The intertemporal utility of demand and price elasticity of consumption in power grids with shiftable loads

This paper presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price elasticity of consumption induced by optimally shifting flexible demands within a fixed time window. The approach is based on deriving the optimal load-shifting policy through a finite horizon stochastic dynamic program, and the analysis is performed under both perfect and partial information about price distribution. An aggregate demand model is constructed from individual demands with random arrivals and random deadlines. Under this model, the aggregate demand becomes a function of price only, and thus allows for quantitative characterization of the utility of demand and price elasticity. While the demand for electricity is often deemed to be highly inelastic, it is shown in this paper that optimal load-shifting can create a considerable amount of price elasticity, even when the aggregate consumption over a long period remains constant.