## 6 Numerical Result of the Proposed Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Results** & \multicolumn{2}{c}{**CASE 1**} & **CASE 2** & **CASE 3** \\ \hline \multirow{6}{*}{Objective (\$)} & Interruption cost & PDR & 17,581.044 & 18,854.366 & 18,981.718 \\ \cline{2-5}  & \multicolumn{1}{c}{PDC andPDI} & 80,093.427 & 70,179.259 & 34,620.604 \\ \cline{2-5}  & Transportation cost & 0 & 0 & 720 \\ \cline{2-5}  & Battery maintenance cost & 0 & 0 & 1325.001 \\ \cline{2-5}  & PEV-PLs operation cost & 0 & 313.491 & 333.031 \\ \cline{2-5}  & Wind-DGs cost & 49.184 & 49.665 & 54.971 \\ \cline{2-5}  & PV-DGs Cost & 12.546 & 13.026 & 13.026 \\ \cline{2-5}  & Total cost & 97,736.202 & 89,409.807 & 56,048.351 \\ \hline \multirow{3}{*}{Load Restoration (\%)} & Priority 1(C andIN-Loads) & 78 & 80.94 & 90.59 \\ \cline{2-5}  & Priority 2(R-Loads) & 38 & 36.5 & 36.11 \\ \cline{1-1} \cline{2-5}  & Total & 66.5 & 68.17 & 74.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results for distribution system restoration. The SOC of MESSs is shown in Figure 12 for all scenarios. Using MESS2 as an example to show the timeline, MESS2 remained in its starting position for charging purposes for 6 h (00:00 to 06:00), but as can be seen, the SOC gradually rose until it reached 80%. Then, as shown in Figure 11, MESS2 departed to MG14 at 07:00 and stayed there for 3 h to charge, discharge, and recharge. As a result, the SOC at the period from 7:00 to 10:00 was slightly raised at 08:00 and decreased at 09:00 to achieve 70% of the SOC level according to the discharging process, then it increased until it reached 90% of the SOC at 10:00. The MESS2 then went from MG14 to MG25 at 11:00 and stayed there for 6 h, discharging from 12:00 to 13:00, charging at 14:00, and discharging from 15:00 to 18:00, reducing the SOC to 10% of its \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**MESS\#1**} & \multicolumn{4}{c}{**MESS\#2**} & \multicolumn{4}{c}{**MESS\#3**} \\ \hline
**Time** & **Location** & **Status** & **Time** & **Location** & **Status** & **Time** & **Location** & **Status** \\ \hline
**1–3** & 14 & C & **1–6** & 21 & C & **1–8** & 25 & C \\ \hline
**4** & 14 & D & **7** & 21–14 & T & **9** & 25 & D \\ \hline
**5** & 14 & C & **8** & 14 & C & **10** & 25 & C \\ \hline
**6** & 14–25 & T & **9** & 14 & D & **11–12** & 25 & D \\ \hline
**7–8** & 25 & C & **10** & 14 & C & **13** & 25–14 & T \\ \hline
**9** & 25 & D & **11** & 14–25 & T & **14–15** & 14 & C \\ \hline
**10** & 25 & C & **12–13** & 25 & D & **16** & 14 & D \\ \hline
**11** & 25 & D & **14** & 25 & C & **17** & 14 & C \\ \hline
**12** & 25–14 & T & **15–18** & 25 & D & **18** & 14–25 & T \\ \hline
**13–14** & 14 & C & **19** & 25–14 & T & **19–22** & 25 & D \\ \hline
**15** & 14–25 & T & **20–21** & 14 & C & **23** & 25 & C \\ \hline
**16–19** & 25 & D & **22** & 14 & hD & **24** & 25 & D \\ \hline
**20–21** & 25 & C & **23** & 14–25 & T & & & \\ \hline
**22** & 25 & D & **24** & 25 & D & & & \\ \hline
**23** & 25 & C & & & & & \\ \hline
**24** & 25 & D & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Status and location of MESSs. Figure 11: A modified 33-bus IEEE distribution with islanding MGs. original level, as shown in Figure 12. At 19:00, MESS2 traveled from MG25 to MG14 for charging purposes between 20:00 and 21:00, thus the SOC level increased to 30%, while at 22:00, MESS2 began discharging for 1 h at the same MG. Last but not least, MESS2 returned to MG25 at 23:00 for discharge purposes during the last hour. Other MESSs have shown a similar pattern of behavior. An MG was modeled as a single bus that pooled all generating resources, an equivalent local load, and charging and discharging services, as was already described. Figure 13 shows the power balance at MG, which further includes the MESS station, Wind-DG generation, and equivalent loads. Indeed, during the time horizon, the power produced by wind turbines was adequate.