3-D Finite-Element Thin-Shell Model for High-Temperature Superconducting Tapes

Thin-shell (TS) models are generally used in the analysis of thin regions with linear constitutive properties, although specialized versions of TS models have been developed for high-temperature superconductor (HTS) tapes. However, due to the intrinsic hypothesis of sheet current density, none of these specialized models can account for all possible configurations of HTS tapes. This article presents a new 3-D time-domain finite-element TS model for the electromagnetic modeling of arbitrary HTS tape configurations. The model is validated against benchmark problems, and it is used to solve a realistic application case, namely the calculation of ac losses in a 14-strand HTS Roebel cable. The 3-D TS model is based on a magnetic field formulation and can take into account the diffusion of the tangential magnetic field into the tapes. The nonlinear behavior of the superconducting tapes is described with an E-J power-law model in a virtual discretization across their thickness. This approach allows the calculation of nonuniform current distributions through the thickness of the tapes, when relevant; thus, losses in multiple HTS tape assemblies in any configuration can be determined accurately. The results of the proposed approach are compared with those obtained with a full 3-D representation of the thin regions and show excellent agreement (a relative difference of less than 2%) while reducing substantially the computational burden (75% fewer DoFs). These features make the new 3-D TS model very promising for simulating large-scale superconducting devices, including high-field magnets and coils of complicated shape.