## 4 Case Study
### Case 1 (Sto = 18, 19, 20)  
The case study compares the difference between the two methods of MG operation (with and without preparation). Further, we evaluate the effect of proactive actions on the load during the event periods. Usually, proactive actions are realized by securing the available power through rescheduling generators and maintaining the battery SoC. In Case 1, all generators in the MG are scheduled for maximum output regardless of the preparation in the pre-event time to supply a high load at the lowest cost in high electricity prices. In the pre-event time, different operations of the MG with and without preparation are (\(P_{t}^{dch.NM}\)) and (\(P_{t}^{Buy.NM}\)). (\(P_{t}^{dch.NM}\)) means the power discharged from the battery at \(t\) in the normal-mode operations. (\(P_{t}^{Buy.NM}\)) means the power bought from the utility grid at \(t\) in the normal-mode operation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Unit** & **Gen. Cost** & **Start Up/Down** & **Min./Max.** & **TO/TS** & **Ramp Up/Down** \\  & **(USD/MWh)** & **Cost (USD)** & **Capacity (MW)** & **(h)** & **Rate (MW/h)** \\ \hline G1 & 27.7 & 15/5 & 1/8 & 3/3 & 3 \\ G2 & 39.1 & 45/8 & 1/4 & 3/3 & 2 \\ G3 & 61.3 & 25/5 & 0.8/2 & 1/1 & 2 \\ G4 & 65.6 & 10/2 & 0.8/2 & 1/1 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the controllable generators  
Figure 5: Forecasted renewable generation and load. In the MG operation without preparation, the battery discharge occurs when electricity prices are high for supplying the load in the normal mode with minimal cost. At pre-event times without preparation, \(P_{t}^{chch.NM}\) is 10.79 MW, 5.4 MW, and 2.7 MW and \(P_{t}^{Buy.NM}\) is 1.81 MW, 6.56 MW, and 5.96 MW. In the MG operation with preparation, \(P_{t}^{ch.NM}\) does not occur at pre-event times, (1) to prepare for the interruption of the external power supply attributed to events and (2) to maintain the SoC of the battery at an appropriate level. In the MG operation with preparation, instead of decreasing \(P_{t}^{ch.NM}\), \(P_{t}^{Buy.NM}\) increases at pre-event times \(P_{t}^{Buy.NM}\). Thus, at the pre-event times, the sums of \(P_{t}^{ch.NM}\) and \(P_{t}^{Buy.NM}\) are 12.61 MW, 11.96 MW, and 8.66 MW in the MG operation without preparation. In this section, the probability that the power delivered to a load is higher than the actual load is called load survivability. We calculated the load survivability to evaluate the effect of proactive actions on the load during the event periods. The formal expression of the critical and normal load survivability is \(\Phi_{\bar{F}_{t}^{A}}\left(P_{t}^{LA}-P_{t}^{IA.STO_{l}}\right)\) and \(\Phi_{\bar{F}_{t}^{B}}\left(P_{t}^{LB}-P_{t}^{IB.STO_{l}}\right)\). Figure 7 shows the different components of the MG operation based on a proactive action at each event period in Case 1. In Case 1, the different components of MG operations are SoC (%), load A survivability (%), and operating costs (USD ). The difference in load B survivability appears very low in Case 1 because load A is large, and there is insufficient power to transfer to load B regardless of preparation. At the pre-event time, the SoC is 90%, 90%, and 90% with preparation and the SoC is 45%, 22%, and 11% without preparation. For maintaining the SoC at a high level, the preparation mode requires more \(P_{t}^{Buy.NM}\) than without preparation when the electricity price is relatively high. Thus, in the normal mode, the preparation mode has a higher operating cost than the MG operation without preparation. The normal-mode operating costs are USD 22,837 and USD 22,263 with and without preparation, respectively. However, the emergency MG operation without preparation cannot adequately guarantee load A survivability because of the lack of available power during the event periods. In the emergency MG operation without preparation, load A survivability is under 95%, which excludes \(t=24\) of \(STO_{20}\).