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

TL;DR

This paper develops and verifies homogenized foil conductor models for HTS coils, enabling accurate and efficient simulations of complex coil geometries with significant computational speedups.

Contribution

It introduces and validates the h, h-$ ho$, and t-$ ho$ foil conductor models for HTS coils, reducing computational complexity while maintaining accuracy.

Findings

All models show >0.99 correlation with detailed simulations.

The t-$ ho$ model achieves 22x speedup and 78% reduction in degrees of freedom.

Models are effective in 2D and 3D geometries with complex coil stacks.

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-$\phi$, and t-$\omega$ 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-$\phi$ and especially the t-$\omega$ 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-$\omega$ FCM achieves a speedup factor of 22 and reduces degrees of freedom by 78 % with respect to a detailed reference model.