Contribution to the analysis of end winding inductances of induction machines — I

Analytical calculation of the operating performance of induction machines requires exact knowledge of the leakage inductances in both the stator and the rotor. In contrast to the flux coupling within the iron core where flux paths are two-dimensional and predominantly determined by permeabilities of different magnitudes (iron core vs. air gap/slots), thus making it easy to separately calculate main and leakage fluxes, the calculation of the leakage flux in the end winding region exhibits an additional set of problems to be accounted for. The paper at hand presents a comprehensive analytical calculation model (AM) which has been set up to physically correctly represent the leakage fluxes and the flux coupling between the stator and rotor by accounting for the complex geometry of the end winding region of induction machines as well as the influence of the machine's active part bounding the end winding region. The model has been validated against results from 3D Finite Element Analysis (FEA), showing good accordance. The results can be directly used in the one-phased T-equivalent circuit model of the induction machine as well as for 2D-FEA. The publication of the research will be divided into two parts, with the first part at hand concentrating on the self inductance of the stator and the mutual inductance between stator and rotor. The second part, which will be published subsequently in the near future, will present a new method of calculating the rotor end ring impedance, including a harmonic consideration of the skin effect in the end ring and the bar overhang.