Stochastic dynamic optimization of consumption and the induced price elasticity of demand in smart grids

Abstract

This thesis presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price-elasticity of demand created by optimal utilization of storage and the flexibility to shift certain demands to periods of lower prices. The approach is based on analytical characterization of the consumer's optimal policy and the associated value function in a finite-horizon stochastic dynamic programming framework. A general model is first presented, which incorporates both load-shifting and storage, and then, the model is decoupled into two subproblems, one for load-shifting and the other for storage. The study of optimal utilization of storage, which is performed analytically and in the presence of ramp constraints, reveals, as a particularly compelling finding, that the value function is a convex piece-wise linear function of the storage state. Moreover, it is shown that the expected monetary value of storage increases with price volatility, and that when the ramping rate is finite, the value of storage saturates quickly as the capacity increases, regardless of price volatility. Furthermore, it is shown that although the demand for electricity is often deemed to be highly inelastic, optimal utilization of local storage capacity induces a considerable amount of price elasticity of demand. The study of the load-shifting problem is performed under both perfect and partial information about price distribution. It is shown that load-shifting induces considerable consumer savings that increase with price volatility. Furthermore, it is shown that the opportunity to optimally schedule the shiftable loads creates a considerable amount of price elasticity, even when the aggregate consumption over a long period remains insensitive to price variations.