Finite-Element Simulation of Homogenized Field Models for Foil Windings

In electrical engineering, foil windings are used in various application areas, such as transformers or magnet systems. A foil winding is a coil that is built from winding a conducting foil that is insulated at its surface. There exists a standard model that allows to efficiently simulate foil windings in a low to medium frequency range. It uses a homogenization technique that prevents the resolution of the typically very thin foil and rather models the foil winding as a whole. Currently, the switching frequency in power electronics components is increasing as higher frequencies allow to build smaller devices with better performance. At higher frequencies, capacitive effects become relevant for foil windings. They can drastically change the behavior of foil windings because above a certain frequency, a foil winding behaves like a capacitor and no longer like a coil. Until now, there did not exist a general homogenization model for the simulation of foil windings that includes capacitive effects. The standard model only considers resistive and inductive effects but neglects capacitive effects. At the same time, a brute force simulation with a full resolution of the details in the foil winding is infeasible due to very high computational costs. This dissertation develops a finite element model for foil windings that includes capacitive effects at moderate computational costs. The model consists of two parts. First, it uses a homogenization of the materials in the foil winding domain that allows to reduce the spatial resolution of the mesh, thereby reducing the computational costs immensely. Second, it defines conditions that ensure the correct current to flow through the foil winding. These conditions enforce conductive currents to flow through the turns and displacement currents to flow across the insulation between the turns. Both parts of the model are implemented into the finite element solver Pyrit in Python. The homogenization is validated and verified with high-resolution reference simulations. Simulation results with the entire model are compared to measurement results for two distinct foil windings, showing the capability of the developed model to predict the behavior of foil windings for a large frequency range. The simulations confirm the transition from a resistive behavior at low frequencies via an inductive behavior at medium frequencies to a capacitive behavior at high frequencies.