## 6 Fault Detection and Classification Case Studies
### Additional Case Studies  
The protection technique is investigated for the identification of the fault with Phase A to the ground, which is realized at 30 km from Bus 1 of the utilized transmission line model during the condition of reverse power flow when the power flows from Bus 2 to Bus 1. The fault indices corresponding to all the phases are detailed in Table 2. It is clearly seen from this table that the peak quantity of the FI related to Phase A is greater relative to the pre-set threshold. The FI related to Phases B and C is lower than the pre-set threshold magnitude (\(5\times 10^{9}\)). Therefore, the fault with an L-G nature realized in Phase A of the modified transmission link system creates the reverse power flow.  
The proposed protection technique is examined for the identification of the Phase A to the ground fault realized at 30 km from Bus 1 of the PTL with the noise level of 10 dB SNR (signal-to-noise ratio). The fault indices corresponding to all the phases are detailed in Table 2. It is clear that the peak of the FI associated with Phase A is greater relative to the pre-set threshold magnitude, whereas the FI related to Phases B and C is lower than the threshold magnitude (\(5\times 10^{9}\)). However, due to the presence of noise, the fault indices corresponding to all the phases increase significantly compared to the condition when the noise is not present. Hence, the fault with an L-G nature on Phase A of the modified test system in the noisy environment is detected successfully.  
The proposed protection technique is investigated for the identification of the fault with Phase A to the ground realized at 50 km from Bus 1 of the modified test PTL considering the hybrid nature  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Case Study** & \multicolumn{3}{c}{**Peak Magnitude of the Fault Index**} \\ \hline  & **Phase A** & **Phase B** & **Phase C** \\ \hline Reverse Power Flow & \(9.5\times 10^{9}\) & 96 & 95 \\ \hline Presence of Noise & \(13.5\times 10^{9}\) & 207 & 204 \\ \hline Hybrid Line & \(7.1\times 10^{9}\) & 71 & 70 \\ \hline \hline \end{tabular}
\end{table}
Table 2: F-index peak magnitude.  
Figure 10: Effect of the varying angle of the fault incidence for detecting and classifying (**a**) L-G, (**b**) LL, (**c**) LL-G, and (**d**) LLL-G faults.  
with the sections of the overhead line and underground cable. The line section of the 20 km from Bus 1 is designed as the overhead line, and the next 20 km section is designed as the underground cable, while the remaining part of the line is designed as the overhead line. The fault indices corresponding to all the phases are detailed in Table 2. It is clear that the peak quantity of the FI related to Phase A is greater relative to the pre-set threshold magnitude. The FI pertaining to Phases B and C is lower relative to the threshold magnitude (\(5\times 10^{9}\)). However, due to the hybrid arrangement of the underground cable and overhead line, the fault indices corresponding to all the phases decrease slightly compared to the condition when the overhead line section is considered. Hence, the fault with an LG nature on Phase A of the hybrid test PTL (overhead line and underground cable) is identified efficiently.