We adopt the perspective of an aggregator, which seeks to coordinate its purchase of demand reductions from a fixed group of residential electricity customers, with its sale of the aggregate demand reduction in a two-settlement wholesale energy market. The aggregator procures reductions in demand by offering its customers a uniform price for reductions in consumption relative to their predetermined baselines. Prior to its realization of the aggregate demand reduction, the aggregator must also determine how much energy to sell into the two-settlement energy market. In the day-ahead market, the aggregator commits to a forward contract, which calls for the delivery of energy in the real-time market. The underlying aggregate demand curve, which relates the aggregate demand reduction to the aggregator’s offered price, is assumed to be affine and subject to unobservable, random shocks. Assuming that both the parameters of the demand curve and the distribution of the random shocks are initially unknown to the aggregator, we investigate the extent to which the aggregator might dynamically adapt its DR prices and forward contracts to maximize its expected profit over a window of T days. Specifically, we design a data-driven pricing and contract offering policy that resolves the aggregator’s need to learn the unknown demand model with its desire to maximize its cumulative expected profit over time. The proposed pricing policy is proven to exhibit a regret over T days that is at most *O*(√*T*).

We present a theoretical analysis of virtual bidding in a stylized model of a single bus, two-settlement electricity market. North-American ISOs typically take a conservative approach to uncertainty, scheduling supply myopically in day-ahead (DA) markets to meet expected demand, neglecting the subsequent cost of recourse required to correct imbalances in the realtime (RT) market. This can result in generation costs that far exceed the minimum expected cost of supply. We explore the idea that virtual bidding can mitigate this excess cost incurred by myopic scheduling on the part of the ISO. Adopting a game-theoretic model of virtual bidding, we show that as the number of virtual bidders increases, the equilibrium market outcome tends to the socially optimal DA schedule, and prices converge between the DA and RT markets. We additionally analyze the effects of virtual bidding on social welfare and the variance of the price spread. Finally, we establish a repeated game formulation of virtual bidding, and investigate simple learning strategies for virtual bidders that guarantee convergence to the Nash equilibrium.

1 aMather, Jonathan1 aBitar, Eilyan1 aPoolla, Kameshwar uhttp://linkinghub.elsevier.com/retrieve/pii/S2405896317300526http://api.elsevier.com/content/article/PII:S2405896317300526?httpAccept=text/xmlhttp://api.elsevier.com/content/article/PII:S2405896317300526?httpAccept=text/plain