Model predictive control of a hybrid heat pump system and impact of the prediction horizon on cost-saving potential and optimal storage capacity

The present paper analyses the cost-optimal sizing and hourly control strategy of a hybrid heat pump system for heating application, composed by an electrically-driven air source heat pump and a gas boiler. These hybrid systems represent a promising solution for the energy retrofit of existing buildings and new installations, being able to increase the efficiency of monovalent systems, especially at low external temperatures. The use of thermal storage can furtherly minimize both the operating cost and the primary energy consumption, shifting the operation of the heat pump to the most profitable periods. In this work, the optimal control problem has been investigated by means of mixed-integer linear programming, considering an ideal forecast of external temperature and thermal load on given horizon periods (i.e. model predictive control). Achievable cost savings with respect to a traditional rule-based control strategy with no storage are presented as a function of both prediction horizon and storage capacity in a dimensionless form. A relation between prediction horizon length and optimal storage capacity is shown. An example of application of the method is illustrated, showing cost savings up to 8%. A sensitivity analysis on the storage tank losses, climatic conditions, generators efficiency, and energy prices is also presented, showing the cost saving potential in all these different conditions.