## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**from**} & \multirow{2}{*}{**1C**} & \multirow{2}{*}{**1C**} & \multirow{2}{*}{**2A**} & \multirow{2}{*}{**3B**} & \multirow{2}{*}{**4C**} & \multirow{2}{*}{**5A**} & \multirow{2}{*}{**6B**} & \multirow{2}{*}{**7C**} & \multirow{2}{*}{**8A**} & \multirow{2}{*}{**9B**} & \multirow{2}{*}{**Total**} \\ \cline{5-10} \multicolumn{1}{c}{} & & & & & & & & & 329 & kWh \\  & & (0.9\%) & & & (6.2\%) & & & & (7.1\%) \\ \hline
**2A** & \(\begin{matrix}-44\\ (-0.7\%)\end{matrix}\) & & 2 & 18 & & & & & \(-23\) & kWh \\  & & (0.0\%) & & & (0.3\%) & & & & (\(-0.4\%)) \\ \hline
**3B** & \(\begin{matrix}-2\\ (0.0\%)\end{matrix}\) & & & & & \(-46\) & & & & \(-49\) & kWh \\  & & & & & (\(-0.6\%)) & & & (\(-0.7\%)) \\ \hline
**4C** & \(\begin{matrix}-28\\ (-4.6\%)\end{matrix}\) & & & & \(-29\) & & \(\begin{matrix}-32\\ (-0.5\%)\end{matrix}\) & & & \(\begin{matrix}-323\\ (-5.2\%)\end{matrix}\) & & & \(\begin{matrix}-638\\ (-10.2\%)\end{matrix}\) \\ \hline
**5A** & \(\begin{matrix}-18\\ (-0.4\%)\end{matrix}\) & & 29 & & \(\begin{matrix}-13\\ (0.6\%)\end{matrix}\) & & & \(\begin{matrix}-181\\ (-0.3\%)\end{matrix}\) & & & \(\begin{matrix}-183\\ (-3.6\%)\end{matrix}\) & kWh \\ \hline
**6B** & & & 46 & 13 & & & & 148 & 207 & kWh \\  & & (0.8\%) & & (0.2\%) & & & (2.4\%) & (3.4\%) \\ \hline
**7C** & & & 323 & & & & 5 & 328 & kWh \\  & & & (4.2\%) & & & & (0.1\%) & & (4.3\%) \\ \hline
**8A** & & & & 181 & & \(-5\) & & 86 & 261 & kWh \\  & & & (2.7\%) & & (-0.1\%) & & (1.3\%) & (3.9\%) \\ \hline
**9B** & & & & & \(-148\) & & \(-86\) & & \(-234\) & kWh \\  & & & & (-1.8\%) & & & (-1.0\%) & & (-2.8\%) \\ \hline \hline \end{tabular}  
* to be read row by column, (-) signs meaning that the row apartment is giving energy to the column apartment; (+) signs meaning that the row apartment is stealing energy to the column apartment.  
\end{table} 
Table 4: Percentage * of heat given or stolen between adjacent apartments, base scenario. \"steals heat\" from both apartments 2A and 4C (respectively 1.0% and 6.2% of its total energy need for space heating). On the other hand, even a central apartment that could benefit from its position (as for example apartment 4C) can nullify this advantage when using set-point temperatures higher than the one of adjacent apartments, losing up to 10% of its energy need. However, an unexpected behavior can be highlighted for apartments 2A, 5A and 8A. Although, in fact, apartment 5A has set the lowest average set point temperature, it still gives heat to both adjacent apartments on the same vertical (2A and 8A). This is because set-point temperature is reached in the apartments only during the operating hours of the heating plant, while, for the rest of the day, the temperature inside the apartment 5A is always higher than that in 8A and 2A, due to its favorable position. This is evident in Figure 7, which reports the indoor temperature for the above-mentioned three apartments in a representative week of the heating season. Referring to Figure 7, it is highlighted that in a day there are two \"heating periods\", according to the schedule of the heating plant (from 6 to 8 a.m. and from 15 to 22 p.m.). From the figure, it is evident that the installed heating system quickly manages to bring the apartment up to the set-point temperature, even in situations of daily temperature excursions. For the sake of completeness, Figure 8a,b show the trends of the daily indoor temperature in the above-mentioned apartments during the warm-up times simulated for January the 5 th, which is representative of a cold winter day. From the figure, it can be highlighted that, even under high load conditions (i.e., low outdoor temperature), the heating system