## 3 Four Kinds of Machine Performance and Comparison
### Comparison of Electromagnetic Properties  
In this paper, finite element analysis (FEA) is used to calculate the core loss and the copper loss. In the calculation process, the mechanical losses of the four types of motor are kept the same. The efficiencies of the four types of motors are shown in Figure 13a. It is seen that the efficiency of the induction machine is 91.76%, while the efficiency of the other three machines ranges from 94% to 95%, about 2.5% higher than that of the induction machine. Due to the special rotor structure of the SynRM, ferrite-assisted SynRM and IPM, the power factor of three machines depends on the contribution of the permanent magnets and the salient pole rate of the rotor structure. The power factor is 0.8 for the SynRM, 0.9 for ferrite-assisted the SynRM and 0.97 for the IPM. The power factor of the ferrite-assisted SynRM is higher than that of the IM, and it is lower than that of the IPM. As shown in Figure 13b, the copper and iron losses of the induction motor are higher than those of several other motors when operating at the rated load. The total losses of the other three motors are equivalent. The torque curves of the four motors are shown in Figure 14. In the present study, it is known that the torque ripple can be effectively reduced by using the skewed slots and skewed poles [26]. Torque ripple needs to be reduced as much as possible in motor design. Torque ripple refers to the motor running stably, and the output torque of the motor is not a constant value but a positive and negative ripple centered on the average value over time. Numerically, the torque ripple is the ratio of the difference between the maximum and minimum values of the output torque at the rated load to the average output torque. Through the analysis and optimization of the rotor structure parameters, the reasonable parameters are selected and skewed slots are adopted to decrease the torque ripple. It can be seen that the torque ripples of the SynRM and the IPM are close, at about 14.6%. The torque ripple of the ferrite-assisted SynRM is 11.4%. The torque ripple of the IM is the smallest, at about 11.23%. Figure 13: Electromagnetic performance of the four motors: (**a**) efficiency and power factor; (**b**) core loss and copper loss. When the four motors operate at the rated speed without any load, the no-load line back-electromotive force (back-EMF) and air gap radial flux density can be obtained, as shown in Figure 15. As seen, the waveform of the ferrite-assisted SynRM is relatively sinusoidal, while the no-load line back-EMF of the IPM has more harmonics. The RMS value of the no-load line back-EMF of the ferrite-assisted SynRM is about 87 V, while that of the IPM is about 338 V. Additionally, due to the different magnetic properties of the ferrites and rare-earth PMs, the radial air-gap magnetic flux density amplitude of the IPM is larger. The radial air-gap flux density of the ferrite-assisted SynRM is smaller, and the flux density is more uniformly distributed. The performances of the four motors are summarized in Table 4.  
Figure 14: Torque curves of (**a**) IM, (**b**) SynRM, (**c**) ferrite-assisted SynRM and (**d**) IPM. Figure 15: (**a**) Back-EMF versus rotor position. (**b**) Air gap radial flux density versus rotor position. It is well known that ferrite-assisted synchronous reluctance motors have the risk of irreversible demagnetization. Since the magnetic properties of ferrites are much weaker than those of rare-earth permanent magnets, irreversible demagnetization can occur very easily under overload conditions. In this paper, the ferrite of Y30 is used in the ferrite-assisted synchronous reluctance motor. The inflection point of the demagnetization curve of the Y30 is about 0.18T. Figure 16 shows the demagnetization of the Y30 under different load conditions. No irreversible demagnetization occurs in the three-layer Y30 under the rated load. Under 1.5 times the load, irreversible demagnetization occurs locally in the second and third layers of the ferrites.