Avoiding overages by deferred aggregate demand for PEV charging on the smart grid

We model the aggregate overnight demand for electricity by a large community of (possibly hybrid) plug-in electric vehicles (PEVs) each of whose power demand follows a prescribed profile and is interruptible. The community is served by a regional electrical utility which is assumed to purchase electricity from a state/national distribution grid according to a flat-rate Φ per kilowatt-unit-time up to a threshold L, and thereafter overage (demand > L) charges π > Φ are leveed per kilowatt-unit-time. Rather than a spot-price system for household consumers (which would necessarily need to be operated by automated means overnight when most consumers sleep), the 'grid' (regional utility) is 'smart' in that it monitors its total load and, when overages threaten, can reduce load by signaling certain consumers to interrupt charging and defer their charging load by one unit of time. In this paper, we model the uninterrupted load by a Gaussian process which we justify by means of a functional central limit theorem (FCLT). This limiting Gaussian process is the arrival process of a discrete-time queue which is used to model the (partially) interrupted and deferred load over a finite time-horizon. We can then compute the mean amount of overage at the end of this time horizon (say at 6 AM when charging is to be completed ahead of the morning commute).