Numerical-field analysis of differential leakage reactance of stator winding in three-phase induction motors

Introduction. The differential leakage reactance (DLR) of the stator winding of three-phase induction motors (TIM) is considered. It is known that DLR is the sum of the self-induction resistances of the winding from all harmonics of its magnetic field, excluding the first one, and its analytical definition is too complicated. But this reactance is a mandatory design element, including for calculating a number of other parameters and characteristics of such motors. Problem. Because of this, in the current classical design methods, the DLR are determined by a simplified formula with the addition of a number of coefficients, tabular and graphical dependencies. As a result, not only the physical and mathematical meaning of DLR is lost, but even the accuracy of its calculation is difficult to assess. Goal. The purpose of the paper consists in the comparative verification of the classical design calculation of the DLR of the TIM stator winding by numerical-field analysis of the harmonic composition of the EMF of self-inductions in this winding and by the determination of the considered DLR on such a basis. Methodology. Harmonic analysis is performed by obtaining the angular and time discrete functions of the magnetic flux linkage (MFL) of the stator winding with their formation in two ways: single-position calculation of the magnetic field and conditional rotation of the phase zones of the winding, or multi-position calculations of the rotating magnetic field and determination of the MFL of stationary phase zones. Results. Computational analysis is performed for nine common variants of TIM, designed according to a single classical method with variation of their power and the number of poles. Originality. A comparison of the results of the classical and numerical-field calculations of the DLR using the FEMM program showed their large discrepancy, which is attributed to the indicated inadequacy of the first one, since the second option is devoid of the shortcomings of the first one due to the fact that it takes into account the dimensions of the TIM structures, the saturation of the magnetic circuit and the physical and mathematical essence of the parameters and values under consideration. Practical value. The presented method of numerical-field analysis and the obtained results of calculating the DLR of the TIM stator winding are recommended as a basis for improving the system of their design. At the same time, a similar approach can be applied to the DLR of the TIM rotor winding, but taking into account its features. References 27, tables 13, figures 7.