The present study analyses the performance of a heating system controlled by a model predictive control strategy, where the impact of different combinations of thermal energy storage tank volumes and installed PV power capacities are analysed. The novelty of the paper lies in studying both economic and energy impacts of each equipment combination in different locations, buildings, and indoor occupancy schedules. The payback period, the reduction of the electricity grid consumption, and the behaviour of the coefficient of performance of the heat pump are studied in detail for all cases. Results point out that from an economic point of view, to invest in a thermal energy storage tank provides shorter payback periods in comparison to scenarios with PV panels, due to the high price of the solar elements. However, the energy performance analysis highlighted that the use of PV panels contributes to achieve up to 34%, 54%, and 90% of reduction of the electricity grid consumption in Helsinki, Strasbourg, and Athens, respectively. Finally, it is worth noting that the increase of the thermal energy storage volume improves the coefficient of performance of the heat pump.