**3. Case Study**

For the case study, a detailed building model was implemented in TRNSYS using Type 56. The model was composed of a single thermal zone and the envelope characteristics were extrapolated by the Tabula Project [38] for detached houses. The building was north-facing, while all the walls faced outwards and the floor was placed on the ground (considered at a constant temperature of 15 ◦C). Table 1 reports the main geometrical and thermal properties of the building that was considered (a single family house), which were extrapolated by UNI-TR 11552:2014 [39].



The structure was characterized by high levels of thermal insulation and double-glazed windows, which were air-filled, were selected (g-value of 0.7). An air change per hour (ACH) equal to 0.2 h−<sup>1</sup> was selected. Internal gains included occupancy and artificial lighting [40]. The former was 120 W per person (occupancy density of 24 m<sup>2</sup> per person), while an artificial light density of 5 W m<sup>−</sup><sup>2</sup> was considered (artificial light turns on if total horizontal radiation is less than 120 W m<sup>−</sup><sup>2</sup> and turns off when the value exceeds 200 W m<sup>−</sup>2). The building was located in Rome, Italy (41◦55' N, 12◦31' E), and a Meteonorm [41] weather file was used as a typical meteorological year.

In this work, the cooling season was chosen for the MPC test. Analogous results, however, could have been obtained for the heating season. As mentioned in Section 2, no specific HVAC system was modeled; instead, an ideal cooling control was used in Type 56 to extrapolate the training data [14]. In this way, the MPC control actions were applied as convective heat gains to the air nodes (positive for heating and negative for cooling). An indoor air temperature range of 25–27 ◦C was chosen as the comfort condition (i.e., *T*min and *T*max in Equation (10)) and a maximum cooling load power of 7 kW was fixed (i.e., *Q*max in Equation (11)) [42]. Since the cooling power was directly applied to the air-zone, the ideal HVAC can be compared to a traditional heat pump split system. Assuming an average COP of 2.5, the thermal energy requirement can be converted into electricity consumption, and the penalty signal can be obtained consequently (Equation (1)).

For the reference case, a fixed set-point of 26 ◦C was simulated in order to provide a comparison between the building as controlled with the MPC and without the MPC.
