# Advancing Fault Detection in Distribution Networks with a Real-Time Approach Using Robust RVFLN
## 4 Results and Discussion
While the ORR-RVFLN method makes 63 incorrect predictions for 100 faults between 0 and 50 m in noise-added data with a fault impedance of 100 ohms, where the most incorrect fault locations are measured, this value is 64 for the Cauchy-M-RVFLN method and 66 for the RVFLN method. Additionally, the average distance error for ORR-RVFLN is 19.5 m for a 50 ohm fault impedance. For the Cauchy-M-RVFLN method, the average distance error is 20.7 m for a fault impedance of 50 ohms and 22.2 m for the RVFLN method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **With Noise** & **Without Noise** & **With Noise** & **Without Noise** & **With Noise** & **With Noise** & **Without 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 & 51 & 49 & 54 & 50 & 57 & 53 & 49 & 56 \\ \hline \(>\)400 m & 0 & 0 & 1 & 2 & 2 & 4 & 5 & 6 \\ \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 & 52 & 53 & 58 & 51 & 58 & 54 & 50 & 56 \\ \hline \(>\)400 m & 1 & 1 & 2 & 3 & 3 & 5 & 6 & 7 \\ \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 & 53 & 51 & 56 & 52 & 59 & 55 & 51 & 57 \\ \hline \(>\)400 m & 2 & 2 & 3 & 4 & 4 & 6 & 7 & 7 \\ \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 & 57 & 55 & 59 & 55 & 62 & 58 & 54 & 61 \\ \hline \(>\)400 m & 3 & 3 & 4 & 5 & 5 & 6 & 7 & 8 \\ \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 & 57 & 55 & 60 & 56 & 63 & 59 & 55 & 61 \\ \hline \(>\)400 m & 4 & 4 & 5 & 6 & 6 & 8 & 8 & 9 \\ \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 & 58 & 56 & 61 & 56 & 63 & 59 & 55 & 61 \\ \hline \(>\)400 m & 8 & 8 & 9 & 10 & 10 & 12 & 13 & 14 \\ \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 & 59 & 57 & 62 & 58 & 65 & 61 & 57 & 64 \\ \hline \(>\)400 m & 7 & 7 & 8 & 9 & 9 & 11 & 12 & 12 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of fault location performance of different methods for a single 2 ph-g.  
Table 5 presents a comparison of various methods, including ORR-RVFLN, Cauchy-M-RVFLN, RVFLN, CNN, LSTM, SVM, and ELM, for three-phase fault localization in the IEEE 39-bar system. The comparison takes into account distances ranging from 0 to 50 m and greater than 400 m, as well as both noisy and noiseless data. Additionally, fault impedance values of 0 ohm, 30 ohm, 50 ohm, and 100 ohm are considered. According to the data presented in Table 5, various methods, including ORR-RVFLN, Cauchy-M-RVFLN, RVFLN, CNN, LSTM, SVM, and ELM, exhibited good fault location accuracy. It is worth noting that the number of faulty fault location predictions in the noise-added data is higher than in the noise-free data. Additionally, the ORR-RVFLN method is found to outperform the other methods in predicting the correct fault location. In the noise-added data with a fault impedance of 100 ohms, the ORR-RVFLN method produces 65 incorrect predictions out of 100 faults between 0 and 50 m, while measuring the most faulty fault locations. The Cauchy-M-RVFLN method produces 67 incorrect predictions and the RVFLN method produces 68. Moreover, when the fault impedance value is 30 ohms, the average distance error for the ORR-RVFLN method is 18.9 m. According to the analysis, it appears that the Cauchy-M-RVFLN method has an average distance error of 20.6 m when the fault impedance value is 30 ohms. On the other hand, the RVFLN method has an average distance error of 21.9 m when the data have added noise.