Flux-Density Harmonics Analysis of Switched-Flux Permanent Magnet Machines

By developing a simple permeance-magnetomotive force (MMF) model of switched-flux permanent magnet (SFPM) machines, the air-gap flux density produced by both PMs and armature current can be derived, in which harmonics with the same order and rotational speed are called an effective harmonic pair (EHP). By investigating the influences of armature current angle $\delta $ on both the phase and amplitude of each EHP, it is found that the amplitudes of both PM and armature reaction flux-density harmonics maintain fixed, whereas the space phase shift between them changes accordingly with armature current angle. Specifically, the PM and armature reaction flux-density harmonics are orthogonal in space if zero ${d}$ -axis current is fed. Therefore, the maximal torque is realized for each EHP. As the total torque of SFPM machines is the superposition of the contributions by each EHP, the zero ${d}$ -axis current control method turns out to be the optimum for maximal torque per ampere, thus verifying analytically that the ${d}$ - and ${q}$ -axes inductances are equal according to the general torque equation for the investigated machine topology. In addition, the torque adjustment mechanism of each EHP in SFPM machines has also been analytically demonstrated to be resemble that of the surface-mounted PM synchronous machine (PMSM). Finally, the finite-element analysis (FEA) has been performed to validate the previous analytical predictions.