Family Phenomenon in Electric Machine Winding MMF Space Harmonics: Attribution and Applications

Research into electric machine windings with reduced magnetomotive force (MMF) space harmonic content has a long history. However, attention has often been confined to lower order harmonics with larger magnitudes. To more clearly and easily visualize the MMF space harmonic spectrum, this paper will explain the phenomenon of harmonic “families” intrinsic to a majority of electric machine windings. With a concise proof, it will be shown that within each family, the harmonic components have magnitudes that are inversely proportional to their orders. As a consequence, harmonics of the same family have the same winding factor. The number of families and, hence, different winding factors is found to be only a fraction of the number of slots of a unit machine. The family phenomenon greatly simplifies the determination of an MMF harmonic spectrum, envisions the behavior of higher order components, and predicts how a design change can improve the winding harmonic profile. When the family phenomenon disappears and the special cases with enlarged periods are also discussed. Two examples, both eliminating the 5th- and 7th-order harmonics but with very different harmonic spectra, are analyzed and compared to illustrate the power of the family phenomenon to aid the design of windings with improved electromagnetic performance.