Deadline differentiated pricing of deferrable electric power service

As the penetration of wind and solar energy into the electric grid continues to grow, there will be an increasing need to evolve demand-side solutions capable of compensating the inherent variability in power supply from such renewable resources. Today, demand is largely treated as inelastic. However, the power requirements of many commercial and residential loads are such that a fraction of power demand at any given moment is inherently deferrable in time subject to a deadline constraint on the total energy supplied. Examples include thermal systems such as refrigerators, water heaters, HVAC systems, data centers, and, assuming mass adoption of plug-in electric vehicles, batteries. In this paper, we discuss some limitations of dynamic pricing mechanisms (e.g., real-time pricing) as a means of inducing demand response and suggest a novel forward contracting mechanism for deadline-differentiated deferrable energy contracts to alleviate some of these difficulties. Essentially, consumers who consent to deferral of their consumption in time - subject to a pre-specified deadline - will receive a discounted per-unit price for said energy. In this way, the supplier is capable of extracting flexibility in the delivery of energy to participating deferrable loads, while consumers receive a discount on energy with an associated deadline guarantee on delivery. The supply side is modeled as random to capture variability in renewable power supply. Using a general model for consumer preferences to capture the effect of consumption deferral on utility, we prove the existence of a competitive equilibrium and provide a characterization of deadline-differentiated prices yielding such an equilibrium. We also discuss provably optimal online scheduling policies to dynamically allocate the variable supply to a bundle of deadline-differentiated energy tasks.