## 3 Research on Tree Flash Fault Discharge Experiments
### Analysis of Tree Flash Fault Discharge Waveform  
Multiple experiments collected a large number of waveforms of tree flash fault discharges. Typical discharge waveforms are shown in Figures 4-7, with voltage values applied by the boosting system at the time of protective action of the test transformer being 92 kV, 103 kV, 110 kV, and 118 kV, respectively. The peak-to-peak values and the main waveform widths of each waveform are shown in Table 1. The sampling frequency of data acquisition card HS5 was set to 20 MHz, with a sampling time of 400 us, 8000 sampling points, and a sampling interval of 0.05 us. During the tree flash fault discharge process, the current waveform contains high-frequency components. Setting a higher sampling frequency ensures capturing sufficient high-frequency information to accurately capture the details and rapid changes during the discharge process. To accurately reconstruct the signal, the sampling frequency should be at least twice the signal frequency. Since tree flash fault discharge involves high-frequency components, a sampling frequency of 20 MHz effectively avoids signal distortion and aliasing effects. A high sampling rate provides richer data, facilitating subsequent signal analysis and processing. In tree flashover fault studies, a high sampling rate can provide more accurate current waveform characteristics, aiding in a thorough analysis of the discharge process. In summary, setting the sampling frequency of the HS5 acquisition card to 20 MHz ensures the full capture of high-frequency signals during tree flash fault discharge experiments, thereby providing more accurate and comprehensive data for subsequent analysis and research. Figure 4: Tree flash fault test discharge current waveform (voltage value of booster system: 93 kV). (**a**) Raw current waveform plot; (**b**) magnified view of waveform; (**c**) tree flash discharge waveform a.  
Figure 5: Tree flash fault test discharge current waveform (voltage value of booster system: 103 kV). (**a**) Raw current waveform plot; (**b**) magnified view of waveform; (**c**) tree flash discharge waveform b.  
Figure 6: Tree flash fault test discharge current waveform (voltage value of booster system: 110 kV). (**a**) Raw current waveform plot; (**b**) magnified view of waveform; (**c**) tree flash discharge waveform c.  
From Figures 4-7 and Table 1, it can be observed that the peak value of the transient current traveling wave signal of the tree flash fault is between \(-\)300 mA and +300 mA, with the main wave width ranging from 30 us to 55 us. Among them, Figure 7b has the largest peak-to-peak value and main wave width. At t = 160.40 us, the transient current of the tree flash fault undergoes a sudden change with an increase in amplitude. This waveform is selected to establish the model of the tree flash fault traveling wave. Through the use of the fast Fourier transform (FFT) technique, a spectral analysis of the waveform in Figure 7b was conducted. The results, depicted in Figure 8, reveal that the tree flash fault discharge current waveform predominantly occupies the frequency range of 0 to 0.4 MHz, with a central frequency of approximately 0.025 MHz. It is observed that amplitudes are more pronounced for frequencies below 0.025 MHz, whereas between 0.025 and 0.4 MHz, the amplitudes noticeably diminish, albeit some waveforms persist. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Discharge Waveform** & **a** & **b** & **c** & **d** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Peak-to-peak value/mA & 404.06 & 380.7 & 403.57 & 469.6 & 137.71 & 110.1 & 151.665 & 59.81341 & 80.46 & 128.69 \\ main pulse width/ μs & 30.55 & 36.4 & 46.9 & 53.35 & 0.3 & 0.15 & 0.15 & 0.1 & 0.15 & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 1: Peak-to-peak values and main pulse widths of tree flash discharge waveforms. Figure 7: Tree flash fault test discharge current waveform (voltage value of booster system: 118 kV).