## 5 Case Study and Input Data  
The planning model [49] was tested using an IEEE 33-bus test system with 8 MVA and 12.66 KV base values, as shown in Figure 5. In this work, the planning model problem was a mixed-integer quadratically constrained programming (MIQCP) task with stochastic scenarios. As a result, the planning model was solved utilizing a stochastic optimization approach using GAMS software, as well as the Gurobi solver. The provided planning model was evaluated using a historical dataset of different types of loads and daily variation levels of (wind and PV) DGs. A significant number of 1000 stochastic profiles for each sort of load demand, and (PV-DGs and wind-DGs) were generated using a normal distribution function. However, a large number of stochastic profiles increase the complexity of the computation burden. To reduce the number of scenarios, a strong scenario reduction technique was necessary. In this work, the SCENTED2 tool by (GAMS) was used for scenario reduction [50]. As a result, five scenarios with joint probability were applied to illustrate stochastic variations in the system. Figure 5: 33-Bus IEEE distribution system. The whole DS was isolated from the main grid by disconnecting line (1, 2), as well as seven lines (3, 4), (12, 13), (21, 22), (24, 25), (6, 26), (8, 21), and (32, 33) were at failure as a result of disastrous occurrences. Loads were divided into three profiles: industrial, commercial, and residential, each type with five scenarios, with joint probabilities as listed in Table 2. However, all of the load demand types were classified into critical (commercial and industrial) and non-critical (residential) loads and supplied according to their priority levels [51]. These daily profiles were considered based on historical data obtained from [52] and the percentage of their maximum values are depicted in Figures 6-8 below. Five MGs were connected to the distribution network through buses, three of which were used for MESSs stations and were linked to MGs 14, 21, and 25, interconnected to each other via a transportation arc based on the (1 h) travel time between any two microgrids. Whereas the remaining two MGs were coupled with PLs and could be optimally located at any MG (e), three MESSs were taken into consideration and are assumed to have the same features as listed in Table 3. This paper assessed the maximum number of PEV-PLs that may be deployed at candidate MG as two and the number of PEVs per hour as 40. As a result, 1500 PEVs were deemed to be in the network, and they should provide different types of loads to minimize power curtailment in the case of all the DS being separated from the main grid. It is important to emphasize that the drivers' travel patterns were assumed to be identical, and the focus was on the impact of PEVs in post-disaster emergency conditions. All the PEV parameters are listed in Table 4 [14]. \begin{table}
\begin{tabular}{l c} \hline Charging/discharging power (KW) & 2.3 \\ \hline Nominal Energy capacity (KWh) & 16 \\ \hline Initial SOC (KWh) & 1.6 \\ \hline SOCmax/SOCmin (KWh) & 0.90/0.10\% \\ \hline Charging/discharging Efficiency & 0.95/0.95\% \\ \hline \end{tabular}
\end{table} 
Table 4: PEVs Parameters. Figure 8: Daily demand profiles for industrial loads. In addition, the maximum allowable limitations related to the rated power for each unit (Wind-DGs and PV-DGs) were 1 MW and 0.8 MW. The daily real dataset was considered for Wind and PV-DGs based on the historical dataset from [53], and the percentage of their maximum values are shown in Figures 9 and 10, with associated joint probabilities tabulated in the above Table 2.  
The costs of power from wind-DGs and PV-DGs were 1.9 and 2.3 USD/MW, respectively [16]. The transportation cost was considered to be USD 80 per transit [31]. For critical and non-critical loads, unit interrupting costs were chosen to be USD 10 per kWh and USD 2 per kWh, respectively [31]. For MESS and PEV, the unit battery maintenance costs were 0.2 and 0.15 USD/KWh, respectively [14; 31].