Contribution to the Modeling of Homogenized Windings with the Finite Element Method — Eddy-Current and Capacitive Effects
This thesis focuses on the development of mathematical models to calculate electromagnetic fields in foil and stranded windings. It aims at devising finite-element formulations that consider the whole stack (bundle) of conductors as a periodic homogenizable structure. In such formulations, the eddy-current and capacitive effects are estimated without the explicit representation of each winding turn in the geometry. By doing so, affordable simulations with sufficient accuracy are intended as the research outcome; since traditional finite-element models remain too computationally expensive to be practical software tools. The proposed models are established upon the well-known Maxwell’s equations. Between the magnetic and electric fields, the strong coupling is neglected to allow a separate estimation of the eddy-current (resistive and inductive) and capacitive effects; full wave models are out of the thesis scope. While homogenized eddy-current models are formulated for both foil and stranded windings; the study of the parasitic capacitive effect is limited to the latter.
To treat eddy-current effects, the foil-winding homogenization is characterized by an unidirectional current-density redistribution and an inter-turn space-dependent voltage. Conversely, when dealing with stranded windings, the model is based on the use of frequency-dependent parameters that are fitted into Foster-network forms, which allows for time-domain analysis. Furthermore, to study the parasitic capacitive effect, this work proposes two electrostatic homogenizations for the computation of a terminal capacitance and one semi-homogenized model, built upon Darwin’s formulation, that locally estimates the displacement currents. By way of validation, the results of all homogenized models are compared to those obtained by accurate but expensive reference finite-element models wherein all turns are explicitly discretized.