## 3 DR and AGC Unit Capabilities
### Aggregated DRP  
Responsive loads are controlled to satisfy the demand requirements, which include load increment and load reduction. DRP is defined that the smart appliances can switch their working status in response to the DR signal without affecting the consumer's comfort. This section discusses the condition when there is a DR signal which needs smart appliances to stop working or continue to work. Figure 1 shows the DRP of AC and WH in different conditions in response to a load reduction signal. For the AC, when the room temperature is between \(T_{\text{AC}}^{set}-T_{\text{AC}}^{d}/2\) and \(T_{\text{AC}}^{set}+T_{\text{AC}}^{d}/2\), the AC has DRP if the room temperature has a downward tendency, and has no DRP if it has an upward tendency. In order to guarantee the comfort of consumers, the comfort range is set previously. In general, the range of thermostat set point \(T_{\text{AC}}^{set}\) within the dead band of \(\pm T_{\text{AC}}^{d}/2\) is between \(T_{\text{comfort\_lower}}^{\text{AC}}\) and \(T_{\text{comfort\_upper}}^{\text{AC}}\), except the condition of AC responding. When the room temperature goes above the \(T_{\text{AC}}^{set}+T_{\text{AC}}^{d}/2\) which is below \(T_{\text{comfort\_upper}}^{\text{AC}}\), the AC has DRP until the room temperature is higher than the maximum temperature of comfort range. Similar logic is suitable for WH. For the EV, when it is connected to the charging station and can charge to the minimum SOC before the desired finish time, it has DRP [29]. The DRP index of the three appliances in time interval \(t+1\) are obtained based on the parameters of time interval \(t\), \"\(1\)\" if the appliance has DRP and \"\(0\)\" if the appliance has no DRP, which are described in Equations (14)-(16):  
\[DP_{\text{AC}}(t+1)= \begin{cases}1,&(T_{\text{AC}}(t+1)<T_{\text{AC}}(t)\& \&T_{\text{AC}}(t+1)\in(T_{\text{AC}}^{set}-T_{\text{AC}}^{d}/2,T_{\text{AC}}^ {set}+T_{\text{AC}}^{d}/2))\\ 1,&||T_{\text{AC}}(t+1)\in(T_{\text{AC}}^{set}+T_{\text{AC}}^{d}/2,T_{\text{ comfort\_upper}}^{\text{AC}})\\ 0,&\text{others}\end{cases}  \tag{14}\]  
\[DP_{\text{WH}}(t+1)= \begin{cases}1,&(T_{\text{WH}}(t+1)>T_{\text{WH}}(t)\&\&T_ {\text{WH}}(t+1)\in(T_{\text{WH}}^{set}-T_{\text{WH}}^{d}/2,T_{\text{WH}}^{set }+T_{\text{WH}}^{d}/2))\\ 1,&||T_{\text{WH}}(t+1)\in(T_{\text{comfort\_lower}}^{\text{WH}},T_{\text{WH}}^ {set}-T_{\text{WH}}^{d}/2)\\ 0,&\text{others}\end{cases}  \tag{15}\]  
\[DP_{\text{EV}}(t+1)= \begin{cases}1,&N_{\text{EV}}(t)=1\&\&SOC(t+1)+\frac{P_{ \text{EV}}(\cdot(T-t-1)}{Q_{\text{EV}}}\cdot\eta\geq SOC_{\text{min}}\\ 0,&\text{others}\end{cases}  \tag{16}\]  
where \(DP_{\text{AC}}(t+1)\), \(DP_{\text{WH}}(t+1)\), and \(DP_{\text{EV}}(t+1)\) are the DRP statuses of the AC, WH, and EV in time interval \(t+1\), respectively. In the condition of the DR requirement which requires more loads work, it is assumed that only the WHs and EVs respond to the increment signal. The reason is that when the WHs and EVs respond to the increment signal, the water temperature increases and then decreases slightly because of its high heat preservation, and the EV's SOC increases and then stays constant in the condition of no charging or discharging because of its storage capacity. These characteristics are beneficial to the later DR actions responding to the reduction signal. The DRP index of these three kinds of appliances in  
Figure 1: Demand response potential (DRP) of air conditioner (AC) and water heater (WH) in response to a load reduction signal. time interval \(t+1\) are obtained based on the parameters in time interval t, \"1\" if the appliance has DRP and \"0\" if the appliance has no DRP, which are described Equations (17)-(19):  
\[DP_{\text{AC}}(t+1)=0 \tag{17}\]  
\[DR_{\text{WH}}(t+1)= \begin{cases}1,&(T_{\text{WH}}(t+1)<T_{\text{WH}}(t)\&\& _{\text{TW}}(t+1)\in(T_{\text{WH}}^{set}-T_{\text{WH}}^{d}/2,T_{\text{WH}}^{ set}+T_{\text{WH}}^{d}/2))\\ 1,&||T_{\text{WH}}(t+1)\in(T_{\text{WH}}^{set}+T_{\text{WH}}^{d}/2,T_{\text{ comfort\_upper}}^{\text{WH}})\\ 0,&others\end{cases}