Christian Deeg

Determination of Stator End Winding Inductance of Large Induction Machines: Comparison Between Analytics, Numerics, and Measurements

Abstract Knowledge of the end winding inductance of electrical machines is decisive for calculating their operating performance. In this article, two different approaches to analytically calculate the stator end winding inductance of large induction machines are discussed. The first method is based on the exact replication of the 3D conductor geometry using serially connected straight filaments, where the inductances are calculated by solving Neumanns integral. In the second method, the end winding flux is resolved into components excited by the axial and circumferential end winding magnetomotive force, resulting in a far simpler geometrical model. In both cases, end face effects are taken into account by adopting the method of images. The analytical approaches are compared to the known analytical calculation method proposed by Alger [1]. In addition, the stator end winding inductance is computed by means of 3D finite-element analysis. Using experimental validation, it is shown that both the analytical and numerical results reasonably correlate with removed rotor inductance measurements taken for several induction machines with different rated powers and frame sizes, if the permeability of the laminated core is taken into consideration.

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 machines 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.