交流电机谐波电动势节距因数出现负值的分析和处理

针对运用现有交流电机谐波电动势节距因数公式计算电动势有效值出现负值问题,采用了电路时域分析、相量分析以及物理学中场强矢量分析相结合的方法,对整距和短距线圈谐波电动势的构成依次进行了研究,对短距线圈谐波电动势构成中的节距因数采用划分区间分段讨论的方法着重进行了探讨,提出了一个基于v次谐波节距半值γv/2(电角度形式)区间的分段函数新节距因数公式,并以通常的线圈节距值y1=5τ/6(槽数形式)选取1~19次奇次谐波分别对新旧公式进行了数据验证。研究结果表明,与现有公式当v=3,9,13,17,19时出现负值不同,新的公式在计算谐波电动势节距因数时全程未出现负值,说明克服了现有公式的缺陷,未来可替代现有公式使用。

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

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 in-tensity 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 valueγv/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.