Review of control strategies for improving the energy flexibility provided by heat pump systems in buildings

•A review of the literature on supervisory controls for heat pumps was carried out.•Rule-based or model predictive controls can provide energy flexibility in buildings.•The economic objective is the most commonly used for model predictive control.•Further flexibility objectives and experimental studies should be developed. The present work constitutes a review of the existing literature on supervisory control for improving the energy flexibility provided by heat pumps in buildings. A distinction was drawn between rule-based controls (RBC) and model predictive controls (MPC), given the clear differences in their concept and complexity. For both kinds, the different objectives claimed by these strategies have been reviewed, as well as the control inputs, disturbances and constraints. Notably in MPC, the monetary objective (reduction of the energy costs) has been the most utilized in the literature, therefore the authors advocate for the further study of other objectives related to energy flexibility. Further than the control strategies themselves, the different thermal storage options (necessary to activate the flexibility) have also been reviewed, the built-in thermal mass seeming more cost-effective than water buffer tanks in this regard. Based on these conclusions, recommendations for further research topics are drawn.