**5. Conclusions**

In this paper, a comparison between a data-driven model implemented with an artificial neural network (ANN) and a physical-based model realized with an RC network is provided in an operative model predictive control (MPC). The controller was designed to provide a minimization of the total energy cost for the thermal demand satisfaction.

Focusing on the evaluation of the cooling season, a 16% reduction in the weekly cost with respect to the reference case was obtained, with an *RMSE* of about 1 ◦C in both cases (1.1 ◦C with the data-driven model and 0.9 ◦C with the physical-based approach). Although the data-driven model shows a good performance in replicating the building's thermal power profile, this trend is not confirmed when it works operatively in the controller. In fact, the comfort constraints are not respected for the 36% of the simulation time, with a maximum temperature deviation from the upper comfort limit of 1.8 ◦C. The physical-based model, instead, shows a discomfort percentage of 24% but a maximum deviation of only 0.5 ◦C.

The main conclusions of the presented work can be summarized as follows:


This latter point highlights the difficulty in implementing MPCs in real controls for energy flexible systems and suggests the need for further investigation. Indeed, it is important to consider that the results presented in this paper are related to a relatively simple building and no dedicated occupancy models were considered. When such advanced controls must be applied to more complex buildings where the role of users is not negligible, a purely physical-based approach can be computationally heavy, and it could be more convenient to use hybrid models. As a future development, it would be interesting to test the use of a hybrid model with an RC network structure and to provide a sensitivity analysis of the model according to the users' behavior in order to assess whether improvements in operational performance are also evident in the case of a simplified building.

**Author Contributions:** Conceptualization, A.M. and G.C.; methodology, A.M. and G.C.; validation, A.M. and G.C.; writing—original draft preparation, A.M.; writing—review and editing, G.C.; supervision, A.A.; project administration, F.P. and A.A.; funding acquisition, F.P. and A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Italian Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) within the framework of PRIN2015 project "Clean Heating and Cooling Technologies for an Energy Efficient Smart Grid", Prot. 2015M8S2PA.

**Conflicts of Interest:** The authors declare no conflict of interest.
