[Paper Review] Three-dimensional electromagnetic modeling of practical superconductors for power applications

Milan Kapolka|arXiv (Cornell University)|May 31, 2016

Physics of Superconductivity and Magnetism64 references3 citations

TL;DR

This paper presents a novel 3D electromagnetic modeling framework, MEMEP 3D, for practical superconductors in power applications, using a variational method based on minimum electromagnetic entropy production with the vector potential T as the primary variable. The method enables accurate simulation of complex 3D current distributions, AC losses, and anisotropic effects in superconducting tapes and bulk materials, validated against analytical solutions and experiments with less than 3% error in coupling loss prediction.

ABSTRACT

HTS are feasible for hight power applications because of the smaller consumption demand of the cooling system in comparison to the whole power device. Real industral devices contain superconductors with 2D and 3D geometry (coated conductors tapes represent an example of 2D geometry, since the superconducting layer is very thin). In order to know the feasibility and the optimum design of a certain device, there is a need of software tools. These Numerical tools have hight requirements like fast computation, a physical model for any E(J) relation of the superconductor and any complex geometry such as coils, motors and generators, where E is the electric field and J is the current density. In this work we present a 3D variational model based on a functional that restricts the problem in the superconductor volume. We show the magnetization process of a thin film and a 3D bulk sample. We compare our model of the thin film geometry with the thin film formula, reaching a good agreement. We also compare a striated tape, where the filaments are connected by linear material, with a FEM model. We present several results for a thin film with constant critical current density, Jc, magnetic-field dependent Jc, and an anisotropic E(J) relation. For the latter, E is not parallel to J when the magnetic flux density is not perpendicular to J (force free situation). The last studied situation is the 3D cubic sample. We find the time dependence of the current density and AC loss for each situation. In the cubic bulk sample, we found a non-negligible component of the current density in the direction of the applied field. The presented numerical method is very promising for 3D modeling of superconducting samples and power applications.

Motivation & Objective

• To develop a fast and accurate 3D electromagnetic modeling framework for practical superconductors used in high-power applications such as motors, generators, and transmission lines.
• To overcome the limitations of 2D models by enabling full 3D simulation of finite-size superconducting components, including effects from end edges and non-uniform current distributions.
• To model complex non-linear E(J) relations, including Jc(B) dependence and anisotropic 'force-free' effects, crucial for realistic performance prediction.
• To implement efficient parallel computing using OpenMP and BoostMPI to handle large 3D meshes with high computational efficiency (80% parallel efficiency).
• To validate the model against analytical solutions, finite element methods, and experimental measurements of AC loss, magnetization, and cross-field demagnetization.

Proposed method

• The method is based on a variational formulation minimizing electromagnetic entropy production in 3D, using the effective magnetization T as the primary unknown variable.
• The governing equations are derived from the Euler equations of the functional, leading to a system of equations solved via finite element discretization with tetrahedral elements.
• The model incorporates arbitrary E(J) relations, including isotropic, Jc(B) dependence via the Kim model, anisotropic, and multi-valued critical state models.
• A thin film approximation is applied for stacked tapes, and sectors with symmetry are used to reduce computational cost while preserving accuracy.
• Parallelization is implemented via OpenMP (shared memory) and BoostMPI (distributed memory), enabling efficient computation on clusters.
• The algorithm uses iterative minimization with tolerance control (tolJ = 1e-5) and includes options for modeling external fields with variable waveforms and directions.

Experimental results

Research questions

• RQ1 How accurately can a 3D electromagnetic model predict AC losses in multi-filamentary superconducting tapes with inter-filament coupling?
• RQ2 What are the 3D current distribution patterns and magnetization behavior in rectangular superconducting prisms with Jc(B) dependence under perpendicular and tilted fields?
• RQ3 How do anisotropic E(J) relations affect the formation of force-free current configurations in superconducting thin films and bulk materials?
• RQ4 Can 3D modeling reproduce the asymmetric field trapping observed in cross-field demagnetization of cubic superconducting bulks?
• RQ5 To what extent can symmetry and sector-based decomposition reduce computational cost without sacrificing accuracy in 3D superconductor simulations?

Key findings

• The MEMEP 3D model predicted coupling AC losses in two soldered tapes with less than 3% deviation from experimental measurements, demonstrating high accuracy.
• The model revealed non-zero z-component of current density in bulk superconductors under transverse fields, indicating 3D current paths not captured by 2D models.
• Cross-field demagnetization simulations correctly predicted asymmetric field trapping in Gd-Ba-Cu-O cubic bulks, matching experimental observations.
• The model successfully reproduced 2D analytical results for finite-length thin films with constant Jc and Jc(B) dependence, validating its core formulation.
• The use of sectors and symmetry reduced computational load, achieving 80% parallel efficiency on a cluster, enabling large-scale 3D simulations.
• Anisotropic E(J) relations enabled the simulation of force-free current configurations in tilted fields, revealing complex 3D current patterns in thin films and prisms.