Deadline Differentiated Pricing of Deferrable Electric Loads

Abstract

Abstract-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 pre-specified 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-deadlinefirst (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.

Market implementation of multiple-arrival multiple-deadline differentiated energy services

“…Hence, we conclude that no consumer will intend to violate the optimal allocation r * (x), T a * (x) , T d * (x) , l * (x) under the prices given by (13).…”

“…In the proof of Theorem 8, the Lagrange multiplier method is applied, which is well known to have a heuristic economic interpretation [27]. In view of the price expression (13), the Lagrange multipliers work as implicit price factors. To further explain this, each multiplier indexed by [k 1 k 2 · · · k r ] adds a nonnegative weight to a corresponding term of demand tail, denoted by [r − d m=a+1 k m ] + .…”

Menu-Based Pricing for Charging of Electric Vehicles With Vehicle-to-Grid Service

“…However, we show that in our setting there exist pricing strategies which maximize the ex-post social welfare. Note that ex-post social welfare maximization is the same as (16).…”

A stochastic approximation method for price-based assignment of Electric Vehicles to Charging Stations

“…In this paper, we consider price-elastic users (users willing to park to a more remote CS in exchange for a lower price). Most previous works consider the self-optimization of a single CS [1], which is only part of the assignment problem considered here. In works where multiple CSs are modeled, the user's elasticity is considered either as known [2] or as a parameter that the user can report to the system if given the right incentives [3].…”