A large fraction of total electricity demand is comprised of end-use devices whose demand for energy is inherently deferrable in time. Of interest is the potential to use this latent flexibility in demand to absorb variability in power supplied from intermittent renewable generation. A fundamental challenge lies in the design of incentives that induce the desired response in demand. With an eye to electric vehicle charging, we propose a novel forward market for deadline-differentiated electric power service, where consumers consent to deferred service of prespecified loads in exchange for a reduced price for energy. The longer a consumer is willing to defer, the lower the price for energy. The proposed forward contract provides a guarantee on the aggregate quantity of energy to be delivered by a consumer-specified deadline. Under the earliest-deadline-first (EDF) scheduling policy, which is shown to be optimal for the supplier, we explicitly characterize a non-discriminatory, deadline-differentiated pricing scheme that yields an efficient competitive equilibrium between the supplier and consumers. We further show that this efficient pricing scheme, in combination with EDF scheduling, is incentive compatible in that every consumer would like to reveal her true deadline to the supplier, regardless of the actions taken by other consumers.

10aRM14-0021 aBitar, Eilyan1 aXu, Yunjian uhttps://certs.lbl.gov/publications/deadline-differentiated-pricing01738nas a2200145 4500008003900000245004300039210004200082260003700124300001400161520129400175653001301469100001701482700001801499856007501517 2016 d00aData-driven pricing of demand response0 aDatadriven pricing of demand response aSydney, AustraliabIEEEc11/2016 a224 - 2293 aWe 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.

10aRM14-0021 aKhezeli, Kia1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/data-driven-pricing-demand-response01673nas a2200145 4500008003900000245008900039210006900128260003700197300001400234520115800248653001301406100001701419700001801436856007301454 2016 d00aDecentralized control of distributed energy resources in radial distribution systems0 aDecentralized control of distributed energy resources in radial aSydney, AustraliabIEEEc11/2016 a296 - 3013 aWe consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and storage devices. For such systems, we consider the problem of designing controllers that minimize the expected cost of meeting demand, while respecting distribution system and resource constraints. Employing a linear approximation of the branch flow model, we formulate this problem as the design of a decentralized disturbance-feedback controller that minimizes the expected value of a convex quadratic cost function, subject to convex quadratic constraints on the state and input. As such problems are, in general, computationally intractable, we derive an inner approximation to this decentralized control problem, which enables the efficient computation of an affine control policy via the solution of a conic program. As affine policies are, in general, suboptimal for the systems considered, we provide an efficient method to bound their suboptimality via the solution of another conic program. A case study of a 12 kV radial distribution feeder demonstrates that decentralized affine controllers can perform close to optimal.

10aRM14-0021 aLin, Weixuan1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/decentralized-control-distributed