## 3 Illustration of the Methodology
### Obtaining the Integrated Interruption Cost Model
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Period** & **1 min** & **20 min** & **1 h** & **4 h** & **8 h** & **24 h** \\ \hline Winter peak & 0.00 & 0.55 & 4.09 & 45.97 & 93.69 & 355.58 \\ \hline Spring peak & 0.00 & 0.32 & 2.38 & 26.71 & 54.43 & 206.60 \\ \hline Summer peak & 0.00 & 0.29 & 2.16 & 24.25 & 49.42 & 187.57 \\ \hline Fall peak & 0.00 & 0.33 & 2.44 & 27.40 & 55.84 & 211.94 \\ \hline Off-peak & 0.00 & 0.30 & 2.21 & 24.87 & 50.69 & 192.37 \\ \hline \end{tabular}
\end{table} 
Table 9: SPD model interruption cost for residential sector. The interruption costs are then normalized by the sector demand during each period of the SPD model obtained by multiplying the per unit demand by the sector annual peak load in Table 3. The sector DNCs calculated using (12) for residential, farm, and commercial are presented in Table 11.  
Next, the sector customer damage function (SCDF) is formed from the expected DNCs for each sector. The industrial sector has one load period, and therefore, the expected DNC is the same as the data in Table 4. The expected DNCs for residential, farm, and commercial sectors are obtained by (13). The SCDF as described in (14) is presented in Table 12.  
The composite customer damage functions (CCDFs) for all load points are finally calculated using (15). The composite power system consists of multiple load points with unique load compositions. Therefore, the CCDFs will vary from one load point to another depending upon the composition of the customer sectors at a given load point. Figure 7 shows the 17 load points of the IEEE-RTS 24-bus system, which has an annual peak demand of 2850 MW and a load factor of 61.4%. Table 13 shows the load sector composition for two selected load points, 4 and 14, that are assumed to illustrate the method. The CCDF obtained at these load points is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Period** & **1 min** & **20 min** & **1 h** & **4 h** & **8 h** & **24 h** \\ \hline \multicolumn{8}{c}{**Farm**} \\ \hline Winter peak & 1.83 & 8.06 & 13.98 & 24.32 & 26.83 & 52.37 \\ \hline Spring peak & 1.06 & 4.68 & 8.12 & 14.13 & 15.59 & 30.43 \\ \hline Summer peak & 0.97 & 4.26 & 7.38 & 12.84 & 14.17 & 27.65 \\ \hline Fall peak & 1.09 & 4.80 & 8.33 & 14.49 & 15.99 & 31.20 \\ \hline Off-peak & 0.99 & 4.36 & 7.56 & 13.16 & 14.52 & 28.34 \\ \hline \multicolumn{8}{c}{**Compmercial**} \\ \hline Peak & 29.69 & 87.81 & 237.21 & 1194.95 & 1920.18 & 2312.68 \\ \hline Off-peak & 16.03 & 47.52 & 128.32 & 646.47 & 1038.81 & 1251.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: SPD model interruption cost for farm and commercial sectors. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Period** & **1 min** & **20 min** & **1 h** & **4 h** & **8 h** & **24 h** \\ \hline \multicolumn{8}{c}{**Residential**} \\ \hline Winter peak & 0.00 & 0.27 & 2.00 & 22.47 & 45.79 & 173.78 \\ \hline Spring peak & 0.00 & 0.21 & 1.57 & 17.62 & 35.90 & 136.26 \\ \hline Summer peak & 0.00 & 0.16 & 1.18 & 13.30 & 27.10 & 102.85 \\ \hline Fall peak & 0.00 & 0.17 & 1.26 & 14.11 & 28.76 & 109.16 \\ \hline Off-peak & 0.00 & 0.27 & 1.97 & 22.22 & 45.29 & 171.88 \\ \hline \multicolumn{8}{c}{**Farm**} \\ \hline Winter peak & 0.68 & 2.99 & 5.18 & 9.01 & 9.94 & 19.40 \\ \hline Spring peak & 0.51 & 2.26 & 3.91 & 6.81 & 7.51 & 14.67 \\ \hline Summer peak & 0.57 & 2.52 & 4.37 & 7.60 & 8.39 & 16.37 \\ \hline Fall peak & 0.43 & 1.91 & 3.32 & 5.77 & 6.36 & 12.42 \\ \hline Off-peak & 0.66 & 2.92 & 5.06 & 8.80 & 9.71 & 18.95 \\ \hline \multicolumn{8}{c}{**Compmercial**} \\ \hline Peak & 3.67 & 10.84 & 29.29 & 147.52 & 237.06 & 285.52 \\ \hline Off-peak & 3.00 & 8.89 & 24.00 & 120.93 & 194.32 & 234.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Residential, farm, and commercial DNCs, \(\mathrm{CAD/KW}\). The CCDF can be used to assess the cost of outages in grid reliability planning or in deciding grid resilience enhancement investments.