## 5 Results and Discussion
### Fault Events Classification  
As presented in Section 3.1, the faults simulated in the considered HVDC systems were classified into three important classes: Class-1 (internal DC faults), Class-2 (external DC faults), and Class-3 (external AC faults). For this instance, if a fault occurred in Line-1, voltage and current waveforms obtained at the relaying points R-3, R-4, R-5, R-6, R-7, and R-8 would be taken as external DC fault cases, whereas the signal measured at R-1 and R-2 would give rise to an internal DC fault. In this regard, 3744 numbers of fault samples were simulated for Class-1, whereas 11,232 and 2088 numbers of samples were simulated for Class-2 and Class-3, respectively. The above-mentioned faulty signal samples were then classified using different DMTs as mentioned in Section 4 according to the extracted features. The performance of the DMTs was analyzed through the output confusion matrix and in terms of the accuracy of the classifier. The mathematical formulation of accuracy is mentioned in Figure 4.  
It is well-known that in the DMTs, feature selection is one of the most important processes as it helps to increase the prediction accuracy by choosing the most sensitive attributes and rejecting the redundant and irrelevant ones. Here, the sequential forward selection (SFS) was used in this work with different DMTs for the selection of the best feature vector. Initially, the ML techniques ANN, ELM, SVM, RF, and KNN were trained and tested with five-fold cross-validation. The output results are presented in Tables 5-9, respectively. The confusion matrix corresponding to each ML technique is presented in Figures 5-9, respectively. As shown in Table 5 and Figure 5, the maximum accuracy was found to be 91.5% with 12 numbers of features utilized by the ANN classifier. Here, it can be seen that, out of 3744 internal DC faults events, only 2538 events were truly detected as Class-1 (otherwise called dependability of fault detection) which was 67.8%. The formula for dependability is presented in Equation (8). However, the AC faults were recognized with 95% detection accuracy, whereas the external DC faults were detected with 97.9% accuracy or true-positive rate (TPR). From this analysis, it can be analyzed that although the overall percentage accuracy in the case of ANN was found to be 91.5%, more than 32.2% of internal DC faults were incorrectly detected as external DC faults which occurred  
Figure 4: Pictorial representation of confusion matrix and mathematical formulation of accuracy. the far end of the transmission line. Compared with ANN, the performance of the ELM classifier was found to be inferior in terms of both the TPR and false negative rate (FNR) of each fault class. With 12 numbers of features, the ELM classifier provides a maximum of 84% overall classification accuracy, where the value of dependability (TPR of Class 1) was found to be 62% (refer to Figure 6 and Table 6). \[\text{Dependibility}=\frac{\text{Numbers of internal DC faults events truely detected as Class-1}}{\text{Total numbers of internal DC faults events tested}}*100\% \tag{8}\] \begin{table}
\begin{tabular}{l l l} \hline \multicolumn{1}{c}{**No. of Features**} & \multicolumn{1}{c}{**Selected Features**} & \multicolumn{1}{c}{**Accuracy (\%)**} \\ \hline
1 & F3 & 65.90 \\ \hline
2 & F3,F8 & 79.28 \\ \hline
3 & F3,F8,F11 & 79.43 \\ \hline
4 & F3,F8,F11,F13 & 79.54 \\ \hline
5 & F3,F8,F11,F13,F6 & 82.00 \\ \hline
6 & F3,F8,F11,F13,F6,F10 & 82.08 \\ \hline
7 & F3,F8,F11,F13,F6,F10,F2 & 83.24 \\ \hline
8 & F3,F8,F11,F13,F6,F10,F2,F14 & 83.58 \\ \hline
9 & F3,F8,F11,F13,F6,F10,F2,F14,F5 & 83.51 \\ \hline
10 & F3,F8,F11,F13,F6,F10,F2,F14,F5,F9 & 83.47 \\ \hline
11 & F3,F8,F11,F13,F6,F10,F2,F14,F5,F9,F12 & 83.59 \\ \hline
**12** & **F3,F8,F11,F13,F6,F10,F2,F14,F5,F9,F12,F1** & **84.00** \\ \hline
13 & F3,F8,F11,F13,F6,F10,F2,F14,F5,F9,F12,F1,F7 & 83.60 \\ \hline
14 & F3,F8,F11,F13,F6,F10,F2,F14,F5,F9,F12,F1,F7,F4 & 83.57 \\ \hline \end{tabular}
\end{table}