## 7 Results and Discussion
### Winter  
On weekdays, the temperature is set to 18 \({}^{\circ}\)C during the night and during working hours when the house is typically unoccupied. It increases to 20 \({}^{\circ}\)C in the morning for waking up and preparation and to 21 \({}^{\circ}\)C in the evening for comfort during home activities, before dropping to 19 \({}^{\circ}\)C for sleeping. On weekends, when people tend to be at home more, the temperature starts at 18 \({}^{\circ}\)C during the night, rises to 20 \({}^{\circ}\)C in the early morning, and stays at 21 \({}^{\circ}\)C throughout the day to ensure comfort during indoor activities, before settling at 19 \({}^{\circ}\)C at bedtime. This profile ensures a comfortable environment, while optimizing energy use. Figures 4 and 5 show the outside temperature profile and the temperature profile inside the enclosures of a typical week during winter, respectively. As mentioned earlier, the MPC model is first executed to obtain the most reliable possible heating consumption curve as a prediction for the optimization model of the energy consumption. Figures 6 and 7 show the temperatures obtained and the thermal power required by the HVAC system, respectively. Figure 4: Outside temperature profile of a typical week during winter. Figure 5: Temperature profile inside the enclosures in a typical week during winter. In Figure 6, it is evident that the actual temperatures follow the evolution of the target temperature. It can also be observed that there is a delay between the setpoint increase and the system response due to thermal inertia. The blue and yellow lines in Figure 6 are coincident and overlapping with the green line, so that only the green line is visible in this figure. In Figure 7, it is shown that the thermal power used exhibits periodic peaks, indicating that the system is responding to changes in the target temperature. It is observed that the living room consistently requires more energy than the other two bedrooms, because it has higher thermal losses and higher heating requirements in this zone due to higher outdoor exposure and higher volume. The peaks in the HVAC system's energy consumption shown in Figure 7 coincide with the moments when the indoor target temperatures change, as illustrated in Figure 6. During winter, the system must quickly compensate for the differences between the ambient temperature and the new, higher target temperatures. This leads to increases in power consumption, especially when the system adjusts the heating to reach the higher temperatures. Once the desired temperature is reached, the consumption decreases, stabilizing until the next significant change in the target temperature. By analyzing both figures together, it can be concluded that the HVAC system is successfully meeting the temperature objectives. Using the total HVAC consumption curve, combined with the electricity consumption of other household loads, photovoltaic production, and grid electricity prices, the optimization model is run to determine the best use of the different energy sources. The results are shown in Figure 8, which shows the electricity consumption of HVAC, other household loads, and the photovoltaic production. Figure 6: Evolution of the temperature inside the enclosures for a winter week. Figure 7: Thermal power required by the HVAC system in each enclosure for a winter week. Figure 8 shows that, during the daylight hours of the first two days, the PV generation significantly exceeds the combined demand of HVAC and other loads, creating an opportunity for energy storage or export to the grid. However, during nighttime or periods of low sunlight, PV generation drops significantly, and the home relies entirely on external power sources to meet the relatively stable consumption of HVAC and the rest of the loads.