3D homogenization of the T-A formulation for the analysis of coils with complex geometries

Abstract

The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing improvements, and computing quantities that are not easy to calculate with an analytical approach. For instance, the estimation of losses in HTS is fundamental during the design stage since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D finite element analysis is used to calculate AC losses in HTS, due to the lack of analytical solutions that can accurately represent complex operating conditions such as AC transport current and AC external applied magnetic field in coils. These 2D models are usually a representation of an infinitely long arrangement. Therefore, they cannot be used to analyze end effects and complex 3D configurations. In this publication, we use the homogenization of the T-A formulation in 3D for the analysis of superconducting coils with complex geometries where a 2D approach can not provide accurate analyses and verification of assumptions. The modeling methodology allows an easier implementation in commercial software (COMSOL Multiphysics) in comparison with the currently available 3D H homogenization, despite the complexity of the geometry. This methodology is first validated with a racetrack coil (benchmark case) by comparing the results with the well-established H formulation. Then, the electromagnetic behavior of coils with more complex geometries is analyzed.

AC Loss Reduction in HTS Coil Windings Coupled With an Iron Core

“…In addition, Neumann boundary conditions are applied to the internal and external surfaces to fulfil the definition as [12], [22]:…”

“…More recently, in our previous work [9], we carried out AC loss simulations on HTS coil windings coupled with an iron core using the 3D T-A homogenization method [10]- [12]. Results showed that the AC loss in the 8DPC (double pancake coil) Manuscript received November 10, 2022.…”

Electromagnetic-mechanical coupling analysis of high-temperature superconducting racetrack coil

“…Over recent decades, several numerical approaches have been proposed to investigate the electromagnetic behavior of HTS devices, for instance, A − V formulation [52,53], H − ϕ formulation [54], H formulation [55,56], and T − A formulation [57,58]. Among them, the T − A formulation has become one of the most popular methods in the field of HTS numerical simulation, which has been used in the electromagnetic calculation of the racetrack coil [59,60]. The T − A formulation is easily implemented in the commercial finite element software package COMSOL Multiphysics [61], which effectively reduces the difficulty of numerical modeling of superconductors.…”

“…To reduce the computation burden of the 3D model, the homogenization technique is adopted to simplify the numerical model [65]. Additionally, the Neumann boundary condition should be applied to the other two boundaries of homogeneous bulk [60,65],…”

A method to evaluate the inductance properties of REBCO excitation process based on magnetic energy density and T–A formula

“…Due to the adoption of the thin-band approximation, its convergence and computational efficiency have been improved and it is suitable for superconducting structures with extremely high aspect ratios. In addition, it can complete electromagnetic field calculations of 3D superconducting magnet models with complex geometric structures combined with curved coordinate systems [20].…”