*5.4. Effect of Fault Distance*

The fault distance will affect the sensitivity of the protection scheme. It is necessary to study the effect of different fault distances for PPF, PGF, LD, and LF in this work. The action accuracy of the protection scheme when different faults occur at different positions is shown in Figure 18. When internal faults occur at different distances, the inequality W5 > 0 is always true. Under different internal faults, the values of A0, W4, and W3 are respectively in accordance with different fault type criterions. The fault types can be distinguished effectively without being affected by the fault distance. The results show the proposed wavelet entropy-based method is immune to the variation of fault distance.

**Figure 18.** The influence of fault distance on the action accuracy.

## *5.5. Effect of Signal-To-Noise Ratio (SNR)*

Noise interference is usually encountered in the practical environment. The influence of Gaussian white noise with different power on the protection is studied. The accuracy of the actions of the protection system under the influence of SNR is shown in Figure 19. As the Gaussian white noise will pollute the high frequency components of transients and the 5th level wavelet entropy will increase accordingly, the external faults will be judged to be internal ones. The noise tolerance of the internal and external fault criterion is only 60 dB. For internal faults recognition, the noise tolerance of the PPF criterion is 30 dB. It has good noise tolerance. The noise tolerance of the PGF criterion is 45 dB. When the noise reaches 30 dB, it will have a misjudgment rate up to 25%. The noise tolerance of the LD criterion and LF criterion is 30 dB. This means the protection method can effectively distinguish faults from disturbances even when the signal is seriously polluted.

**Figure 19.** The influence of signal-to-noise (SNR) on the action accuracy.

From the above analysis, the proposed protection scheme is proved to be feasible in the absence of noise. The protection method can accurately distinguish the transient type under different scenarios, such as different ground resistors, different fault distances, different numbers of faulted SMs, and different SNRs. These results demonstrate the proposed wavelet entropy-based method can distinguish faults from interferences with high accuracy and reduce the misjudgments of protections.
