**6. Conclusions**

This paper illustrates the importance of the mother wavelet for fault classification in electrical systems. When faults occur in transmission line systems and transformers, the coefficients in three phases and a positive sequence are detected. The behavior of the coefficients is dependent on the fault type, fault angle, and fault position. Phase faults have higher coe fficients than phase unfaults. In addition, fault conditions can be detected by a positive sequence.

The mother wavelets, i.e., Daubechies (db), symlets (sym), biorthogonal (bior), and Coiflets (coif), are used to compare the coe fficient values and behaviors. Figures 5–8 show the coe fficient values and behaviors. Each mother wavelet has a similar behavior, but its value is not the same. The same behavior can be obtained by di fferent fault classification algorithms in data simulation, as shown in Figure 9. The data are divided into three parts: 1. algorithm design—50% (888 data), 2. data testing—25% (444 data points), and 3. case study—25% (444 data points).

For the case study of the di fferent mother wavelets, the accuracy of the results is summarized in Table 3. The faults in the case study are discriminated by using the proposed algorithm. It is found that there is an average accuracy of internal fault detection (relay 1) of 96.12% and of external fault detection (relay 2) of 99.07%. The mother wavelet types of Daubechies (db2) and symlets (sym2) provide the highest accuracy under condition 1, while the mother wavelet type of biorthogonal (bior3.1) provides the highest accuracy under condition 2, as shown in Figure 10.

**Figure 10.** Average accuracy of the mother wavelet in the experimental setup.

The results from the study illustrated the performance of di fferent mother wavelets on the fault classification algorithm. The di fferent mother wavelets provide a di fferent level of accuracy on the fault classification on a transformer, while they do not show a significant impact on fault classification in the transmission line. Thus, this mother wavelet is also one of the factors that must be considered in order to select the suitable mother wavelet for an application. Future work will broaden the suitable mother wavelet selection on other applications and to test the performance of the fault classification algorithm on di fferent power system topologies to verify its application.

**Author Contributions:** D.A.A. and I.M.Y.N., conceptualization; J.K., formal analysis and design of the experiment. A.N. performed the experiments and investigation; C.P. and A.N. analyzed the data; C.P. and C.J. carried out funding acquisition; D.A.A. and I.M.Y.N. contributed to resources; J.K. and C.J. wrote the paper; C.P and A.N carried out review and editing; A.N., D.A.A., and I.M.Y.N. carried out project administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by KING MONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG RESEARCH FUND, THAILAND, gran<sup>t</sup> number No. KREF156001.

**Acknowledgments:** The authors wish to gratefully acknowledge financial support for this research (No. KREF156001) from King Mongkut's Institute of Technology Ladkrabang Research fund, Thailand.

**Conflicts of Interest:** The authors declare no conflict of interest.
