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

Carlos Roberto Vargas-Llanos, Felix Huber, Nicolò Riva, Min Zhang, Francesco Grilli

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
28 Downloads (Pure)


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 cannot 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.
Original languageEnglish
Article number124001
Number of pages16
JournalSuperconductor Science and Technology
Issue number12
Early online date21 Oct 2022
Publication statusPublished - 1 Dec 2022


  • T-A formulation
  • 3D modeling
  • homogenization
  • high-temperature superconductors
  • AC losses
  • superconducting coil


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