## 5 Simulation Results
### Analysis of Temperature and Energy Consumption in the Coordinated Preheating Process  
To further explore the details of the preheating process, Figure 11 shows the temperature and power curves of users participating in Round #1, including the adjusted and original curves. In the temperature chart, the blue dotted line represents the temperature limit when awaking at home; The red dotted line represents the temperature limit when sleeping at home; The green area represents the sleeping period set by the user; The grey area refers to the period of awaking at home. Therefore, the indoor temperature curve must be in the orange and blue areas to meet user demands. The original curve adopts an on-off adjustment mode to ensure that the temperature does not exceed the limit.  
Figure 11b is the original temperature curve, and Figure 11d is the corresponding IAC power curve. It can be seen that the black solid line representing the indoor air temperature is located at the bottom of the orange and blue areas, which both meet the user's temperature demands and save energy. From 04:00 to 07:15, the user was sleeping, so the IAC adjusts the power to ensure that the temperature does not exceed the lower limit. The power is increased around 07:00 to ensure a comfortable temperature when the user wakes up. After the user leaves home, the IAC stops running, so \(T_{a}\) and \(T_{m}\) starts to drop. \(T_{m}\) decreases more slowly than \(T_{a}\) because the heat capacity of internal mass is larger than that of air. At this time, the internal mass transfers heat to the air. As the temperature difference between \(T_{a}\) and \(T_{m}\) gradually decreases, the heat loss becomes smaller, so the  
Figure 11: Comparison between optimization curves and original curves of a family participating in the Round #1.  
temperature drops faster first and then slower. The IAC power starts to rise at about 18:15 to ensure a comfortable temperature when users get home. As the air heat capacity is small, \(T_{a}\) rises rapidly. And due to the large temperature difference between the air and internal mass, the air begins to transfer a lot of heat to internal mass until temperature \(T_{m}\) is close to temperature \(T_{a}\). In addition, as the temperature demand decreases during sleep, although the IAC power drops to zero at 23:15, the temperature still meets the demands when the user sleeps (around 23:30).  
Figure 11a,c are the temperature and power curves after preheating adjustment. The marginal cost curve received by the user is the baseline curve in Figure 10c. It can be seen that the marginal cost is lower in the period of 04:00-04:30 and the period out of home, so the two periods are selected for preheating. Compared with the original power curve, the power of the IAC is higher during the preheating period, and the room temperature also increases while keeping within the set range. It is worth noting that, in order to reduce heat loss, the preheating power increases gradually in the second half of the time out of home. When users get home, the IAC is shut down for a long time, while the indoor temperature is still in a comfortable range, thus reducing the energy consumption during the high marginal cost period.