## 2 Demand Response Modeling for ACL  
### Thermal Parameter Model for the ACL  
Two methods for building the thermal parameter model for ACLs are widely discussed and used in previous research: (1) a modeling method based on equivalent thermal parameters [15; 27], and (2) a modeling method based on cooling load calculations [28]. The latter is based on simpler principles but may involve complex calculations and a low degree of preciseness. Hence, we chose to build our model on the basis of equivalent thermal parameters. The models built upon the equivalent thermal parameter method can be further categorized as physically based electrical models [27] and simplified equivalent thermal parameter models [15]. Although the physically based electrical model is more precise, it involves a complex structure and a large number of calculations. Therefore, it is difficult to apply the physically based electrical model in practice on a large scale. This study focuses on how to reduce the peak load by using ACLs as a load shedding measure. In practice, the proposed strategy requires a quick calculation of schedulable capacity of ACLs on the basis of factors such as temperature. Hence, considering the practical application of the proposed strategy, we chose to use the simplified equivalent thermal parameter model.  
Figure 1 illustrates a simplified equivalent thermal parameter model. This model is applicable to the simulation analysis of the ACL for residential users and small commercial customers. In the figure, \(C_{m}\) is the mass heat capacity; \(C_{a}\) is the air heat capacity; \(Q\) is the heat rate; \(UA\) is the standby heat loss coefficient, where \(R_{1}=1/UA\); \(UA_{mass}\) is the standby mass heat loss coefficient, where \(R_{2}=1/UA_{mass}\); \(T_{in}\) is the air temperature inside the house; \(T_{out}\) is the ambient temperature; and \(T_{m}\) is the mass temperature inside the house [15].  
As simplified from Figure 1, the following dynamic model can be derived for the indoor temperature [15]:  
\[T_{in,t+1}=T_{out,t+1}-(T_{out,t+1}-T_{in,t})e^{-\Delta t/RC},\ s_{AC}=0 \tag{1}\]  
\[T_{in,t+1}=T_{out,t+1}-COP\cdot P_{AC,t}/A-(T_{out,t+1}-COP\cdot P_{AC,t}/A-T_{ in,t})e^{-\Delta t/RC},\ s_{AC}=1 \tag{2}\]  
In the model, \(T_{in,t}\) refers to the indoor temperature at time \(t\), \(T_{out,t+1}\) to the outdoor temperature at time \((t+1)\), \(e^{-\Delta t/RC}\) to the heat dissipation parameters, \(\Delta t\) to the time interval, \(R\) to the equivalent thermal resistance, \(C\) to the equivalent thermal capacity, \(COP\) to the coefficient of performance, \(P_{AC,t}\) to the the ACL power output at time \(t\), \(A\) to the conduction coefficient, and \(S_{AC}\) to the the switching state of the air conditioner, where \"1\" and \"0\" denote the air conditioner being on and off, respectively. In addition, although certain variations might exist in \(R\) compared to the uncertainty of wind energy, the uncertainty in \(R\) may have a relatively small influence on the simulation results of UC. Hence, in this study, we do not consider the uncertainty in \(R\) and assume it as a constant.  
Figure 1: The simplified equivalent thermal parameter model for air-conditioning loads (ACLs).