Minimum-cost control of HVAC systems under real time prices

Dynamic optimal control strategies for HVAC equipment can be derived to minimize electrical power usage or cost of operation. By accounting for the thermal dynamics of the building structure and furnishings and any dedicated thermal storage systems, dynamic approaches permit equipment use to be rescheduled, within constraints of equipment size and permissible indoor temperature variations, in order to improve part-load performance or to operate equipment when the price of electricity is lower. This paper focuses on the rescheduling problem under a very general rate structure known as real-time pricing, designed to accurately express short-term variations in the cost to the utility for producing and transmitting electricity. It examines the mathematical properties of the set of linear difference equations used to model thermal dynamics which are to be asymptotically stable, positive dynamic systems. This permits a much more rapid and elegant series of calculations to establish the optimal schedule than is possible with conventional linear programming techniques. Also presented are results from a hypothetical case study and from actual performance of an HVAC control system with storage