Analysis of negative values appearing in the calculation of theharmonic electromotive force distribution factor of AC machines
                                                 LONG Fei1, JIANG Wei2, XU Minwei1, MO Yueping2
(1.Yangzhou OptoElectrical Products Testing Institute, Yangzhou 225009, China;2.School of Hydraulic Energy and Power Engineering, Yangzhou University, Yangzhou 225002, China)

Abstract: In order to solve the problem of negative values appearing in the calculation of effective values of harmonic electromotive forces(EMFs) of AC machines by using the existing harmonic distribution factor formula, the distribution factor in the resultant harmonic EMF for a polephase group was studied and a new phasesynthesis theory of a polephase group that there must be a circumcircle for q equalphasedifference nonzero phasors which are linked end to end according to the sum rule of translation was put forward.By applying this theory combined with phasor diagram analysis in circuit theory and complete induction in mathematics,a new 3piecewise distribution factor formula was induced corresponding to the vth harmonic included angle between two adjacent slots αv2kπ which is inferior angle, straight angle or reflex angle respectively,followed by the limit form of the formula when q→∞. The data validations for the existing and new formulae were carried out respectively by selecting q=2，…8，∞ and intercepting the 1st~19 th odd harmonics for 3phase windings.The results indicate that no negative value appears in the whole process of calculating the distribution factor of harmonic EMFS by the new, which can substitute the existing formula and be generalized to the calculation of the distribution factor of harmonic magnetomotive forces.

Key words: harmonic electromotive force(harmonic EMF); distribution factor; phasor diagram analysis; complete induction; limit analysis