Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model

2026-03-31

AI Summary

This work addresses the prohibitive computational cost of full-scale finite element simulation for high-temperature superconducting (HTS) coils in engineering design. The authors propose a homogenization approach based on the foil conductor model (FCM), integrating the h-, h-φ-, and t-ω-formulations of electromagnetic fields. Voltage-based basis functions are introduced to ensure physical consistency of current density, while the magnetic scalar potential is employed in non-conducting regions to substantially reduce degrees of freedom. The method incorporates a field-strength- and angle-dependent critical current density model and achieves excellent agreement with fine-grained models in both 2D axisymmetric and 3D pancake coils, yielding R² > 0.99 for AC loss predictions. For 3D racetrack coil stacks, the t-ω FCM delivers high accuracy with a 22-fold speedup and a 78% reduction in degrees of freedom, significantly enhancing the scalability of three-dimensional simulations.

Abstract

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.

Problem

• homogenization
• high temperature superconductor
• foil conductor model
• AC loss
• computational efficiency

Innovation

• foil conductor model
• homogenization
• high-temperature superconductor
• t-omega formulation
• AC loss simulation