# An Improved Arc Fault Location Method of DC Distribution System Based on EMD-SVD Decomposition
## 4 Case Study
### Locating Results  
Analyze the positive current data within 0.002 s before and after the fault occurred at the sending-end detection point. As depicted in Figure 10, the system is in stable operation prior to the occurrence of a fault; following the occurrence of a fault, the high-frequency fault traveling wave signal propagates along the line to the sending end, and the current at the monitoring point at the sending end experiences a sudden change. Figure 9: Schematic diagram of the converter control strategy. (**a**) Schematic diagram of the control strategy at the delivery end. (**b**) Schematic diagram of the control strategy at the receiving end. As shown in Figure 11, EMD is conducted on the positive sender current signal to get the \(imf_{1}(t)\) component with the highest frequency in the IMF cluster. The current amplitude tends to decrease with the propagation of the faulty traveling current on the line and the fold-reflection behavior. From the analysis in Chapter III, it can be seen that SVD can detect the singularities of the signal itself and its derivatives. In order to obtain the mutation points of the \(imf_{1}(t)\) component, two layers of singular value decomposition are used in this paper. The main component reflects the main frame of the signal, and the detail component can detect the mutation points of the signal itself. As shown in Figure 12, the detail component's maximum modulus point corresponds to the component's mutation point. Figure 11: Component. Figure 10: Positive current at the sending end. Take the modulus value of the svd2 component, as shown in Figure 13, where 1 is the first modulus maximum point, and its corresponding time represents the time when the initial fault traveling wave current propagates from the fault point to the sending-end monitoring point, and 2 is the second modulus maximum point, and its corresponding time represents the time when the initial fault traveling wave current returns to the monitoring point after being refracted twice by the sending-end bus and the fault point. The distance from the fault point to the monitoring point at the sending end can be obtained by substituting the two time points into the ranging formula to achieve fault location. Based on the above ranging scheme, several groups of different fault locations were set up for the experiments. Tables 1 and 2 show the results of single-end ranging experiments with faults set near the line midpoint and at the end of the line, respectively. In Table 1, X is the actual fault point, and the initial fault traveling wave propagates to the sending-end measurement point for the first time along the line at T\({}_{\text{M1}}\) time; After two refractions of the bus and fault point, it reaches the sending-end measurement point again at T\({}_{\text{M2}}\) time. \(X_{\text{M}}\) is the distance calculation result from the fault position to the sending-end monitoring point, and \(X_{\text{R}}\) is the ranging error. In addition, the ranging errors for more fault points are shown as a scatter plot in Figure 14. The error range over the entire line is between 0.055% and 1.157%. Obviously, the proposed locating scheme did not fail when the fault occurred close to the end of the line. \begin{table}
\begin{tabular}{c c c c c} \hline
**X/km** & **T\({}_{\text{M1}}\)/s** & **T\({}_{\text{N2}}\)/s** & **X\({}_{\text{M}}\)/km** & **X\({}_{\text{R}}\)/\%** \\ \hline
5 km from M end, 15 km from N end 10 km from M end, 10 km from N end 15 km from M end, 15 km from N end & 3.000051 & 3.000153 & 10.088310 & 0.442 \\
15 km from M end, 5 km from N end & 3.000076 & 3.000230 & 15.231370 & 1.157 \\ \hline \end{tabular}
\end{table} 
Table 1: Distance measurement results of fault location near the midpoint of the line.