## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline
**Fault Types** & **Fault Resistance = 50 \(\Omega\)** & \\ \hline Three-phase to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358.7 & 355.8 & 117.9 \\ \hline TMS (Seconds) & 2.989 & 5.93 & 1.966 \\ \hline Trip Time (Seconds) & 0.01 & 0.9198 & 0.01 \\ \hline Double phase to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358.7 & 355.7 & 118.3 \\ \hline TMS (Seconds) & 2.989 & 5.929 & 1.971 \\ \hline Trip Time (Seconds) & 0 & 0.9193 & 0 \\ \hline Single line to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358.5 & 355.5 & 118.5 \\ \hline TMS (Seconds) & 2.987 & 5.925 & 1.975 \\ \hline Trip Time (Seconds) & 0 & 0.9185 & 0 \\ \hline \end{tabular}
\end{table} 
Table 5: Threshold current at fault resistance of 50 \(\Omega\). The threshold current also varied as the fault resistance increased and was slightly different in the different fault types, as seen in Table 6, where the threshold current was an average of 358 kV in relay 1 and was slightly different in relay 3 of the single phase-to-ground fault. Transmission line faults can be found and identified with less accuracy when there are noise signals. When choosing and extracting fault characteristics, noise signals such as voltage sag, transients, harmonics, and voltage interruption must be considered. In [15], the DWT was utilised for feature extraction, and the SVM was used for fault classification, with 100% accuracy when there was no disturbance and 98% and 95.6% accuracy when there was 30 dB and 20 dB noise, respectively. It is recommended that noise be removed using the DWT approach during fault extraction to obtain a denoised signal. Validation of the Result Using the Threshold Current and Voltage with Other Models for the Sensitivity of TMS  
Two scenarios were created in Figures 4 and 5 to show when three phase-to-ground faults were initiated to bus A and B, and the relay was applied in bus B while bus A was without a relay. In the implementation of the proposed model in Figure 4, at the maximum threshold current, the circuit breaker tripped at 0.05 s and was restored. When the relay was initiated, the line tripped at 0.04 s, and the operating time delay was 0.035 s, as seen in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Types** & **Fault Resistance = 100 \(\Omega\)** & \\ \hline Three-phase to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358.2 & 353.9 & 117.9 \\ \hline TMS (Seconds) & 2.985 & 5.899 & 1.966 \\ \hline Trip Time (Seconds) & 0 & 0.9149 & 0.9039 \\ \hline Double phase to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358.1 & 353.8 & 118.3 \\ \hline TMS (Seconds) & 2.984 & 5.897 & 1.971 \\ \hline Trip time (Seconds) & 0 & 0.9145 & 0.9035 \\ \hline Single line to ground fault & Relay 1 & Relay 2 & Relay 3 \\ \hline Threshold Current (kA) & 358 & 353.7 & 349.5 \\ \hline TMS (Seconds) & 2.984 & 5.895 & 5.824 \\ \hline Trip Time (Seconds) & 0 & 0.9136 & 0.9026 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Threshold current at fault resistance of 100 \(\Omega\). Figure 3: Time multiplier settings at 1 second. The application of the instantaneous overcurrent relay has reduced the operating time drastically, thereby protecting the entire system from collapsing. The threshold value is an easy way to detect faults and prevent transmission line fault protection tripping delays. The overshoot at Bus B/\(l_{1}\) in Figure 5 shows that the maximum threshold coefficient was at the highest with 620.4303 kA as seen in Table 2 (AC-G). Additionally, the minimum threshold was at the lowest at the no-fault condition with 10.6870 kA. The instantaneous overcurrent and voltage relay function model is shown in Figure 6 of relay 1. The trip time for the current is smaller (Figure 6a) compared to the voltage, while the time delay was at zero seconds in each case.