## 3 Energy-Saving Optimization Model
### Energy-Saving Optimization Algorithm Flow
#### 3.3.2 Temperature Dimension  
For temperature-type appliances like air conditioners, the key to optimization is to predict the environment changes of air conditioners in a future period. In the case of keeping the operating status unchanged in the coming period and adopting a certain control command to change the operating status, respectively, the indoor temperature is predicted with the first-order indoor temperature model proposed in [11], as shown in Equation (12).  
\[x^{in}[t+1]=x^{in}[t]+a(x^{out}[t]-x^{in}[t])+g\cdot p^{HVAC}[t]+c. \tag{12}\]  
In this equation, \(a\) is the sensitivity coefficient of the indoor and outdoor temperature difference, \(g\) is the appliance's operating contribution coefficient, and \(c\) is the constant parameter. The temperature  
Figure 2: Energy saving optimization flow for time-sensitive appliances.  
utility value is pre-evaluated in combination with the corresponding operation status and the predicted indoor temperature value.  
The process of energy-saving optimization in the temperature dimension is shown in Figure 3.  
The above process can be divided into the following steps:  
1. Predict the indoor temperature change under the condition that the operating mode remains unchanged in the future period of \(\Delta t\);
2. Pre-evaluate the temperature utility during the future time period of \(\Delta t\) in combination with the operating status and the indoor temperature prediction curve;
3. Mark the set of all the currently operational control commands as the control command set, and determine whether the control command set is empty. If it is empty, go to (7); if not, go to (4);
4. Select one of the operable control commands to predict the operating status, operating power, and indoor temperature change of the future period of \(\Delta t\) after the control command is issued;
5. Pre-evaluate the temperature utility by combining the new operation status and indoor temperature prediction;
6. Combine the temperature utility estimation result before and after taking the control command, calculate the energy-saving costs brought by the control command, and judge whether it is less than the setting energy-saving temperature utility cost threshold \(\xi\). If it is less than \(\xi\), the control command is put into the available control command set and would be deleted from the control command set; if it is higher than \(\xi\), delete the control command from the control command set. Then, return to step (4);
7. Traverse all control commands of the available control command set, perform an integral calculation on the power curve predicted in (4), and find the control command with the smallest total power consumption, which is the optimal energy-saving control strategy.  
Figure 3: Energy saving optimization flow in the temperature dimension.  
In particular, the cluster optimization of multiple air conditioners in the same area can be abstracted into the optimization problem of an air conditioner with multiple-gear operating power. In addition to turning on, turning off, and adjusting the set temperature, the control command of the air conditioner includes selecting a power gear position, so the operational control command set is a combination command for setting the temperature and the power gear position. After that, the optimization algorithm flow is consistent with a single air conditioner.  
Combined with the operation principle of the fixed-frequency air conditioner and Formula (12), the power curve of the air conditioner and the indoor temperature in future periods are predicted, as shown in Figure 4.