*3.2. Full-Load Analysis*

The three-phase input armature current of inverter-1 (*Iabc*1) for the *3r<sup>d</sup>* and *6th* harmonic injection-based brushless WFSM topologies is 5 A (peak) at a 60 Hz frequency. This current is presented in Figure 8a. In the case of the *3r<sup>d</sup>* harmonic injection-based WFSM topology, the magnitude of the single-phase input armature current for inverter-2 is 1 A (peak) at a 180 Hz frequency, whereas it is 1 A (peak) at a 360 Hz frequency in the case of the proposed high-harmonic injection-based WFSM topology, as presented in Figure 8b,c, respectively. Figure 8d,e show the three-phase armature currents flowing across A, B, and C windings employing the *3r<sup>d</sup>* and *6th* harmonic injection-based brushless WFSM topologies. Fast Fourier transform (FFT) plots for phase *A* of the armature currents are produced to show the amplitude of the fundamental and harmonic current components for the *3r<sup>d</sup>* and *6th* harmonic injection-based WFSM topologies. These graphs are presented in Figure 9a,b, respectively.

**Figure 6.** (**a**) Back-EMF of the employed machine, and (**b**) its FFT plot.

**Figure 7.** Cogging torque of the employed machine.

**Figure 8.** *Cont.*

**Figure 8.** (**a**) Inverter-1 current, (**b**) inverter-2 current for the *3r<sup>d</sup>* harmonic injection-based topology, (**c**) inverter-2 current for the *6th* harmonic injection-based topology, (**d**) armature currents for the *3r<sup>d</sup>* harmonic injection-based topology, and (**e**) armature currents for the *6th* harmonic injection-based WFSM topology.

**Figure 9.** *Cont.*

**Figure 9.** FFT plot of phase *A* of the armature currents for (**a**) typical brushless WFSM topology based on *3r<sup>d</sup>* harmonic field excitation scheme, and (**b**) proposed high-harmonic injection-based WFSM topology.

The shaft of both machines is rotated at a speed of 1800 rpm, whereas the simulations are performed for 1 s. The flux linkages of the machine using the conventional and proposed WFSM topologies are presented in Figure 10a,b, respectively. Figure 11a,b show the magnetic field density plot of the analyzed machines employing the *3r<sup>d</sup>* and *6th* harmonic injection-based brushless WFSM topologies, respectively. These figures show that the operation of the investigated machines is under a saturation level of 2.24 T, and none of its parts become saturated during the operation. The rotor harmonic and field currents for the *3r<sup>d</sup>* and *6th* harmonic injection-based brushless WFSM topologies are presented in Figure 12a,b, respectively. As seen in the figures, the magnitude of the average field current for the brushless WFSM topology based on the *3r<sup>d</sup>* harmonic field excitation scheme is around 2.007 A, whereas, for the proposed high-harmonic injection-based WFSM topology its magnitude is 2.08 A, which is 3.63% higher than the *3r<sup>d</sup>* harmonic injectionbased topology. Figure 13a,b show the output torque of the analyzed machines. The comparative performance analysis of the *3r<sup>d</sup>* and *6th* harmonic injection-based brushless WFSM topologies is presented in Table 4.



**Figure 11.** *Cont.*

**Figure 11.** Magnetic flux density graph for (**a**) *3r<sup>d</sup>* harmonic injection-based, and (**b**) *6th* harmonic injection-based WFSM topologies.

**Figure 12.** Rotor currents for (**a**) *3r<sup>d</sup>* harmonic injection-based, and (**b**) *6th* harmonic injection-based WFSM topologies.

**Figure 13.** Output torque for (**a**) *3r<sup>d</sup>* harmonic injection-based, and (**b**) *6th* harmonic injection-based WFSM topologies.
