## 3 Results and Discussion
Indeed, these small deviations may be caused by different causes, as following:  
1. potential differences between real and estimated thermal transmitances and thermal mass of the building;
2. for the purposes of the present analysis, the set-point temperature is set as average measured weekly temperature of the entire thermal zone;
3. the energy consumption of single dwellings is estimated based on HCAs readings, which depend also on the estimation of radiators' thermal output performed through the dimensional method described in [18,19]. It has been demonstrated that different installation conditions can lead \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Dwelling Number**} & **Estimated Normalized Energy** & **Estimated Normalized Energy** & **Measured Normalized** & **Error [\%]** \\  & **Consumption, BC [KWh]** & **Consumption, AC [kWh]** & **Energy Consumption [kWh]** & **BC** & **AC** \\ \hline
1C & 4918 & 5424 & 5673 & \(-13\%\) & \(-4\%\) \\
2A & 6578 & 6847 & 6796 & \(-3\%\) & \(1\%\) \\
3B & 7686 & 7704 & 7334 & \(5\%\) & \(5\%\) \\
4C & 6600 & 7351 & 7685 & \(-14\%\) & \(-4\%\) \\
5A & 4552 & 5934 & 5578 & \(-18\%\) & \(6\%\) \\
6B & 4470 & 7151 & 7386 & \(-39\%\) & \(-3\%\) \\
7C & 5846 & 9015 & 9617 & \(-39\%\) & \(-6\%\) \\
8A & 5206 & 7885 & 8919 & \(-42\%\) & \(-12\%\) \\
9B & 8042 & 9882 & 9460 & \(-15\%\) & \(4\%\) \\ \hline TOTAL & 53897 & 67193 & 68449 & \(-21\%\) & \(-2\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of validation before and after the calibration process (respectively BC and AC). to deviations between operating and standard radiators' thermal output in a range of about 5-15% [27]. The heat flowing through the adjacent wall (\(Q_{h}\) [Wh]) of two dwellings in one hour, \(h\), has been calculated as per Equation (4):  
\[Q_{h}=U\cdot A\cdot(T_{in}-T_{out})\cdot h \tag{4}\]  
where U, [W m\({}^{-2}\) K\({}^{-1}\)] is the thermal transmittance of the wall, A [m\({}^{2}\)] is the area of the wall and \(T_{in}-T_{out}\), \([K]\) is the temperature difference between the inner and the outer layer of the wall (with \(T_{in}\) indicating the temperature measured at the inner surface--i.e., the surface of the analyzed dwelling--while \(T_{out}\) the outer surface temperature--i.e., the temperature of the adjacent dwelling). The total heat stolen/given through each wall separating adjacent dwellings was calculated as per Equation (5). \[Q_{stolen/given}=\sum_{h=1}^{8760}Q_{h} \tag{5}\]  
In this way, the heat calculated as per Equations (4) and (5) is positive when the reference environment is gaining heat; on the contrary, it is negative when the heat is transferred from the reference environment to the adjacent one. For each \(i\)-th apartment, the heat flowing through the walls adjacent with other apartments was calculated and it was assessed how much these heat flows would impact on the total energy consumption of the apartment itself as per Equation (6). \[\frac{Q_{stolen/given,i}}{Q_{tot,i}}\cdot 100 \tag{6}\]  
The results are reported for each apartment in Table 4 for the base scenario first. It is worth to observe that results obtained by this calculation depend both on the set-point temperature and the 'position' of the dwelling with respect to the others. For sake of completeness, a summary of the average seasonal value of the set-point temperature used to simulate the base scenario is given in Table 5.  
Generally speaking, results show that in case of full operation of the building, the phenomenon of heat-thefts is almost negligible, representing on average 0.5% of the annual energy consumption for heating purposes of a single dwelling with the maximum absolute value of 6.2%. Observing the apartment with the lowest average set-point temperature (1C), it is possible to notice that this