## 6 Numerical Result of the Proposed Model  
In this article, the suggested planning model was used to determine the 33-bus DS optimal operation in both the restorative and post-restoration states. The test results were divided into three groups as a consequence. In Case I, the DS had MGs with wind-DGs and PV-DGs and did not consider PEV-PLs or MESSs; in Case II, the DS had MGs and considered PEV-PLs and DNR; and in Case III, the DS had MGs and considered PEV-PLs, DNR, and MESSs. According to objective value and load recovery, the optimization findings of three cases are reported and compared in Table 5.  
Figure 10: Daily output power profiles for PV-DGs. Figure 9: Daily output power profiles for Wind DG. In Case 1, microgrids depended entirely on local distributed generation for service restoration in distribution systems in the case absence of PEV-PLs and MESSs. As a result of applying the default faults, the network reconfiguration result was that switches (9, 15), (12, 22), (18, 33), and (25, 29) were opened. According to the table above, the estimated total cost was USD 97736.202, and the recovery percentage of critical (Priority-1), non-critical (Priority-2), and overall loads were, 78%, 38%, and 66.5%, respectively. In the second case, it was taken into account that local PV-DG resources coordinated with PLs at the microgrids. For the restoration of various load demands, the PEV-PLs were dispatched to microgrids at #15, and #20, respectively. The findings collected show that the open switches were (9, 15), (12, 22), (18, 33), and (25, 29). As listed in Table 5, the whole cost was USD 89409.807, which is 8.52% less than Case 1 (The base cost). The critical load (Priority-1) restoration percentage was 80.94%, the non-critical (Priority-2) load restoration percentage was 36.5%, and the overall load restoration percentage was 68.17%. The results demonstrate the advantages of appropriately utilizing PEV-PLs to pair up with microgrids for efficient service recovery. Case 3 is achieved when PEVs-PLs cooperate with the scheduling of MESSs, and DGs at MGs and DNR. Regarding the DS reconfiguration, the same line switches became energetic as mentioned in Case 1 and Case 2, as depicted in Figure 11, due to the location of the same events that were considered for all test cases. By following Table 5, the total cost decreased by 37.3% when compared with Case 2 and by 42.65% when compared with Case (1) to reach USD 56048.351. Critical, non-critical, and total load restorations improved to 90.59%, decreased to 36.11%, and increased to 74.93%, respectively. It should be noticed that the restoration of the non-critical load was slightly less than in Case 2; this is because MESSs transmit energy across microgrids to energize the critical loads, which results in increased losses during charging and discharging. These findings indicate that MESSs can greatly increase the resilience of DSs. The hourly position and status of the MESSs are described in Table 6. As specified in Table 5, MESS2 remained at the starting position, MG21, for 6 h (00:00-06:00) for charging purposes. Then, it transferred from MG21 to MG14 at 7:00 and stayed there for 3 h (8:00-10:00) for charging and discharging. Then, it transferred to MG25 at 11:00 to stay for 7 h until being discharged between 12:00 and 13:00 and charged from 15:00 to 18:00. Following that, travel was performed from MG25 to MG14 at 19:00, and then charging began for 2 h (20:00-21:00) before discharging started at 22:00 for 1 hour, until 23:00. The final trip was back to MG25 at 22:00 to be discharged during the last hour (24:00).