## 2 Setting of the Analysis
### Building  
In order to present general results that have not been influenced by the characteristics of a specific building, a building derived from the reference building proposed by IEA [24] was considered in this work. The simulated building was a two-floor family house characterized by a space heating demand of 45 kWh/m\({}^{2}\)y in the standard climate of Strasburg. The total floor area of the building considered in the simulations was 360 m\({}^{2}\), and the main building envelope thermal properties are presented in Table 2; in Figure 2, the 3D model of the building is sketched.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Envelope Component** & **Thickness (m)** & **U-Value (W/m\({}^{2}\)K)** \\ \hline Ground floor & 0.385 & 0.241 \\ Floor & 0.185 & 0.235 \\ Roof & 0.285 & 0.694 \\ Internal wall & 0.200 & 0.885 \\ External wall & 0.318 & 0.364 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometrical and thermo-physical data of the building envelope components. [25].  
Figure 1: Heating degree days for the selected locations and the considered years.  
Figure 2: 3D model of the building.  
The air change rate due to infiltration was considered to be 0.3 h\({}^{-1}\) for all of the thermal zones, and all of the windows were double pane characterized by a 4-16-4 mm construction and were filled with Argon gas. The frame was 15% of the total area of the window (total area of the glass and frame), and the overall transmittance of the window was U-window = 1.5 W/m\({}^{2}\)K. The window arrangement is shown in Table 3.  
Gains due to inhabitants and thermal gains caused by electric equipment were considered variable during the day, as shown in Figure 3. The thermal gain caused by a single inhabitant was divided in two parts: 20 W was considered the convective part of the thermal gain, and 40 W was the radiative part. The thermal gains due to electrical equipment were subdivided in half between the convective and radiative parts instead. For any parameter not explicitly mentioned in this section, the value proposed by IEA Task 44 for SFH45 was employed and not was not explicitly reported here for the sake of brevity [24].  
Obviously, the building considered in this study has different thermal load, depending on its location. In Table 4, the building design thermal load is reported as a function of the design temperature of the different locations.  
In the present paper, the software package TRNSYS was used to model the building, and in particular, the multizone building TRNSYS type 56 [26; 27].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Town** & \(\mathbf{t_{des}}\) (\({}^{\circ}\mathbf{C}\)) & \(\mathbf{P_{th,des}}\) (\(\mathbf{k}\)W) \\ \hline S. Benedetto del Tronto & \(-1\) & 6.2 \\ Milan & \(-5\) & 7.9 \\ Livigno & \(-19\) & 13.9 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Design temperature t\({}_{des}\) of the three towns and design thermal load P\({}_{th,des}\) of the HP at design temperature.  
Figure 3: Thermal gain profiles due to inhabitants and electrical equipment over a period of 24 h.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Orientation** & **Total Windows Area (m\({}^{2}\))** \\ \hline North & 14 \\ East & 20 \\ West & 20 \\ South & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Window arrangements of the considered building.