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{\textquoteright}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{\textquoteright}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 consider the setting in which an electric power utility seeks to curtail its peak electricity demand by offering a fixed group of customers a uniform price for reductions in consumption relative to their predetermined baselines. The underlying demand curve, which describes the aggregate reduction in consumption in response to the 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 utility, we investigate the extent to which the utility might dynamically adjust its offered prices to maximize its cumulative risk-sensitive payoff over a finite number of T days. In order to do so effectively, the utility must design its pricing policy to balance the tradeoff between the need to learn the unknown demand model (exploration) and maximize its payoff (exploitation) over time. In this paper, we propose such a pricing policy, which is shown to exhibit an expected payoff loss over T days that is at most O(\√T), relative to an oracle who knows the underlying demand model. Moreover, the proposed pricing policy is shown to yield a sequence of prices that converge to the oracle optimal prices in the mean square sense.

}, keywords = {RM14-002}, doi = {10.1109/SmartGridComm.2016.7778765}, author = {Khezeli, Kia and Eilyan Bitar} }