## 3 Illustration of the Methodology
### Obtaining the Integrated Interruption Cost Model  
The data obtained from the outage cost survey [43] conducted in the year 2017 for Saskatchewan electricity customers are used to illustrate the interruption cost model. The cost per interruption data obtained for six different outage durations as shown in Table 2 are used in this study. The interruption cost data from the survey are converted to the 2023 price equivalence using the inflation calculator in [44]. It should be noted that the interruption cost data for all the required time periods and outage durations were not directly available from the 2017 survey since it was targeted to obtain data for generation planning. The data in Table 2 therefore pertain to the winter peak period, which can be expressed as shown in (11). An approximate cost estimation method as described in this section was followed to indirectly obtain the relevant interruption costs incurred at other periods of the years. The next step is to normalize the sector interruption cost by the load demand at each time period of the SPD model to obtain the DNC using (12). Table 3 shows the annual peak loads of the different customer sectors considered in the study. \begin{table}
\begin{tabular}{c c c} \hline
**Period** & **Load (p.u. of Sector Peak)** & **Probability** \\ \hline \multicolumn{3}{c}{**Residential**} \\ \hline Winter peak & 1.0000 & 0.009247 \\ \hline Spring peak & 0.7410 & 0.003767 \\ \hline Summer peak & 0.8913 & 0.003196 \\ \hline Fall peak & 0.9489 & 0.010300 \\ \hline Off-peak & 0.5470 & 0.973500 \\ \hline \multicolumn{3}{c}{**Farm**} \\ \hline Winter peak & 1.0000 & 0.011758 \\ \hline Spring peak & 0.7685 & 0.006279 \\ \hline Summer peak & 0.6254 & 0.006507 \\ \hline Fall peak & 0.9305 & 0.019064 \\ \hline Off-peak & 0.5538 & 0.956393 \\ \hline \multicolumn{3}{c}{**Commercial**} \\ \hline Peak & 1.0000 & 0.068493 \\ \hline Off-peak & 0.7227 & 0.931507 \\ \hline \multicolumn{3}{c}{**Industrial**} \\ \hline One period & 1.0000 & 1.00000 \\ \hline \end{tabular}
\end{table} 
Table 1: SPD Model. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Sector** & **1 min** & **20 min** & **1 h** & **4 h** & **8 h** & **24 h** \\ \hline Residential & 0.00 & 0.54 & 4.06 & 45.52 & 92.78 & 352.07 \\ \hline Farm & 1.83 & 8.06 & 13.98 & 24.32 & 26.83 & 52.37 \\ \hline Commercial & 29.69 & 87.81 & 237.21 & 1194.95 & 1920.18 & 2312.68 \\ \hline Industrial & 252,912.00 & 417,959.00 & 822,855.00 & 2,719,105.00 & 5,239,916.00 & 15,431,217.00 \\ \hline \end{tabular}
\end{table} 
Table 2: Interruption cost (CAD/Int) data from the 2017 survey (in 2023 CAD). Residential, farm, and commercial sectors have more than one load period in the SPD model. The interruption cost data for periods other than the winter peak period were not available from the survey [43] results. The approximate cost estimation method to obtain the interruption costs for the other periods in the SPD model is illustrated for the residential sector. A similar approach was used for the other remaining sectors. The 2017 survey also obtained data on preparatory action costs of five alternative electric supplies shown in Table 5 and the six-point Likert Scale shown in Table 6 to reflect the undesirability of power outages in different outage scenarios. The 4 h outage duration undesirability Likert Scale for weekly and monthly outage frequency during different seasonal periods obtained from the survey is shown in Table 7. These data are used in the approximate method to estimate the interruption costs during other periods of the SPD model. It should be noted that the residential sector has five periods in the SPD model as shown in Table 1.  
The six-point Likert scale is reduced to a five-point scale by merging Scale 3 (moderate-low) and Scale 4 (moderate-high) together. This is performed to match the five-point scale to the five preparatory action costs. The interruption costs for the different seasonal periods