Finite-Element Modeling of Thin Wires Including Skin- and Proximity Effects

This thesis presents an accurate and inexpensive treatment of thin conducting wires in finite element (FE) models for the magnetic vector potential magneto- dynamics formulation in frequency domain. The idea of the proposed technique, called Semi-Analytical (SA) method, is three-fold. Real conductors are represented in the FE model by idealized thin wires with vanishing radius. The implied mod- elling error is then canceled by means of a field truncation based on the solution of a small auxiliary FE problem. Finally, analytical results are invoked to reconstruct the local field solution and to accurately evaluate the losses and impedances. The SA method is first demonstrated and then systematically compared against the results of a conventional fully discretized finite element model (FM) in case of a single conductor and of multiple parallel conductors. The method’s accuracy at a broad range of frequencies is studied, particularly emphasizing the impact of spacing between conductors. Lastly, the formulation is extended to include ex- citation sources (e.g., voltage, current) and analytical expressions accounting for frequency-dependent effects on the inductance and resistance of multi-turn coils.