*3.4. Effect of Distance*

As transient signals are analyzed in this research, the effect of distance cannot be ignored. Longer transmission distance suggests greater attenuation which will lead to waveform distortion, as well as frequency spectrum variation. Reliable judgments are required for protection. To analyze the characterization of wavelet entropy for transient signals in different fault distances, the wavelet entropy of different fault distances is discussed.

Figure 13 shows the distribution of wavelet entropy when the internal fault occurs in different locations. The faults are located at 20, 100, and 180 km along the line. As shown in Figure 13a, at different fault distances, the wavelet entropies of the 2nd to 4th levels are 0. From the 6th to 8th level, the wavelet entropies have some fluctuations. In Figure 13b, from the 5th to 8th level, the wavelet entropies have some fluctuations, but they are larger than 0 and are different from external faults. In Figure 13c, the values of the 2nd to 3rd levels are 0, the entropy of each level changes insignificantly, and the overall trend is consistent. In Figure 13d, the values of the 3rd level are larger than zero and different from LDs. Fluctuations are mainly concentrated from levels 5 to 8. Although the wavelet entropy changes under some decomposition levels, the overall distributions of wavelet entropy under different propagation distances are similar.

**Figure 13.** Effect of distance. (**a**) PGF; (**b**) PPF; (**c**) LD; (**d**) LF.
