# Advancing Fault Detection in Distribution Networks with a Real-Time Approach Using Robust RVFLN
## 4 Results and Discussion
Figure 4: ORR-RVFLN detection rate on data with no noise added. Table 3 clearly demonstrates the superiority of the Cauchy-M-RVFLN, ORR-RVFLN, RVFLN, CNN, LSTM, SVM, and ELM methods over a range of fault conditions in the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **With** & **Without** & **With** & **Without** & **With** & **Without** & **Without** & **With** & **Without** \\  & **Noise** & **Noise** & **Noise** & **Noise** & **Noise** & **Noise** & **Noise** & **Noise** \\ \hline ORR-RVFLN & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 61 & 59 & 63 & 60 & 66 & 62 & 69 & 65 \\ \hline \(>\)400 m & 0 & 1 & 4 & 5 & 7 & 9 & 10 & 14 \\ \hline Cauchy-M-RVFLN & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 64 & 62 & 66 & 63 & 69 & 65 & 72 & 68 \\ \hline \(>\)400 m & 3 & 4 & 6 & 7 & 9 & 11 & 12 & 16 \\ \hline RVFLN & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 66 & 64 & 68 & 65 & 71 & 67 & 73 & 69 \\ \hline \(>\)400 m & 5 & 5 & 8 & 9 & 11 & 13 & 14 & 18 \\ \hline CNN & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 69 & 67 & 71 & 68 & 74 & 70 & 76 & 72 \\ \hline \(>\)400 m & 6 & 7 & 9 & 10 & 12 & 14 & 15 & 19 \\ \hline LSTM & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 70 & 67 & 71 & 68 & 74 & 70 & 77 & 73 \\ \hline \(>\)400 m & 7 & 7 & 10 & 11 & 13 & 15 & 16 & 20 \\ \hline SVM & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 70 & 68 & 72 & 69 & 75 & 71 & 78 & 73 \\ \hline \(>\)400 m & 8 & 8 & 11 & 12 & 14 & 16 & 17 & 21 \\ \hline ELM & \multicolumn{3}{c}{0 ohm} & \multicolumn{3}{c}{30 ohm} & \multicolumn{3}{c}{50 ohm} & \multicolumn{3}{c}{100 ohm} \\ \hline
0–50 m & 72 & 70 & 73 & 70 & 76 & 72 & 79 & 75 \\ \hline \(>\)400 m & 10 & 11 & 14 & 15 & 17 & 19 & 20 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of fault location performance of different methods for a single 1 ph-g.  
Figure 5: ORR-RVFLN detection rate on data with procedural noise. IEEE 39-bar system. Despite the presence of noise, these methods still outperform other techniques in terms of their fault location accuracy. Specifically, the table shows that the number of incorrect fault location estimates is higher for noisy data than for noiseless data. The ORR-RVFLN method is the most accurate in estimating the fault location, with only 49 incorrect predictions out of 100 faults between 0 and 50 m in noise-added data with a fault impedance of 100 ohms. In comparison, the Cauchy-M-RVFLN method has 50 incorrect predictions and the RVFLN method has 51. Furthermore, the average distance error for the ORR-RVFLN method is only 16.2 m for a fault impedance value of 100 ohms. The Cauchy-M-RVFLN method achieves an average distance error of 16.9 m for a fault impedance of 100 ohms, demonstrating its superior performance compared to the RVFLN method, which has an average distance error of 17.9 m.  
Table 4 shows the comparison of the ORR-RVFLN, Cauchy-M-RVFLN, RVFLN, CNN, LSTM, SVM, and ELM methods for phase-to-phase fault location in the IEEE 39-bar system for distances between 0 and 50 m and greater than 400 m. This comparison was performed on both noisy and noiseless data for fault impedance values of 0 ohms, 30 ohms, 50 ohms, and 100 ohms. A careful examination of Table 4 shows that the number of incorrect fault location estimates is higher for noisy data than for noiseless data. The ORR-RVFLN method estimates more correct fault locations than the other methods.