Multi-phase winding modelling. Analysis of the space harmonics properties

In electromechanical conversion, the function of the winding is to generate a magnetomotive force (MMF), defined as the cumulative sum of ampere-turns encountered during movement along the air gap. As the current is generally temporally variable, the magnetomotive force is a wave whose space variable is the mechanical angle. Modulation of the magnetomotive force by the air gap permeance defines the rotating field wave. In many cases, the winding is designed to allow the development of a sinusoidal progressive MMF wave and sinusoidal fluxes. Achievement of these two criteria is measured by the quality of the MMF wave and the winding factors. Spatial harmonics refer to undesirable MMF wave components resulting, in particular, from the practical constraint of distributing the winding in the slots. The winding factor accounts for the way these spatial harmonics affect electrical quantities (flux, voltage, current).

When defining the winding, the designer must master these two criteria. For calculating winding factors, the "Stars of slots" or Voltage Phasor Diagram method is generally used, but its use requires prior classification and enumeration of the coils making up the winding, operations that cannot be trivially automated. For the prediction of space harmonics, there don't seem to be any clear, easily implemented formulations that can be applied to all windings. In other words, published approaches concern particular three-phase distributions (so-called fractional distributions) and cannot be extended to all polyphase configurations.

Today, however, due to the frequent use of a static converter to interface the machine to the electrical source, the winding arithmetic (i.e. the triplet number of pole pairs, number of phases and number of notches) can be freed up at the design stage, thus allowing fractional and polyphase configurations, which are more difficult to characterize. In this context of intensive exploration of new solutions, the need for a general method that is concise (based on minimal parameterization), simple to implement and physically meaningful is more keenly felt. The aim of this article is to build such an approach.

The proposed method is applicable to polyphase windings of rotating machines satisfying the following two conditions. Firstly, the winding is distributed over identical, evenly-spaced slots around the periphery of the air gap. Secondly, the phase windings are identical and evenly spaced. Basically, the method consists of representing such a distribution in matrix form and extracting its harmonic properties by discrete Fourier transform (DFT). In this way, a concise, general and easy-to-implement formulation is proposed for winding factors. As a corollary, the use of the concept of power sequences enables arithmetic...