General, compact and easy‐to‐compute winding factor formulation
Franck Scuiller
Abstract
With the use of the discrete Fourier transform (DFT), the study provides a compact relation to calculate the winding factor of any winding distribution among regularly space‐shifted slots. The new expression is general, meaningful and particularly easy‐to‐compute. The phase winding layout is represented with a distribution vector whose length equals the slot number: each component corresponds to a slot and indicates the proportion of conductor allocated to the considered phase (forward turns positively counted and backward turns negatively counted). From winding factor definition, mathematical developments allow to demonstrate that, in any case, the winding factors simply relate to the DFT of the distribution vector: each component of the DFT vector corresponds to a space harmonic order and equals the so‐called complex winding factor. The module of the complex winding factor is the usual winding factor while the angle of the complex winding factor reveals the magnetic axis position for the considered space harmonic.