Magnetic Field Conforming Formulations for Foil Windings
For engineers simulating foil windings, this provides a more efficient numerical method that reduces problem size while maintaining accuracy.
The authors extend foil winding homogenization to magnetic field conforming formulations, introducing a scalar potential in non-conducting regions to reduce degrees of freedom. The models yield reliable results with reduced computational size in 2-D and 3-D benchmarks and a transient HTS coil simulation.
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the magnetic scalar potential in non-conducting regions to improve the efficiency of the model. This leads to a significant reduction in the number of degrees of freedom, particularly in 3-D applications. The proposed models are verified on two frequency-domain benchmark problems: a 2-D axisymmetric problem and a 3-D problem. They reproduce results obtained with magnetic flux density conforming formulations and with resolved conductor models that explicitly discretize all turns. Moreover, the models are applied in the transient simulation of a high-temperature superconducting coil. In all investigated configurations, the proposed models provide reliable results while considerably reducing the size of the numerical problem to be solved.