Winding Function Approach for Winding Analysis

The winding factor is an operand in order to consider the effect of winding distribution and chording on the spatial distribution of the magnetic field in the air gap of synchronous and induction machines. The sinusoidal functions for winding factor calculation presented in literature are not defined and valid for every irregular winding, e.g., single-layer fractional-slot, combined star-delta, multilayer (greater than two), and asymmetrical windings. Although the summation of induced voltage phasors (star of slots) is the most accurate method, asymmetrical windings require to be decomposed in symmetrical components. In this paper, in addition to deriving the symmetrical components for asymmetrical multiphase windings, the analytical formulation is presented to relate the harmonic content of winding functions to winding factors. The harmonic leakage factor is accurately formulated from the winding function instead of the Görges diagram without the need for summing up an infinite number of normalized winding factors quadratically. Without restriction of the number of layers and the distribution of the winding, including full-pitch, chorded and fractional-slot symmetrical and asymmetrical windings, the suggested analysis method is validated with the star of slots and sinusoidal functions of distribution and pitch factors, where applicable.