Analytical Calculation of Yoke Flux Patterns in Fractional-Slot Permanent Magnet Machines

Machine design problems are often solved under the assumption of no-load when calculating iron flux densities. However, it is particularly important to account for the fluxes from the stator currents, the armature reaction, in fractional-slot machines. The fluxes from the permanent magnets and the armature reaction both vary in time with the electrical frequency. By studying the flux that flows along the stator yoke behind every slot in such a machine, it is revealed that the armature reaction flux does not have the same amplitude behind all slots. In addition, it is revealed that the time-varying no-load and armature reaction fluxes are shifted in time, with different phase shifts behind different slots. The sum of the no-load and armature reaction fluxes, namely, the load flux, depends on both the amplitudes of the fluxes and the phase shift between them. The resulting load flux behind each slot varies significantly. In four investigated machines, the ratio of the highest to the lowest load flux amplitude ranges between 1.6 and 6. The load flux can be significantly higher than the no-load flux. The flux calculations are verified through finite-element analysis in all four machines, and the error in the maximum load flux ranges between 2% and 6%.