# Research on Optimal Voltage Control of Distribution Network with the Participation of EVs and PVs
## 2 Materials and Methods
### A Two-Stage Voltage Regulation Scheme for Distribution Networks with PVs and EVs
#### 2.4.1 Modelling of the Day-Ahead Control Stage  
The day-ahead control stage is to determine the optimal OLTC taps settings and CB settings one day in advance, based on the day-ahead forecasting of EV charging demands, PV generations, and preliminary load demands. The time resolution of the day-ahead control stage is assumed to be one hour. The corresponding control objective is to avoid any potential bus voltage violations as well as minimize the total network loss and voltage regulation costs, as in (20) and (21). The voltage regulation costs of the day-ahead control are made up of the switching action costs of OLTCs and CBs (represented by \(\lambda_{2}\) and \(\lambda_{3}\) in (20)). The action costs of OLTCs and CBs can be estimated by their equipment investment costs, maintenance costs, daily action limits, and expected lifespans, while the information on the marginal cost of power losses is provided by the electricity system operator. Specifically, the action cost of OLTC, \(\lambda_{2}\), can be calculated from the purchase and installation cost of  
Figure 8: The SoC constraints of a single EV supporting V2G technology. OTLC (\(C_{TC}\)), the maintenance cost (\(C_{m,TC}\)), the expected lifespan (\(L_{TC}\)), and the daily action limit (\(AT_{TC}\)), as in (26). The maintenance cost of OLTC is further made up of OLTC repair cost (\(C_{rp}\)) and engineering study cost for load transfer (when an OLTC unit is removed, \(C_{es}\)) [39]. For example, according to [39], for a 7620 V (phase-to-neutral), 438 A OLTC transformer with its \(C_{TC}\), \(C_{rp}\), \(C_{es}\), \(L_{TC}\), and \(AT_{TC}\) equaling 120,000 USD, 4167 USD/year, 1667 USD/year, 30 years and 15 times/day, respectively, the corresponding OLTC action cost calculated from (26) is 1.80 USD/time. Similarly, the action cost of CB, \(\lambda_{3}\), can be calculated from the purchase and installation cost of CB (\(C_{CB}\)), the maintenance cost (\(C_{m,CB}\)), the expected lifespan (\(L_{CB}\)), and the daily action limit (\(AT_{CB}\)) of CB, as in (27). For example, according to [40], for a 4.16 kV, 200 kVAr CB with its \(C_{CB}\), \(C_{m,CB}\), \(L_{CB}\), and \(AT_{CB}\) equaling 5200 USD, 200 USD/year, 10 years and 10 times/day, respectively, the corresponding CB action cost calculated from (27) is 0.20 USD/time. The variation of the action costs can result in different optimal settings for the switching actions of OLTCs and CBs but does not affect the applicability of the prosed control strategy. The considered constraints are the operational constraints of OLTC transformers and CBs ((22)-(25)). \[minf_{dc}=\lambda_{V}C_{V}+\sum_{t=1}^{24}\left(\lambda_{1,t}P_{loss,t}+ \lambda_{2}\sum_{n=1}^{N_{tp}}\left|tp_{t}^{n}-tp_{t-1}^{n}\right|+\lambda_{3} \sum_{n=1}^{N_{cb}}\left|cb_{t}^{n}-cb_{t-1}^{n}\right|\right) \tag{20}\]  
\[C_{V}=\sum_{t=1}^{24}\sum_{i=1}^{N_{b}}\{\left|min(V_{lo},V_{i,t})-V_{lo} \right|+\left|max\big{(}V_{up},V_{i,t}\big{)}-V_{up}\right|\} \tag{21}\]  
\[tp_{min}^{n}\leq tp_{t}^{n}\leq tp_{max}^{n} \tag{22}\]  
\[0\leq\sum_{t=1}^{24}tp_{t}^{n}\leq tp_{d,max}^{n} \tag{23}\]  
\[0\leq cb_{t}^{n}\leq cb_{max}^{n} \tag{24}\]  
Figure 9: The framework of the proposed two-stage voltage regulation scheme for distribution networks with PVs and EVs.