## 7 Unoccupied Room Case  
After the analysis presented in the previous sections, another important aspect will be investigated hereafter. Actually, in many (residential) buildings, there are rooms that are not occupied for long time intervals and for these time intervals there is not a desired temperature \(\hat{T}_{i}\). Thus, the problem of managing the temperature of unoccupied rooms (that is, managing an intermittent use of some rooms) must be faced during the optimization, by assuming that the occupation schedule for a given day is known a priori. In fact, due to the existence of the thermal coupling between adjacent areas it is not always true that the minimization of the energy consumption is obtained by just switching off the heating system in the unoccupied rooms. For this purpose, the temperature set-point in a room in a time interval when it is not occupied (that is, when the user has not specified a desired temperature value), must be inserted into the optimization search space. As an illustrative example, we consider again the building of Section 5 on 5 December, where the scheduling of Table 3 has been applied but in this case the set-point values of rooms 2, 3 and 5 are not defined from 6:00 a.m. to 12:00 a.m.  
We consider only the case of ramp signals with radiators, because this is the most interesting case, as it turns out from the analysis of the previous section. In Figures 11 and 12, two rooms (room 3 and 5, respectively) in which the occupation is intermittent during the 24 h simulation are shown when the ARMAX model is used in simulation. On the other \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**Previous Day**} & \multicolumn{3}{c}{**Current Day**} \\ \hline
**Room** & **Step Case [K]** & **Ramp Case [K]** & **Saving [\%]** & **Step Case [K]** & **Ramp Case [K]** & **Saving [\%]** \\ \hline
1 & 8493 & 8498 & \(-0.06\) & 8523 & 8529 & \(-0.077\) \\
2 & 7787 & 7745 & 0.54 & 7821 & 7770 & 0.66 \\
3 & 7916 & 7822 & 1.2 & 7961 & 7863 & 1.24 \\
4 & 8393 & 8082 & 3.84 & 8468 & 8151 & 3.89 \\
5 & 8286 & 8040 & 3.05 & 8349 & 8105 & 3.01 \\
6 & 7660 & 7646 & 0.18 & 7696 & 7678 & 0.23 \\
7 & 6520 & 6479 & 0.62 & 6522 & 6495 & 0.41 \\ Total (J) & 55,055 & 54,313 & 1.37 & 55,340 & 54,592 & 1.37 \\ \hline \end{tabular}
\end{table} 
Table 7: Performance index value (4) for fan-coil units in both step and ramp case evaluated by applying the optimal set-point signals with the TRNSYS model using weather conditions of the previous days (4 December, i.e., those used by the genetic algorithm) and of the current day (5 December). Figure 10: External temperature and solar radiation in the two days considered for the simulation results, 4–5 December. Blue line: previous day. Green line: current day. hand, results related to the TRNSYS model are shown in Figures 13 and 14. It is possible to verify that the minimum energy consumption might be achieved by avoiding switching off the heating system during the unoccupied periods. Indeed, in this case the radiator of the room 3 is never switched off, although the room is empty. On the other hand, in room 5 the behavior is different, the radiator is off for a couple of hours during the unoccupied period. The energy consumption in the different cases is reported in Table 8.  
It appears that the genetic algorithm-based optimization can be also effectively employed in providing useful information to the user in deciding the policy of selection of the use of the rooms in the different periods of the day. Figure 11: One day simulation, 5 December, for room 3 with radiators in case of no set-point given by the user for given time intervals (ARMAX model). Figure 12: One day simulation, 5 December, for room 5 with radiators in case of no set-point given by the user (ARMAX model).