# Fault Sensing Using Fractal Dimension and Wavelet
## 6 Experiment and Results
### Experiment Results and Analysis  
Table 5 shows the IFBD recognition process and the results with an initial angle of 30\({}^{\circ}\) and a fault resistance of 30 \(\Omega\). Table 6 shows the DMWC recognition process and the results with the initial angle of 30\({}^{\circ}\) and fault resistances of 30 \(\Omega\) and 300 \(\Omega\). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Initial Angle** & **Fault Resistance** & \(\mathbf{I_{0}}\) & \(\mathbf{I_{a}}\) & \(\mathbf{I_{B}}\) & **Recognition Result** \\ \hline
30\({}^{\circ}\) & 30 \(\Omega\) & 5.3462 & 5.3462 & 5.3462 & Single-phase grounded fault of \(A\) \\
30\({}^{\circ}\) & 30 \(\Omega\) & 11.8208 & 11.8208 & 0.0015 & Single-phase grounded fault of \(B\) \\
30\({}^{\circ}\) & 30 \(\Omega\) & 6.4669 & 0.0105 & 6.4746 & Single-phase grounded fault of C \\
30\({}^{\circ}\) & 30 \(\Omega\) & 0 & 20.4730 & 10.2362 & Phase-between fault of \(AB\) \\
30\({}^{\circ}\) & 30 \(\Omega\) & 0 & 0.6722 & 1.3458 & Phase-between fault of \(AC\) \\
30\({}^{\circ}\) & 30 \(\Omega\) & 0 & 10.9097 & 10.9091 & Phase-between fault of \(BC\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 0.8570 & 0.8571 & 0.8570 & Single-phase grounded fault of \(A\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 1.8927 & 1.8927 & 0.0015 & Single-phase grounded fault of \(B\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 1.0367 & 0.0105 & 1.0379 & Single-phase grounded fault of \(C\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 0 & 2.8251 & 1.4122 & Phase-between fault of \(AB\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 0 & 0.0922 & 0.1857 & Phase-between fault of \(AC\) \\
30\({}^{\circ}\) & 300 \(\Omega\) & 0 & 1.5057 & 1.5051 & Phase-between fault of \(BC\) \\ \hline \end{tabular}
\end{table} 
Table 6: DMWC recognition with different fault resistances. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Dim(S\({}_{A}\))** & **Dim(S\({}_{B}\))** & **Dim(S\({}_{C}\))** & **F\({}_{A}\)** & **F\({}_{B}\)** & **F\({}_{C}\)** & **Recognition Result** \\ \hline
1.56129 & 1.58036 & 1.54921 & 6.20045 & 6.96163 & 5.79713 & Single-phase grounded fault \\
1.5953 & 1.58077 & 1.54182 & 6.13833 & 6.98000 & 5.57463 & Single-phase grounded fault \\
1.56304 & 1.58127 & 1.54840 & 6.26345 & 7.00254 & 5.77191 & Single-phase grounded fault \\
1.47034 & 1.43155 & 1.20976 & 4.04967 & 3.51537 & 1.93227 & Phase-between fault of \(AB\) \\
1.47022 & 1.43993 & 1.22141 & 4.04778 & 3.61930 & 1.98314 & Two-phase grounded fault of \(AB\) \\
1.47985 & 1.21997 & 1.44359 & 4.20460 & 1.97674 & 3.66650 & Phase-between fault of \(AC\) \\
1.47701 & 1.22034 & 1.44819 & 4.15717 & 1.97388 & 3.72746 & Two-phase grounded fault of \(AC\) \\
1.03145 & 1.43805 & 1.47034 & 1.34675 & 3.59549 & 4.04967 & Phase-between fault of \(BC\) \\
1.05752 & 1.43032 & 1.46975 & 1.41522 & 3.50058 & 4.04041 & Two-phase grounded fault of \(BC\) \\
1.16057 & 1.12408 & 1.19392 & 1.73838 & 1.61290 & 1.86633 & Three-phase grounded fault of \(ABC\) \\ \hline \end{tabular}
\end{table} 
Table 5: IFBD recognition with initial angle of 30\({}^{\circ}\) and fault resistance of 30 \(\Omega\). Figure 6: Experimental system structure. Table 7 shows the comparison of the DMWC recognition method and the FS method with different initial angles 0\({}^{\circ}\), 30\({}^{\circ}\), and 90\({}^{\circ}\), and fault resistances of 30 \(\Omega\), 150 \(\Omega\), and 300 \(\Omega\). Table 8 shows the comparison of the DMWC recognition method and the FS method with different initial angles of 0\({}^{\circ}\) and 30\({}^{\circ}\), and different fault distances of 0.8 km, 8 km, and 30 km. It can be seen from Table 5 that the IFBD recognition algorithm could classify 8 of the 10 types of short circuit faults. It could recognize the single-phase grounded faults, but could distinguish the detailed fault phase of \(A\), \(B\), or \(C\). The experiments proved that the DMWC recognition algorithm could correctly classify all 10 types of short circuit faults. In addition, the fault resistances had no influence on the recognition result of the DMWC recognition algorithm.