## 4 Voltage Regulation Strategy  
The OLTC has a time delay when the tap position changes to respond to the voltage problems. The ACs have huge voltage regulation potential that can provide a voltage regulation service during the time delay of the OLTC through demand-response technology. The voltage regulation strategy includes three processes when coordinating control of the OLTC and ACs. When the distribution network has a voltage problem, the tap position of the OLTC is adjusted according to the voltage violations. Due to the time delay of the OLTC's action, the ACs will regulate the operating power to provide the voltage regulation service. The room temperature should be controlled within [\(T_{\text{min}}\), \(T_{\text{max}}\)] to avoid impacting the comfort of occupants during the voltage regulation service provided by ACs. After the time delay of the OLTC finishes, the ACs exit the voltage regulation service. The number of ACs on the user side is limited, which cannot provide enormous regulation power for the distribution network. Therefore, when calculating the regulation power provided by the ACs, the quantity of ACs should be considered. This paper proposes a voltage ranking optimization algorithm to calculate the voltage regulation power provided by the limited ACs. The voltage should be controlled within a limited range in the distribution network to avoid harming electrical equipment on the user side. The brief distribution network model is shown in Figure 2. The nodal voltage can be obtained according to the information on the power flow:  
\[U_{n}=U_{n-1}+Z_{n}\cdot\left(I_{\text{PV\_}n}-I_{\text{Load\_}n}\right) \tag{12}\]  
where \(U_{n}\) and \(U_{n-1}\) are the nodal voltages at node \(n\) and \(n-1\). \(Z_{n}\) is the impedance between node \(n-1\) and node \(n\) on the distribution line. \(I_{\text{PV\_}n}\) is the output current of PV at node \(n\). \(I_{\text{Load\_}n}\) is the current flowing into node \(n\) for the load at the user side. It can be seen from (11) that the main factors affecting the fluctuations of nodal voltage \(U_{n}\) are \(I_{\text{PV\_}n}\) and \(I_{\text{Load\_}n}\). The power consumption of ACs accounts for a huge proportion of daily loads. Therefore, regulating the operating power of the ACs at the node with the most severe voltage problem can solve the voltage problem of the distribution network. The PID algorithm can obtain the regulation power of the ACs:  
\[\Delta P_{n}(t)=K_{p}\cdot err_{n}(t)+K_{i}\cdot\sum err_{n}(t)+K_{d}\cdot \left(err_{n}(t)-err^{\prime}_{n}(t)\right) \tag{13}\]  
where \(err_{n}(t)\) is the difference between nodal voltage and setpoint. \(K_{p}\), \(K_{i}\), and \(K_{d}\) are the coefficients of the PID algorithm. When the ACs of node n cannot provide enough regulation to keep the voltage of the distribution network within the permissive range, the ACs of the adjacent node will provide the regulation power \(\Delta P_{n-1}(t)\) for the voltage regulation. According to the voltage regulation performance of the ACs, the voltage regulation potential can be evaluated. To make full use of the voltage regulation potential of the ACs, classifying will be implemented based on the SOC\({}_{\text{AC}}(t)\). The classification process is shown in Figure 3. The ACs are classified into five groups in this paper. During over-voltage regulation, the SOC\({}_{\text{AC}}(t)\)s of each group are [0.975, +\(\infty\)] (Group 0), [0.75, 0.975], [0.5, 0.75], [0.25, 0.5], [\(-\infty\), 0.25]. During under-voltage regulation, the SOC\({}_{\text{AC}}(t)\)s of each group are [\(-\infty\), 0.025] (Group 0), [0.025, 0.25], [0.25, 0.5], [0.5, 0.75], [0.75, +\(\infty\)]. The ACs in Group 0 have no or only little voltage regulation potential. Therefore, those ACs will not participate in the voltage regulation service. Excluding the ACs of Group 0, the other groups will be allocated different regulation power based on their voltage regulation performances. Figure 3: The classification process of the ACs. Figure 2: The distribution network model and regulation strategy.