Study of the optimal control problem formulation for modulating air-to-water heat pumps connected to a residential floor heating system

For implementation in controllers with limited computational power, simplified optimal control formulations are desirable. For the case of a modulating heat pump system, the optimization problem is nonlinear due to the supply water temperature and load dependency of the heat pump coefficient of performance (COP). By neglecting these nonlinearities, e.g., by assuming a constant COP, the optimization problem becomes convex and fast convergence to the global minimum is ensured. This study quantifies the impact of these simplifications for the case of a modulating air-to-water heat pump connected to a residential floor heating system. A first comparison suggests a significant deterioration of the control performance. While the nonlinear formulations result in continuous operation at part load, the convex approximations give rise to large power fluctuations, increasing the energy cost with 7% to 16%. However, by penalizing power peaks in the cost function, the achieved control performances are almost identical. This reveals that the cost function is flat near the optimum. Compared to a conventional heating curve control strategy, the energy cost savings amount to 5% for optimization-based control strategies (in the case of a day/night tariff structure). Although less than expected, this improvement is still significant given the wide spread presence of the application.

► We study model based optimal control of a modulating air-to-water heat pump with floor heating.
► When accounting for heat pump nonlinearities, continuous part load operation is optimal.
► Optimal control performance can be achieved with simplified heat pump models.
► The energy savings compared to heating curve control are 1%.
► The cost savings with a day-night electricity price tariff are 5%.