# Research on Optimal Voltage Control of Distribution Network with the Participation of EVs and PVs
## 2 Materials and Methods  
### Impact of EV and PV Penetration on the Voltage Profiles of Distribution Networks  
The typical configuration of a distribution network feeder having distributed EVs and PVs connected is illustrated in Figure 3. The voltage difference between adjacent buses can be represented by (1), indicating that the voltage difference is determined by the distribution cable impedance and the active and reactive powers flowing across the distribution cables. As EVs and PVs are mainly connected to LV distribution networks that are characterized by large resistance and relatively small reactance, (1) can be simplified as (2), indicating that the voltage difference between adjacent buses varies with the change of active and reactive power flows. By ignoring the power losses, the active and reactive power flowing from bus \(k-1\) to bus \(k\), \(P_{k}\), and \(Q_{k}\), can be written as (3) and (4). Accordingly, the voltage profiles of distribution networks can be altered with the change of EV charging schemes and the fluctuating PV power outputs.  
\[U_{k-1}-U_{k}=\frac{R_{k}P_{k}+X_{k}Q_{k}}{U_{k}}+\frac{X_{k}P_{k}-R_{k}Q_{k}} {U_{k}} \tag{1}\]  
\[U_{k-1}-U_{k}\approx\frac{R_{k}P_{k}+X_{k}Q_{k}}{U_{k}} \tag{2}\]  
\[P_{k}=P_{k+1}+P_{load,k}+P_{EV,k}-P_{PV,k}=\sum_{i=k}^{N}P_{load,i}+\sum_{i=k}^ {N}P_{EV,i}-\sum_{i=k}^{N}P_{PV,i} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Distribution Voltage** & **Advantages** & **Disadvantages** \\
**Regulation Types** & & \\ \hline \multirow{4}{*}{Local voltage control} & no communications required & cannot achieve the globally \\  & between different voltage & optimized voltage distribution \\  & support resources & patterns \\  & can achieve the globally & require dedicated \\ Centralized voltage control & optimized voltage distribution & communication systems for \\  & patterns & the whole grid \\  & do not require centralized & \\ Distributed voltage control & voltage controller; limited & require sophisticated control \\  & communication resources are & algorithms \\  & required & \\  & coordination of all available & \\  & voltage support resources & \\  & achieved; limited & need to define proper \\  & communication resources are & coordination schemes at \\  & required; can incorporate the & multi-time scales \\  & other three types of voltage & \\  & regulation methods & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Advantages and disadvantages of different types of distribution voltage regulation methods.  
\[Q_{k}=Q_{k+1}+Q_{load,k}+Q_{EV,k}-Q_{PV,k}=\sum_{i=k}^{N}Q_{load,i}+\sum_{i=k}^{N}Q_{ EV,i}-\sum_{i=k}^{N}Q_{PV,i} \tag{4}\]  
where \(U_{k}\) (V) is the terminal voltage of bus \(k\), the active and reactive power flows from bus \(k-1\) to bus \(k\) are represented by \(P_{k}\) (W) and \(Q_{k}\) (Var), the distribution cable impedance between bus \(k-1\) and bus \(k\) is represented by \(R_{k}+jX_{k}\), \(P_{load,k}\) (W), \(P_{EV,k}\) (W), and \(P_{PV,k}\) (W) are the active powers of load, EV, and PV connected to bus \(k\) with the corresponding reactive powers represented by \(Q_{load,k}\) (Var), \(Q_{EV,k}\) (Var), and \(Q_{PV,k}\) (Var),and \(N\) is the last bus number of the feeder.