# Transmission Line Fault Classification Using Conformer Convolution-Augmented Transformer Model
## 3 Simulation Results and Discussion
### Comparison with the State-of-the-Art Method  
We compare our methods (Methods II and III) with a previously developed approach using the ELM, described in [3], which itself was compared with 11 state-of-the-art methods spanning from 2015 to 2022. In [3], two different ELM models were developed for fault detection (binary labels) and fault classification (multi-labels) purposes, both featuring a hidden layer of 700 nodes. When a fault is detected using the ELM for fault detection, it is subsequently classified using the ELM for fault classification. The ELM is a type of artificial neural network (ANN) with one or more hidden layers. ELMs are known for their simple structure, no parameter adaptation, shorter processing times, and lower computational complexity.  
Table 13 presents a performance comparison of Method II, Method III, and the ELM, all trained on the same training dataset. While training and validation accuracies are near 100% for all methods, testing accuracies vary significantly: the ELM achieves 62%, whereas Methods II and III record higher accuracies of 87.04% and 88.88%, respectively, demonstrating the superior performance of our models. In terms of prediction time on the validation dataset, the ELM requires the least time, followed by Method III, which is faster than Method II, likely due to the lower sampling rates utilized in Method III. Notably, the performance of the Conformer model is not significantly affected by changes in sampling rates. These inferences were conducted on a desktop PC equipped with Windows 11 Enterprise 22H2, and an NVIDIA GeForce RTX 3060 GPU sourced from Santa Clara, California, USA.  
Figure 10 illustrates the confusion matrixes on validation and testing datasets for the ELM, and Figure 11 for Method III. For the validation dataset, our methods accurately classify fault types across all terminals in all events, whereas the ELM has one instance of incorrect classification. Specifically, Figure 10a shows one CAG fault misclassified as CA. Figure 11b highlights the most significant misclassifications for Method III, with eleven AG faults misclassified as ABG, ten AG faults as CAG, and six BG faults as ABG. In contrast, Figure 10b shows four ABC faults misclassified as CAG, and two AG faults as CAG.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Terminals**} & \multirow{2}{*}{**Event Counts**} & \multirow{2}{*}{**Terminal Counts**} & \multicolumn{4}{c}{**Testing Accuracy (\%)**} \\ \cline{3-6}  & & & **Method II** & & **Method III** \\  & & & **Event** & **Single End** & **Event** & **Single End** \\ \hline Two & 25 & 50 & 96.00 & 97.87 & 96.00 & 97.87 \\ \hline Three & 76 & 228 & 84.21 & 88.57 & 86.84 & 93.14 \\ \hline Four & 7 & 28 & 85.70 & 87.50 & 85.70 & 87.50 \\ \hline  & & Average & 87.04 & 90.43 & 88.88 & 93.91 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Testing accuracy of Methods II and III across various transmission line configurations.  
Figure 11: Confusion matrix for Method III. (**a**) Validation dataset. (**b**) Testing dataset.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Method II** & **Method III** & **ELM [3]** \\ \hline Samples per cycle & 16 (960 Hz) & 4 (240 Hz) & 333.33 (20 kHz) \\ \hline Training accuracy (\%) & 99.23 & 99.54 & 99.65 \\ \hline Validation accuracy (\%) & 100.00 & 100.00 & 99.94 \\ \hline Testing accuracy (\%) & 87.04 & 88.88 & 62.04 \\ \hline \multirow{3}{*}{Hardware} & Desktop PC equipped with the Windows 11 Enterprise 22H2 operating system, NVIDIA GeForce RTX 3060 GPU. & \multirow{3}{*}{0.32} \\  & & (Intel Core i5-12500 CPU) & \\ \hline Validation dataset sizes & & 851 events/1702 terminals & \\ \hline Prediction time on validation & 0.67 (with GPU) & 0.56 (with GPU) & \\ \cline{1-1} dataset (s) & 4.61 (with CPU) & 1.08 (with CPU) & \\ \hline \hline \end{tabular}
\end{table}
Table 13: Comparison between our proposed method and state-of-the-art model.  
Figure 10: Confusion matrix for ELM. (**a**) Validation dataset. (**b**) Testing dataset.