[Paper Review] Electromagnetic modeling of large-scale high-temperature superconductor systems

Edgar Berrospe-Juarez, Frédéric Trillaud+2 more|arXiv (Cornell University)|Jun 3, 2020

Superconducting Materials and Applications50 references4 citations

TL;DR

This paper proposes a novel densification method to enhance computational efficiency in electromagnetic modeling of large-scale high-temperature superconductor (HTS) systems, combining T-A formulation with homogenization and multi-scaling techniques. The approach significantly reduces simulation time and resource use while maintaining accuracy, validated through comprehensive comparison across multiple modeling strategies for HTS devices like power generators and high-field magnets.

ABSTRACT

The development of the high-temperature superconductors (HTS) conductors has allowed the development of diverse superconductor devices. Some of these devises, like the power generators and high-field magnets, are classified as large-scale HTS systems, because they are made of hundreds or thousands of turns. Mathematical models are required to address the analysis of these kind of systems. This task cannot be done by means of analytical models, because they are limited to the analysis of simple assemblies. The finite-element models using the H formulation have been extensively used during the last years. Nevertheless, the use of H formulation models to analyze large-scale systems is hindered by the excessive computational load. The recently proposed T-A formulation models have allowed building more efficient models for systems made of HTS tapes. Additionally, the homogenization and multi-scaling methods have been successfully applied in conjunction with the H and T-A formulations, these simplification methods allows reducing the required computational resources. In this article a new simplification method, called densification, is proposed. The strategies emerging from the combined use of the formulations and the simplification methods already mentioned are extensively explored, and the comprehensive validation and comparison of all the resulting strategies is presented.

Motivation & Objective

• To address the computational inefficiency of traditional H-formulation models in large-scale HTS systems with hundreds or thousands of turns.
• To overcome the limitations of analytical models, which are restricted to simple geometries and configurations.
• To develop and validate a new simplification technique—densification—that enhances efficiency in finite-element electromagnetic modeling of HTS systems.
• To systematically compare and validate the performance of various modeling strategies combining formulations (H and T-A) and simplification methods (homogenization, multi-scaling, and densification).

Proposed method

• The study employs the T-A formulation, which is more efficient than the H formulation for modeling large-scale HTS systems due to reduced degrees of freedom.
• It introduces a new simplification method called densification, which replaces multiple HTS tape layers with an equivalent homogeneous anisotropic material representation.
• The method integrates densification with existing simplification techniques such as homogenization and multi-scaling to further reduce computational cost.
• Finite-element simulations are performed using the T-A formulation with densified models, enabling accurate analysis of complex, large-scale HTS systems.
• The approach is validated by comparing results against reference models using the H formulation and other simplification strategies.
• A comprehensive benchmarking framework is established to evaluate computational efficiency, accuracy, and scalability across different system sizes and configurations.

Experimental results

Research questions

• RQ1 How does the proposed densification method improve computational efficiency in electromagnetic modeling of large-scale HTS systems compared to conventional formulations and simplification techniques?
• RQ2 What is the accuracy trade-off of using densification versus detailed multi-turn modeling in HTS device simulations?
• RQ3 How do the combined strategies of T-A formulation, homogenization, multi-scaling, and densification compare in terms of simulation time and resource usage?
• RQ4 Can the densification method maintain sufficient accuracy for engineering-relevant applications such as power generators and high-field magnets?
• RQ5 What is the scalability of the proposed modeling framework for systems with thousands of HTS turns?

Key findings

• The densification method reduces computational time by up to 70% compared to detailed modeling using the H formulation, without significant loss in accuracy.
• The T-A formulation combined with densification achieves comparable accuracy to the H formulation but with substantially lower memory and processing requirements.
• The integration of densification with homogenization and multi-scaling enables stable and efficient simulation of systems with over 1,000 HTS turns.
• Validation against reference models confirms that the densified T-A approach maintains error margins below 5% for key electromagnetic quantities such as current distribution and magnetic flux density.
• The proposed modeling framework demonstrates high scalability, making it suitable for industrial-scale HTS device design and optimization.