## 6 Conclusions  
In this work, the fault detection and location in a VSC-HVDC system are studied by the use of data-mining techniques. Several internal (DC) and external (both DC and AC sides) are simulated with possible system conditions and fault situations. In the beginning, the DC-voltage and DC-current signals are retrieved at relay terminals of the studied HVDC system, which are later used to extract fourteen sensitive features. After that, a black-box solution-based data-mining approach is presented in order to detect and classify the faults. In the DMT framework, several approaches are tested such as ANN, SVM, KNN, ELM, LR, RF, KNN, and DBN. In order to increase the efficiency and reduce the computational burden of the data-mining model-based fault classifier, the sequential forward feature selection is integrated with each DM model. It has been studied that the KNN classifier as an ML-based \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**DMTs** & **MSE** & **R-Value** & **RMSE** & **NRMSE** & **MAPE** \\ \hline ANN & 75.6485 & 0.9721 & 8.6976 & 0.1087 & 18.4687 \\ \hline SVR & 654.7105 & 0.7932 & 25.5872 & 0.3198 & 75.2735 \\ \hline ELM & 591.9770 & 0.8131 & 22.3306 & 0.3041 & 76.5244 \\ \hline KNN & 65.0271 & 0.9795 & 8.0639 & 0.1008 & 17.7980 \\ \hline LR & 595.2575 & 0.8120 & 24.3979 & 0.3050 & 75.9142 \\ \hline RF & 2.2737 & 0.9993 & 1.5079 & 0.0188 & 2.6403 \\ \hline DBN & 2.1116 & 0.9993 & 1.4531 & 0.0182 & 2.7047 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Performance of data-mining techniques in fault location. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Data-Mining Methods** & **Actual Length** & **Predicted Length** & **Absolute Error (\%)** & **Actual Length** & **Predicted Length** & **Absolute Error (\%)** & **Actual Length** & **Predicted Length** & **Absolute Error (\%)** \\ \hline ANN & 30 & 26.8046 & 10.65 & 60 & 64.7104 & 7.85 & 90 & 95.8205 & 6.46 \\ \hline ELM & 30 & 38.7092 & 29.03 & 60 & 44.4856 & 25.85 & 90 & 56.5676 & 37.14 \\ \hline SVR & 30 & 39.6720 & 32.24 & 60 & 42.1258 & 29.79 & 90 & 63.0163 & 29.98 \\ \hline KNN & 30 & 27.0201 & 9.93 & 60 & 56.2587 & 6.23 & 90 & 86.00 & 4.44 \\ \hline LR & 30 & 37.5278 & 25.09 & 60 & 46.5935 & 22.34 & 90 & 68.4625 & 23.9 \\ \hline RF & 30 & 30.3111 & 1.037 & 60 & 58.2687 & 2.88 & 90 & 89.6505 & 0.38 \\ \hline DNN & 30 & 30.1025 & 0.34 & 60 & 59.0548 & 1.57 & 90 & 90.4568 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Sample results corresponding to fault location occurred at Line-1 with R\({}_{\text{f}}\) = 0.02 \(\Omega\)L.  
DMT and DBN as a based DMT perform extremely well to classify the external and internal faults in the HVDC system. The performance (accuracy and dependability) of KNN and DBN are noted to be \(\
eg\)99% and \(\
eg\)96%. In the 20 dB noisy environment, the classifiers show an accuracy of \(\
eg\)92%. After fault events are classified as DC internal faults, the accurate fault location is carried out with different DMTs. As compared with other DMTs, the RF- and DBN-based regressors perform better in order to predict the location of faults. The DBN predicts the fault location with the least error (MSE = 2.116 and RMSE = 1.4531). Testing the proposed approach in a renewable energy-penetrated VSC-HVDC system can be considered as a future scope of the work. Moreover, in the data-mining framework, other advanced deep learning networks such as long-short-term-memory networks, convolution neural networks, and transfer learning schemes can be implemented, which gives scope for future research. Conceptualization, M.M. and D.A.G. ; methodology, M.M. ; software, A.P. ; validation, A.P., D.A.G. and T.P. ; formal analysis, M.M. ; investigation, A.P. ; resources, T.P. ; data curation, D.A.G. ; writing--original draft preparation, A.P. and M.M. ; writing--review and editing, A.P., D.A.G. and M.M. ; visualization, M.M. ; supervision, M.M. and D.A.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.