General modeling of the windings for multi-phase ac machines

Abstract

This paper, which deals with the winding modeling of ac multi-phase machines with a regular distribution of the stator slots, details an original matrix modeling of the stator winding. First, the properties of the balanced multi-phase windings (with integral-slot and fractional-slot patterns) are analysed. The winding function approach, one of the most common way to model the winding distribution effects on the stator rotating field, is then introduced. For multi-phase machines, it will be shown that the pole number generated by the winding distribution depends on a new parameter: the circularity index. The discrete nature of the winding, imposed by the stator slots, leads to the development of a discrete modeling of the winding obtained from sampling the winding function: two matrices, the winding function matrix and the distribution function matrix, are introduced to characterize the multi-phase winding. This matrix approach is thus a concise way to calculate the winding factors and to estimate the set of self and mutual stator inductances for smooth air gap multi-phase machines. A particularly original method of obtaining an analytical expression for the leakage mutual inductance is described. The results are validated with two experimental 5-phase PM machines by using experimental measurements and numerical simulations.