Star of slots-based graphical assessment of the back-EMF of fractional-slot PM synchronous machines

Fractional-slot PM synchronous machines are presently given an increasing attention especially in propulsion applications where they exhibit interesting features. These could not be accessed without a suitable arrangement of the armature winding which could be achieved using the star of slots approach. The paper deals with an extension of the star of slots to the assessment of the back-EMF of fractional-slot machines. To do so, a case study of a twelve slot ten pole machine is treated. The star of slots is systematically considered for each possible back-EMF harmonic. The corresponding winding factor and initial phase are then graphically found out. Accounting for the Fourrier transform of the PM air gap flux density, the back-EMFs induced by the fundamental rotating field and the harmonic ones are derived, whose superposition yields the waveform of the back-EMF per phase.