## 4 Case Study
### Case 2 (\(\text{STO}=\text{27,28,29}\))  
At pre-event times in Case 2, regardless of preparation, the output of the generators with relatively high fuel costs stopped, and the renewable generation and \(P_{t}^{Buy.NM}\) supply the loads. Further, the battery is operated to charge power with a low economic value and to utilize it during times of high load and high electricity price. However, based on the preparation, the output patterns of some generators with minimum downtime and SoC are different. Figure 8 shows the optimization results between the two modes in Case 2 in pre-event times. In the normal MG operation without preparation, G1 and G2 shut off at \(t=26\) and \(25\). At \(t=26\), while \(P_{t}^{Buy.NM}\) increases, all CG shuts off, and the battery starts charging through renewable generation. At pre-event times, the normal MG operation without preparation, \(P_{t}^{Buy.NM}\), is 0.25 MW, 11.09 MW, 7.63 MW, and 2.8 MW and \(P_{t}^{ch.NM}\) is 0 MW, \begin{table}
\begin{tabular}{c c c c} \hline  & \(STO_{18}\) & \(STO_{19}\) & \(STO_{20}\) \\ \hline with preparation & USD 168,229 & USD 113,152 & USD 70,632 \\ \(w/o\) preparation & USD 178,818 & USD 139,032 & USD 108,664 \\ \hline Cost improvement & 5.92\% & 18.61\% & 35.00\% \\ \hline \end{tabular}
\end{table} 
Table 3: Total MG operation costs according to \(STO_{l}\) in Case 1. Figure 7: Different components (SoC, load A survivability, and operating costs) of the MG operation in accordance with proactive action at each event period in Case 1. 11.35 MW, 5.67 MW, and 2.84 MW. In the normal MG operation with preparation, G1 maintains the on-state, and the G2 shuts off at \(t\) = 24 for generating \(t\) = 27, 28, and 29 for \(STO_{27}\), \(STO_{28}\), and \(STO_{29}\), respectively. The battery starts charging at \(t\) = 25. It is earlier than that in the normal mode of operation without preparation. At pre-event times with preparation, \(P_{t}^{Buy.NM}\) is 11.61 MW, 4.41 MW, 2.79 MW, and 0 MW; \(P_{t}^{ch.NM}\) is 11.32 MW, 5.66 MW, 2.83 MW, and 1.42 MW. Therefore, in the MG operation mode with preparation, the SoC is 68%, 79%, and 84%, which is 23%, 11%, and 6% higher than that of the MG operation without preparation at pre-event times. As in Case 1, the preparation requires more costs because of the uneconomical power adjustment of the generator and for maintaining SoC at a high level. Therefore, the preparation mode has higher operating costs in Case 2. The normal MG operating costs are USD 22,581 with preparation and USD 22,263 without preparation. The load survivability and total available power of CGs, considering minimum stop time and ramp capability, are calculated to evaluate the effect of proactive actions on the load during the event periods in Case 2. Table 4 shows the total available power of CGs at each \(STO_{l}\). With preparation, most CGs can generate the maximum output in the emergency MG operation. In the emergency MG operation without preparation, the total available power of CGs is under the maximum output of CGs due to the minimum stop time and ramp capability of G1 and G2. Without preparation, the total available power of CGs can be maxed at \(t\) = 31. Figure 9 shows the different components of the MG operation based on the proactive action at each event period in Case 2. The different components are SoC (%), load A survivability (%), load B survivability (%), and operating costs (USD) in Case 2.