## 3 Methodology
### Theory for Analyzing Incident Key Performance Indicators
* MV/LV transformer (22/0.4 kV) labeled as DT2-DT3 is determined by study [17], where the study introduces MTBF 43,800.361 h and MTTRes 0.361 h for MV/LV transformers. * Load break switch (LBS1) on 22 kV overhead line is determined from study [17], where all power switches are generalized under one category. The study introduces MTBF 224,621.087 h and MTTRes 5.702 h for 22 kV switches. Figure 9: Graphic display of the relationship between parameters MTTRes, MTTI, MTTK, MTTRep, and MTTV. * Overhead MV line (22 kV) labeled L1-L4 is determined as a MTBF per km and MTTRes. The numbers are collected from various studies in [18; 35; 36; 37; 38; 39; 40] that introduce MTBF between 41,714.286 and 62,571.429 h and MTTRes 11.417 h (as \"\(\tau\)\") for 22 kV overhead lines. * Underground LV cable (0.4 kV) labeled C2-C4 is determined by MTBF per km and MTTRes from [18; 35; 36; 37; 38; 39; 40], which generalized LV under 11 kV power line cables from various sources in the literature. Equations (1) and (4) are then utilized to calculate the MTT and MTBF parameters for cables and overhead lines, with adjustments made for the lengths of the individual sections. The summary table for these components is presented in Table 1, which also includes the \(\beta\) parameter required for unavailability calculations. The \(\beta\) values are adopted from [26] for all devices in the power grid. This study also follows with the summary of the components of (ii)-(iii) which is shown in Table 2. These components are obtained and defined as follows:  
* ER is determined from study [19], which introduces the values MTTF and MTTR for the edge and core router. However, the representative architecture introduced in this paper's case brings together the ER and the Core Router (CR), so it is more accurate to obtain the numbers for the \"core\" router. The authors use the same methodology and provide clear values for MTTF and MTTRes (as \"MTTR\"). Therefore, Equation 4 is used to determine the MTBF. * Indicators for Optical Line Terminal, Passive Optical Splitter, and Core Optical Switch are all determined from study survey [20]. The study introduces the Failure In Time (FIT) values and MTTRes (as \"MTTR\") and the relationship between FIT and \"MTBF\" (or as defined in the proposed methodology, MTTF in hours): \[\text{MTTF}=\frac{10^{9}}{\text{FIT}}.\] (5) Equations (4) and (5) are used to obtain the required values. The study uses four sources, but only one source contains all necessary information for all three components. Therefore, values marked as \"b-Chen1\" from [21] are used for the purposes of this paper. * The optic fiber communication link is divided into a buried link labeled BO1-BO3 and an aerial link labeled AO1-AOn. The indicators are obtained from [22], where the authors published three values for various scenarios: optimistic, nominal, and conservative. Nominal values are used, considered per km for their study. * Remote terminal units labeled RTU1-RTUn (as well as advanced metering meter, AMM1-2) are determined from studies [23; 24], where MTTF (as \"MTBF\") and MTTRes \begin{table}
\begin{tabular}{l r r r} \hline \hline
**Component** & **MTBF (h)** & **MTTRes (h)** & \(\beta\) **(-)** \\ \hline Transformer T1 (110/22 kV) & 26,310.709 & 4.403 & 2 \\ Distribution transformer DT2 (22/0.4 kV) & 43,800.361 & 0.361 & 2 \\ Distribution transformer DT3 (22/0.4 kV) & 43,800.361 & 0.361 & 2 \\ Load break switch LBS1 (22 kV) & 224,621.087 & 5.702 & 2 \\ Overhead line L1 (22 kV) & 54,570.000 & 11.417 & 2 \\ Overhead line L2 (22 kV) & 41,714.286 & 11.417 & 2 \\ Overhead line L3 (22 kV) & 62,571.429 & 11.417 & 2 \\ Overhead line L4 (22 kV) & 48,666.666 & 11.417 & 2 \\ Overhead line L5 (22 kV) & 43,800.000 & 11.417 & 2 \\ Underground cable C2 (0.4 kV) & 57,737.828 & 85.000 & 2 \\ Underground cable C3 (0.4 kV) & 38,491.886 & 85.000 & 2 \\ Underground cable C4 (0.4 kV) & 153,967.543 & 85.000 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic values of power grid components. (as \"MTTR\") are given.