly focus on the control problem, Chapter 5 is dedicated to the study of optimal pricing mechanisms in order to recruit heterogeneous customers in a demand response program in which an aggregator can directly manage their appliances' load under their specified preferences. Prices are proportional to the wholesale market savings that can result from each recruitment event.