MMF Harmonic Analysis of $\mathbf{Multi}-\boldsymbol{M}-\mathbf{Phase}$ Fractional-Slot Permanent-Magnet Machines with Partial Operating Winding Sets

This paper investigates the magnetomotive force (MMF) harmonics in
$\mathbf{multi}-\boldsymbol{m}-\mathbf{phase}$
fractional-slot machines when one or more
$\boldsymbol{m}- \mathbf{phase}$
channels are disconnected due to faults. Employing a universal
$\boldsymbol{Q}-\mathbf{set}\ \boldsymbol{m}-\mathbf{phase}$
winding arrangement, this study reveals the intrinsic relationships between MMF harmonics generated by different winding sets. Through analytical derivation, results show that harmonics of the same order from different winding sets share the same amplitude but differ in phase shifts. For harmonics of different orders, certain symmetries and similarities are found in their phasors. Based on the discovered rules, all composite MMF harmonics can be classified into
$(\boldsymbol{Q}/\mathbf{2}+\mathbf{1})$
groups when
$\boldsymbol{Q}$
is even and
$(\boldsymbol{Q}+\mathbf{1})/\mathbf{2}$
groups when
$\boldsymbol{Q}$
is odd. The MMF harmonics within the same group vary synchronously as the faulty condition changes. The findings are validated by the finite-element method, which will be provided in detail in the full paper.