Analysis and treatment of negative values appearing in calculation of harmonic electromotive force pitch factor of AC machines

LONG Fei1, JIANG Wei2, XV Minwei1

(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 pitch factor formula, the compositions of harmonic EMFs were studied with fullpitch coils and fractionalpitch coils in turn by using a method combined with timedomain analysis, phasor analysis in circuit theory and field intensity vector analysis in physics. With an approach of segmentation discussion by dividing intervals,the pitch factor in the composition of harmonic EMFs for fractionalpitch coils was discussed emphatically so as to put forward a new pitch factor formula in the form of piecewise function based on the interval of the vth harmonic pitch half value γv/2 (electric angle form).By the normal coil pitch value y1=5τ/6(slot number form),the data validations for the existing and new formulae were carried out respectively by selecting the 1st~19th odd harmonics. The results indicate that negative values appear when v=3,9,13,17,19 in the calculation of the pitch factor of harmonic EMFs by using the existing formula,while no negative value appears in the whole process of calculating by using the new formula,which overcomes the defect of the existing formula and therefore can substitute the existing formula in the future.

Key words: harmonic electromotive force(harmonic EMF);pitch factor;timedomain analysis;phasor analysis;vector analysis