## 4 Numerical Results
### Simulation Results and Analysis
#### 4.2.3 Effects of BESS on the FEVCS Location  
A BESS of 1 MW capacity and 2.5 MWh storage was added to all solar farms in Cases 0, 1, and 2 to obtain Cases 3, 4, and 5. The network configuration of the restored grid is presented in Figure 12. The active nodes in the restored distribution network have increased from Case 2. In Case 4, the model solved the optimal location of the FEVCS in the presence of renewables backed by the BESS. The optimal location of the FEVCS is node 25 in the distribution network. \begin{table}
\begin{tabular}{l|c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Time**} \\ \cline{2-7}  & **15:00** & **16:00** & **17:00** & **18:00** & **19:00** & **20:00** & **21:00** \\ \hline EV/\#1 & 2-3 & 3-2 & 2-3 & 3-3 & 3-3 & 3-3 & 3-3 \\ \hline EV/\#2 & 1-1 & 1-2 & 2-2 & 2-2 & 2-3 & 3-3 & 3-3 \\ \hline EV/\#3 & 4-3 & 3-3 & 3-3 & 3-2 & 2-2 & 2-2 & 2-2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mobility of fleet vehicles in the transportation network in Case 2. Figure 11: Variation in SOC and charging power of fleet EVs in Case 2. Figure 10: Grid service restoration by microgrid formation for fault in Scenario 2, Case 2. Figure 13 shows that, when compared to Case 3, Case 4 adds node 24 and sheds node 26. Node 24 has a higher VOLL compared to node 26 because of the commercial load capacity on node 26. Compared with Case 2, EV-1 and EV-2 charge when there is surplus energy during some hours to support the grid during other hours. As shown in Figure 14, EV-1 discharges during 17:00 h, charges during 18:00 h, and discharges during 19:00-21:00 h. Adding a BESS for the solar farm at node 25 has provided the network with this flexibility compared with Case 2. The model solved the problem in Case 5 for the best two locations for the FEVCS on the presented network in the presence of renewables backed by BESS, with a MIPGap of 0.13%. The best two locations for the FEVCSs are node 25 and node 22. In comparison to Case 4, Case 5 powers a lower number of nodes because the model prioritizes loads with higher VOLL. Both microgrids have one FEVCS each. The configuration after service restoration of the distribution network in Case 5 is shown in Figure 15. Table 3 shows the mobility and variation in the SOC of the EVs. EV-1 is called to node 3 at 16:00 h. At 17:00 h, EV-1 is in the arc 3-3 of the TSN, indicating that EV-1 is connected to node 3 of the transportation network, which is node 25 of the power distribution network. EV-1 discharges at 17:00 and 18:00 h, supporting microgrid 3. At 19:00 h, EV-1 is called to node 2 to support microgrid 2 during 20:00-21:00 h. EV-2 is called to node 25 at 15:00 h, discharges at node 25 to support microgrid 3, and is called to node 22 to charge from microgrid 2 at 18:00 h. EV-2 goes back to node 25 during 19:00 h and supports microgrid 3 in 20:00 and 21:00 h. EV-2 transports energy from microgrid 2 to microgrid 3 to power more critical loads on microgrid 2. Similarly, EV-3 is called to node 22 at 14:00 h. EV-3 supports microgrid 2 during 15:00 h, recharges during 16:00 h, and supports microgrid 3 during 18:00-20:00 h. Figure 16 shows the variation in the objective function for all cases. Adding a BESS to the mix has increased the effects of the FEVCS in improving the objective function. Figure 12: Grid service restoration in fault for Scenario 2, Case 3. Figure 14: Variation in SOC and charging power of fleet EVs in Case 4.