A large fraction of the total electric load is comprised of end-use devices whose demand for energy is inherently deferrable in time. Of interest is the potential to leverage on such latent flexibility in demand to absorb variability in power supplie
d from intermittent renewable generation. The challenge, however, lies in designing incentives to reliably induce the desired response in demand. With an eye to electric vehicle charging, we propose a novel forward market for differentiated electric power services, where consumers consent to deferred service of pre-specified loads in exchange for a reduced per-unit price for energy. The longer a consumer is willing to defer, the larger the reduction in price. 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 (IC) in that every consumer would like to reveal her true deadline to the supplier, regardless of the actions taken by other consumers.
In an electric power system, demand fluctuations may result in significant ancillary cost to suppliers. Furthermore, in the near future, deep penetration of volatile renewable electricity generation is expected to exacerbate the variability of demand
on conventional thermal generating units. We address this issue by explicitly modeling the ancillary cost associated with demand variability. We argue that a time-varying price equal to the suppliers instantaneous marginal cost may not achieve social optimality, and that consumer demand fluctuations should be properly priced. We propose a dynamic pricing mechanism that explicitly encourages consumers to adapt their consumption so as to offset the variability of demand on conventional units. Through a dynamic game-theoretic formulation, we show that (under suitable convexity assumptions) the proposed pricing mechanism achieves social optimality asymptotically, as the number of consumers increases to infinity. Numerical results demonstrate that compared with marginal cost pricing, the proposed mechanism creates a stronger incentive for consumers to shift their peak load, and therefore has the potential to reduce the need for long-term investment in peaking plants.
We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand functi
on is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.
