## 3 Case Study
### Data Collection and Estimation of the Fraction of Time for Each POS  
To estimate the fraction of time spent in each POS for each unit in the case study, the Hanul NPP site with six reactor units in the Republic of Korea was selected as the reference site, and its refueling outage (O/H) experience, in other words, the start and end dates of each O/H, during the period 2006-2016 was collected from the KHNP website. Unscheduled plant outages were excluded because refueling outages account for the majority of outages in Korean NPPs [13]. There were 45 refueling outages with an average duration of 66 days. Figure 7 shows the periods during which the individual units were in O/H from 2006 to 2016. The gray shaded areas represent periods where two or more units were in O/H at the same time. Table 2 shows the fraction of time for different numbers of units being in O/H. It can be seen that up to three units were in O/H at the same time. However, the fraction of time for three units being in O/H was only 1.5%, while the case where all six units were in full-power operation accounted for about 50% of the total period. The KHNP website only provides the duration of each O/H, not the duration of each POS. Therefore, for each of the six units, the fraction of time spent in each POS was estimated using the O/H durations shown in Figure 7 and the duration in hours of each POS applied in an LPSD PSA for an OPR1000 plant, where the O/H experience for 10 OPR1000 units during 2003-2012 was analyzed in detail [18]. The duration of each O/H is different, but generally, there is no significant difference in the durations of the other POSs except for POS 8, where maintenance work is intensively performed on a defueled unit. For this reason, in this study, after calculating the average O/H duration for each unit, for example, 55.3 days for Unit 1, the durations used in the LPSD PSA [18] were equally applied to the POSs (e.g., 2.2 h for POS 1, 22.6 h for POS 2) except for the duration of POS 8, which was applied differently. Figure 7: Refueling outage experience of Hanul Units 1–6 during 2006–2016. Table 3 shows the results of estimating the fraction of time spent in each POS of Hanul Units 1-6. The first POS here, \"At-Power,\" includes POS 1 (from low-power operation to reactor trip) and POS 15 (from reactor startup to low-power operation) in the LPSD PSA, as well as full-power operation. Accordingly, each fraction of time in Table 3 was calculated using the following equations:  
\[ \begin{array}{l}\text{(Fraction of time for at-power state of Unit j)}=\\ \text{(Average O/H interval of Unit $j$)}-\text{(Average O/H duration of Unit $j$)}+\text{(Durations of POS 1 and 15)}\end{array}  \tag{1}\]  
\[ \begin{array}{l}\text{(Fraction of time for POS $i$ of Unit $j$)}=\frac{\text{ Duration of POS $i$}}{\text{ Average O/H duration of Unit $j$}}\times\text{(Fraction of time for O/H of Unit $j$ )}\end{array}  \tag{2}\]  
where \(i\) is the POS number from 2 to 14 and \(j\) is the unit number from 1 to 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Units in O/H** & **Number of Days** & **Fraction of Time (\%)** \\ \hline
0 & 1875 & 46.7 \\ \hline
1 & 1484 & 36.9 \\ \hline
2 & 599 & 14.9 \\ \hline
3 & 60 & 1.5 \\ \hline
4 to 6 & 0 & 0.0 \\ \hline Sum & 4018 & 100.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fraction of time for each number of units in \(\text{O/H}\).