## 2 Integration Service Restoration  
This section presents a successful service restoration strategy that coordinates MESS, PEV-PLs, microgrid resource dispatching, and distribution network reconfiguration. Resilience is referred to as the ability to anticipate and adapt to changing situations, as well as to resist and recover quickly from disturbances [44]. For demonstration purposes, a hypothetical resilience curve related to an event in [45] is used in this work, as illustrated in Figure 1 (R), as a measure of the level of system resilience. The set of points is as follows: pre-event robust state (t\({}_{0}\), t\({}_{1}\)), event progress (t\({}_{1}\), t\({}_{2}\)), post-event damaged state (t\({}_{2}\), t\({}_{3}\)), restoration state (t\({}_{3}\), t\({}_{4}\)), post-restoration state (t\({}_{4}\), t\({}_{5}\)), and infrastructure recovery (t\({}_{5}\), t\({}_{6}\)).  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline
**Ref. No.** & **DNR** & **MESS** & **PEL-PLs** & **DGs** & **Considering MGs** & **Uncertain Parameters** & **Contingency** & **Test System** \\ \hline
[19] & \(\times\) & ✓ & \(\times\) & ✓ & \(\times\) & Load and wind & \(\times\) & 118-bus 14-bus 14-bus 14-bus 14-bus 14-network \\ \hline
[20] & \(\times\) & ✓ & \(\times\) & ✓ & \(\times\) & PV & ✓ & 33-bus \\ \hline
[22] & \(\times\) & ✓ & \(\times\) & \(\times\) & \(\times\) & \(\times\) & ✓ & 33–123 bus \\ \hline
[23] & \(\times\) & ✓ & \(\times\) & \(\times\) & ✓ & Line failure & ✓ & 15-bus 15-bus 14-bus 14-bus 14-network \\ \hline
[24] & \(\times\) & ✓ & \(\times\) & ✓ & \(\times\) & Wind, PV & ✓ & 33-bus \\ \hline
[26] & \(\times\) & \(\times\) & ✓ & ✓ & \(\times\) & \(\times\) & \(\times\) & 6-bus 118-bus 14-bus 14-bus 14-bus 14-bus 14-  
In this article, it was considered that catastrophic occurrences create transmission grid failures at (t\({}_{1}\)) and that distribution systems can no longer be powered by transmission grids. As a result of the faults and their effects being noted in (t\({}_{2}\), t\({}_{3}\)), microgrids were used to coordinate PEV-PLs and MESSs to restore service at the distribution level. To increase the system resilience level to (R\({}_{2}\)), the suggested joint restoration strategy was applied from (t\({}_{3}\)). Until the main transmission systems resumed operation, the DS continued in the post-restoration condition. Therefore, the period (t\({}_{3}\), t\({}_{5}\)) in this study refers to the restorative state and the post-restorative period. The joint restoration technique for the DS was implemented throughout the optimization horizon (T), as illustrated in Figure 1, and it was considered that the upstream grid was repaired at (t\({}_{5}\)). As a result, during the time (T), the employment of MESSs and PEV-PLs in the DS was suggested for a cooperative post-disaster restoration strategy that utilizes MESSs and PEV-PLs in MGs in cooperation with renewable DGs for post-disaster recovery. Utility firms were expected to own and control MESSs. At the same time, PEV parking lots (PEV-PLs) could be represented by the DER [14]. Furthermore, it was expected that a transportation network connected all MGs inside the DS. As a result, PEVs could play an important role in sourcing system loads. Even though PEVs absorb electric power and operate as consumers, the deployment of vehicle-to-grid (V2G) technology enables PEVs to share energy with the power network.  
A resilient service restoration in a DS after natural disasters was made possible by the scheduling of MESSs, PEV-PLs, and the reconfiguration of the distribution network using MGs. By adjusting the ON/OFF status of remote-controlled switches, the DS was divided into a few islands and reconfigured. An MG on each island had a different load profile (residential, commercial, and industrial) and served as a root bus to deliver power to critical loads while also acting as an interface between DSs and transportation systems.