**1. Introduction**

In contrast to the widespread range of applications and the speedy production increase of the permanent magne<sup>t</sup> (PM) machines due to their high efficiency, power density, and power factor, the price of rare-earth permanent magnets with high magnetic properties have ridiculously increased. On the other hand, the rare-earth material industry is facing serious environmental issues in keeping the prolonged and stable supply of rare-earth materials to the PM machines manufacturing industry [1].

In order to deal with these problems and to attain high flux-weakening-based performances of electrical machines in electrical vehicle (EV) and hybrid vehicle (HV) applications, other possibilities, such as PM-assisted synchronous reluctance machines and wound field synchronous machines, have sparked interest among the researchers [2–10].

The rotor field is excited in a typical WFSM, utilizing an excitation approach that includes brushes, slip rings, and a separate exciter. On the rotor side, a brushes and slip rings assembly connects the machine field winding to the excitation system [11–14]. The usage of brushes in a typical WFSM increases its maintenance cost due to their periodic replacement and continuous sparking. On the other hand, an additional exciter rises the overall size and cost of the system [15–18].

**Citation:** Bukhari, S.S.H.; Mangi, F.H.; Sami, I.; Ali, Q.; Ro, J.-S. High-Harmonic Injection-Based Brushless Wound Field Synchronous Machine Topology. *Mathematics* **2021**,*9*, 1721. https://doi.org/10.3390/ math9151721

Academic Editors: Vladimir Prakht, Mohamed N. Ibrahim and Aleksey S. Anuchin

Received: 26 June 2021 Accepted: 20 July 2021 Published: 22 July 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Therefore, to ge<sup>t</sup> rid of the obligation of brushes, slip rings, and additional exciters, a number of brushless topologies have been presented by various researchers in the available literature. In general, for the brushless operation of WFSM, a distinct excitation winding is housed in the rotor in addition to the field winding. However, another winding, named the auxiliary winding, is housed in the stator along with the main armature winding. This auxiliary winding produces an additional MMF in the air gap that induces a harmonic current in the excitation winding of the rotor. The induced harmonic current is then rectified and supplied to the field winding of the rotor. This field current generates a rotor field that becomes coupled with the armature field to produce torque. A basic diagram of such a system is presented in Figure 1.

**Figure 1.** Typical *3r<sup>d</sup>* harmonic injection-based brushless WFSM topology employing two dual-stator winding configurations.

Many researchers have proposed various schemes to attain the brushless operation of WFSMs by modifying the typical brushless topology in order to attain the maximum advantages of brushless excitation. These schemes are either based on space–harmonics generation or on time–harmonics generation.

A brushless WFSM topology based on a sub-harmonic field excitation scheme is proposed in [6]. In the proposed brushless topology, a dual-inverter configuration is utilized to provide two different magnitudes of current to the armature winding that is divided into two halves with a distinct star connection distributed in a symmetric arrangement. The difference in the magnitudes of the current supplied by the inverters produces sub-harmonics, besides the fundamental-harmonic, which can be utilized to induce currents in the excitation winding of the rotor. This topology is further investigated using a single inverter with a different number of turns for each half of the armature winding in [7]. In order to generate unbalanced radial forces associated with the subharmonically excited BL–WFSM topology and to attain its variable speed operation, an eight-pole machine topology is proposed in [8].

In [19], a brushless WFSM topology based on the *3r<sup>d</sup>* harmonic field excitation scheme is presented. In this topology, two inverters are utilized to develop an armature current shape which comprises of a fundamental and *3r<sup>d</sup>* harmonic. The required armature current shape is attained using thyristor switches operating at −180◦ phase-shifted after the completion of each cycle of the phase. The *3r<sup>d</sup>* harmonic component of the armature current is utilized to induce a harmonic current in the excitation winding of the rotor in order to attain a brushless operation. The proposed topology is further investigated using an open-winding pattern in [13]. In this topology, the required armature current shape is attained using a dual-inverter configuration without employing the thyristor switches. The proposed topology is also realized by using a modified inverter that has a different number of switches when compared to the typical three-phase inverter topology in [20].

In [14], a *3r<sup>d</sup>* harmonic-based brushless WFSM topology using zero-sequence currents is proposed. In this topology, the armature winding is supplied current from an inverter by the thyristor switches that operate a zero-crossing of each phase, generating a zerosequence current which predominantly contains a *3r<sup>d</sup>* harmonic current component for the armature winding. The generated *3r<sup>d</sup>* harmonic current is induced in the exciter winding of the rotor to provide DC to the main rotor field winding after rectification in order to attain brushless operation.

A brushless WFSM topology that employs an additional armature winding beside the main winding is proposed in [15]. Both windings are electrically connected by a rectifier and are supplied current from a single inverter. The main armature winding current produces the main armature field, whereas the rectified current flowing in the additional armature winding produces the harmonic field that is not coupled with the main armature field and is utilized in order to induce a harmonic current in the rotor exciter winding.

In general, the typical brushless WFSM topologies employ either sub-harmonic or the *3r<sup>d</sup>* harmonic field excitation schemes in order to achieve a brushless operation.

In this paper, a high-harmonic injection-based field excitation scheme for the brushless operation of WFSMs is proposed. In the proposed topology, two inverters are utilized. One of the inverters gives the regular three-phase current i.e., fundamental-harmonic to the armature winding, whereas the second inverter injects a single-phase *6th* harmonic current to the neutral-point of the Y-connected armature winding. The inverters are of customary design, without holding any modification in their structure. The fundamentalharmonic current produces the main armature field, whereas the high-harmonic i.e., *6th* harmonic current, in this case, develops the high-harmonic field in the air gap of the machine. The high-harmonic field induces the harmonic current in the exciter winding of the rotor that is connected to the field winding by means of the rectifier. The induced harmonic current is rectified and utilized to excite the main rotor field winding. The interaction of the main armature and rotor fields produces electromagnetic torque. Unlike the conventional brushless WRSM topologies, which require dual three-phase inverter configurations with a parallel or open-winding pattern-based operation, or a modification in the stator armature winding to hold a dual-winding configuration, the proposed topology just utilizes customary three-phase and single-phase inverters. The operation of the singlephase inverter does not require any sophisticated control strategy, which eliminates the complications related to the control of the inverters associated with conventional brushless topologies based on an open-winding pattern. In addition, the operation of the proposed topology does not require any additional power electronics components, such as thyristor switches, as in the case of the conventional brushless topologies presented in [14] and [18]. The proposed topology along with its operating principle and electromagnetic analysis are discussed in subsequent sections. A comparative performance analysis of the proposed topology with the typical brushless WFSM employing the *3r<sup>d</sup>* harmonic injection-based field excitation scheme is carried out and is presented in these sections.
