Mixed-integer model predictive control of variable-speed heat pumps

Abstract

Heating and cooling buildings cause a large and growing portion of the world’s carbon emissions. These emissions could be reduced by replacing inefficient or fossil-fueled equipment with efficient electric heat pumps. Recent research has shown that variable-speed heat pumps (VSHPs) could also provide a variety of power system services, such as price- or carbon-based load shifting, peak demand reduction, emergency demand response, and frequency regulation. By providing some or all of these services, VSHPs could facilitate the integration of wind and solar power into the grid, accelerating decarbonization of other economic sectors. However, the provision of power system services poses new and challenging VSHP control problems. Model predictive control (MPC) is a promising approach to these problems. MPC combines weather and load predictions, online optimization, and a mathematical model of a VSHP’s performance under varying ambient conditions. With few exceptions, existing VSHP models neglect two important features that arise in practice: (1) dependence of efficiency and capacity on compressor speed and indoor and outdoor temperatures, and (2) inability of VSHPs to operate at low compressor speeds. In this paper, we develop a new VSHP control model that considers both features. The model expresses the VSHP’s power consumption and heat production as affine functions of the driving temperatures and compressor speed. The model also includes a binary variable that constrains the VSHP to be either turned off, or operating within a range of acceptable compressor speeds using mixed-integer programming (MIP). This VSHP model and optimization strategy is combined with neural network based heat load prediction in MPC simulations. These simulations suggest that this approach could reduce energy costs by 9–22% and carbon emissions by up to 22%, relative to MPC with existing VSHP models.