**4. Conclusions**

A high-harmonic injection-based field excitation scheme for the brushless operation of WFSMs has been discussed in this paper. This scheme utilized two inverters. One inverter provided the regular three-phase current, while the second inverter injected the singlephase *6th* harmonic current to the neutral-point of the Y-connected armature winding. The regular three-phase current was used to produce the main armature field, whereas the single-phase *6th* harmonic induced the harmonic current in the rotor excitation winding. The induced harmonic current was used to supply DC to the field winding of the rotor after rectification, in order to attain a brushless operation.

A four-pole, 24-slot machine was utilized to validate the operation of the proposed scheme and attain its electromagnetic performance by FEA. The proposed high-harmonic injection-based field excitation scheme attains a better performance for the output average torque, maximum torque, and efficiency. However, the torque ripple of the proposed scheme is 0.5% higher than the typical brushless WFSM topology, based on the *3r<sup>d</sup>* harmonic field excitation scheme.

**Author Contributions:** Conceptualization, S.S.H.B. and F.H.M.; software, S.S.H.B. and I.S.; formal analysis, S.S.H.B. and Q.A.; writing—original draft preparation, S.S.H.B.; funding acquisition, J.-S.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the Brain Pool (BP) Program funded by the Ministry of Science and ICT through the National Research Foundation of Korea under Grant 2019H1D3A1A01102 988, and in part by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education under Grant 2016R1D1A1B01008058.

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