Optimal control of heat-pump/heat-storage systems with time-of-day energy price incentive

The maximum principle of optimal control theory is applied to the problem of optimizing the operation of a heat pump, when a storage capability is available and the electrical utility offers time-of-day price incentives in order to help level its diurnal load profile. The cost functional for optimal control is the monetary cost of purchased electrical energy. A bilinear model for the heat pump is assumed. When the ambient temperature is cyclic over the 24-hour period of the price pattern, periodic boundary conditions apply and the closed extremal trajectories are found to be unique and easily determined with a one-dimensional numerical search. These extremals have simple characteristics and reveal plausible strategies for minimizing the cost of purchased energy. They are potentially implementable with a simple, micro-processor-based controller.This work was supported in part by Energy, Mines, and Resources, Canada, Research Agreement No. 89.