Abstract：In recent years, Vernier permanent magnet (VPM) machines have attracted increasing attention due to the advantages of high power density at low speed in the research field of electric vehicles (EVs), aerospace actuation, and ship propulsion. However, compared with traditional PM machines, VPM machines generally suffer from a low power factor due to increased PM pole number and flux leakage. Various methods have been proposed from the perspective of machine design to enhance the power factor of VPM machines. However, current research often focuses on the design and optimization of VPM, while the power factor improvement from the theory perspective needs to be addressed. Consequently, in this paper, the power factor mechanism of the magnetic field modulation machine is investigated based on the principle of magnetic field modulation, and a power factor improvement method is proposed for VPM. Taking the V-type Vernier permanent magnet machine (VTVPM) as an example, the inherent mechanism of the power factor of the VTVPM is theoretically studied, and the formulas are derived from the permanent magnet flux linkage layer and synchronous inductance layer using the hierarchical optimization strategy. Firstly, according to the classical power factor formula of the machine, the power factor of the machine is mainly related to the permanent magnet flux linkage and synchronous inductance. Therefore, this paper, from the perspective of optimizing the permanent magnet flux linkage and synchronous inductance, taking harmonics as a bridge, derives and establishes the internal relationship between the permanent magnet flux linkage and synchronous inductance with the design parameters. By the scanning analysis of the parameters θtr and θv of the permanent magnet flux layer motor, it can be concluded that θtr and θv obtain extreme values at 1.5 ° and 56 °, which is the optimal design of the VTVPM motor, and the amplitude of the fundamental wave of the permanent magnet flux linkage is increased from 135.4 mWb to 149.2 mWb. The synchronous inductance layer combines the sensitivity analysis and response surface methods to reduce the synchronous inductance from 11.1 mH to 9.59 mH. Finally, the power factor is increased from 0.54 to 0.67. In addition, the fundamental amplitude of the back EMF is increased from 65 V to 97 V, and the optimized machine load torque is close to 76.94 N·m, increased by 18.07 %. Moreover, the torque ripple is reduced from 2.60 % to 1.73 %. The simulation results verify the feasibility of the optimization design method. Based on the study of power factor production mechanism of the field modulated machine, this paper presents an optimal design method for the power factor of the VPM machine. The proposed design method adopts hierarchical optimization to theoretically deduce and optimize the permanent magnet flux linkage and synchronous inductor layers, respectively. The power factor and other electromagnetic performance of the machine before and after optimization are compared. Finally, the prototype machine is built, and the basic experiments are carried out. Both the theoretical analysis and experimental results verify the effectiveness and rationality of the proposed optimization design method.
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2023, Vol. 38 
