## 6 Tree Flash Fault Location Simulation Analysis  
In the experimental setup, we initially acquired the signal data of tree flash faults. These signal data may contain rich frequency components and temporal characteristics, requiring further analysis and processing. Through HHT, we can decompose the signal into Intrinsic Mode Functions (IMFs) and obtain the instantaneous frequency information of each IMF. The key to associating HHT with the experimental setup is to ensure that the HHT transformation accurately reflects the characteristics and variations of the tree flash fault signals. Therefore, selecting the Butterworth filter as the implementation algorithm for the HHT filter is crucial. The Butterworth filter is a common digital filter with smooth frequency response characteristics, suitable for smoothing signal processing to reduce interference and highlight the main frequency components. The filtered signal retains important frequency components of the tree flash fault signal while filtering out unwanted frequency components and noise. The implementation of HHT mainly involves IMF decomposition and instantaneous frequency extraction. The decomposition of IMFs uses the Empirical Mode Decomposition (EMD) method, which decomposes the signal into a series of Intrinsic Mode Functions. Each IMF represents an inherent vibration mode of the signal. The extraction of instantaneous frequency can be achieved through the Hilbert transform. HT is a mathematical tool used to calculate the instantaneous frequency of a signal, which can extract the instantaneous frequency from the analytic signal of the original signal. Finally, combining EMD and HT forms the Hilbert-Huang transform. This transformation can extract instantaneous frequency from the original signal to better understand the signal's time-frequency characteristics. The simulation model adopts the hybrid line model shown in Figure 9. The tree flash fault is set on the overhead line of the hybrid line M-end, 38 km away. The occurrence time of the tree flash fault is set to 2 us, and the tree flash fault wave signal is decoupled. When selecting the VMD decomposition parameter K value, refer to the Optimal Variational Mode Decomposition (OVMD) algorithm and set the K value to 4. The settings for other VMD parameters are as follows: penalty factor alpha = 8000; convergence tolerance tol = 0.000001. The zero-mode component after decoupling is subjected to VMD decomposition, and the decomposition result is shown in Figure 14.  
From Figure 14, it can be observed that the first sequence represents the amplitude of the decoupled zero-mode component of the original signal, while the last sequence represents the residual component trend term. The three intermediate sequences represent the intrinsic mode functions obtained after VMD decomposition, namely IMF1 to IMF3, arranged in descending order of frequency from high to low. The variation trend of the IMF3 component exhibits the closest resemblance to the original zero-mode component. Figure 15 illustrates the variation of the instantaneous frequency of the IMF3 component signal obtained through the Hilbert transform. The time of the initial traveling wave of the tree flash fault is determined by the abrupt point of the first instantaneous frequency. From Figure 15, it can be observed that the frequency of the first instantaneous frequency abrupt point of the zero-mode component is 55,653.2 Hz, and the corresponding time is 334.95 \(\upmu\)s. Therefore, the time for the zero-mode component of the tree flash fault traveling wave to reach terminal M is 334.95 \(\upmu\)s.  
Figure 14: The measured zero-mode component at terminal M and its VMD decomposition results.