Analytical investigation on the power factor of a flux-modulated permanent-magnet synchronous machine

In this paper, partial differential equations are used to describe the magnet field behavior in terms of magnetic vector potentials. The whole calculation domain is partitioned into six regions, viz. the stator slot and slot opening, the inner and outer air-gaps, the slots between modulation pole-pieces, and the PMs. The magnetic vector potentials are governed by Laplace´s equations. And in Region I and Region VI, magnetic vector potentials are of Poisson´s equations due to the existence of current and PMs, respectively. By applying the constraints on the interfaces between these regions, the solution of the magnetic field could be derived. The analytically and numerically calculated distribution of the radial flux density in the inner air-gap due to the PMs on the outer rotor are compared. As can be seen, the analytical results have a good agreement with the FEM calculation, which indicates the developed analytical model could be employed as a powerful tool for predicting and analyzing the power factor of the FM-PMSM. With the knowledge of the solution of the magnetic field, the flux linkage of each phase winding could be obtained through the surface integral of the magnetic vector potential in Region I_i. Then, the self and mutual inductances of each winding could be deducted, which are 4.06 mH and 2.02 mH, respectively. Similarly, the analytically and numerically calculated inductances have a good agreement. Substituting the inductances, currents and resistances into the voltage equation, the voltage of each phase winding could be obtained as well. The waveforms of the voltage and current of phase-A winding versus the time at the rated power is presented. Finally, the active and reactive power could be calculated by expressing the flux linkage in terms of impedances, and the predicted power factor of the studied FM-PMSM is 0.6, which is quite low compared with conventional PM machines. And the low power factor will inevitably lead to the increase of the capaci- y, volume and loss of the inverter.