Paavo Rasilo

Louis Denis, Elias Paakkunainen, Paavo Rasilo et al.

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.

Elias Paakkunainen, Louis Denis, Benoît Vanderheyden et al.

Efficient numerical models are required for the design of systems with high temperature superconductor (HTS) coils, as fully resolved finite element simulations of individual coated conductors become computationally prohibitive. This work applies the foil conductor model (FCM) to insulated HTS coils using magnetic field conforming h-(full), h-$ϕ$, and t-$ω$ formulations. The approach replaces individual turns by a homogenized bulk and ensures physically consistent current density distributions in the coils by using additional voltage basis functions in the finite element formulations. The models are verified in 2D axisymmetric and 3D geometries with a pancake coil simulation under AC transport current excitation. All FCM formulations show excellent agreement with reference detailed simulations, with coefficients of determination above 0.99 for instantaneous AC losses. In 3D, the h-$ϕ$ and especially the t-$ω$ formulation substantially reduce the number of degrees of freedom by using the magnetic scalar potential in non-conducting regions. Scalability is demonstrated with a 3D stack of racetrack coils model with a field- and angle-dependent critical current density. For the stack of racetrack coils, while maintaining accurate loss prediction, the t-$ω$ FCM achieves a speedup factor of 22 and reduces degrees of freedom by 78 % with respect to a detailed reference model.