Optimal control of electrical and thermal energy storage to minimise time-of-use electricity costs

Abstract

The advent of new electricity metering technologies means that consumers can now be billed for electricity using prices that vary with time-of-use. At the same time, new electrical energy storage systems and thermal energy storage systems give consumers an opportunity to control when they import electricity from the grid. In this paper we construct a power flow model of a system with both electrical and thermal energy storage, and use Pontryagin's principle to derive necessary conditions for a control strategy that minimises the cost of energy from the grid. The optimal control has just three control modes for each storage system: charge, off, and discharge. Which mode should be used at any instant for each of the storage system depends on the price of electricity relative to two critical prices for each of the storage systems. We use a realistic example to illustrate how the critical prices for each subsystem can be determined, and to determine the ideal capacity of each storage system.