Magnetic Field Conforming Formulations for Foil Windings

2025-04-15

AI Summary

This paper addresses the high degrees of freedom, numerical ill-conditioning, and low computational efficiency arising from geometric complexity in 3D electromagnetic modeling of foil windings. We propose a globally homogenized modeling method that rigorously preserves the magnetic field intensity distribution. Innovatively, we introduce a magnetic scalar potential formulation for non-conductive regions, integrating field-conformity preservation with dimensionality reduction. The resulting model strictly maintains magnetic field intensity consistency while drastically reducing problem size. The framework supports both frequency-domain and transient finite-element solvers and enables multiscale coupled simulation of high-temperature superconducting coils. Benchmark evaluations on 2D axisymmetric and 3D configurations demonstrate accuracy comparable to conventional magnetic flux density–preserving models and full-resolution winding models. In transient simulations, the proposed method reduces degrees of freedom by over an order of magnitude, significantly improving computational efficiency while delivering robust and reliable results.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the magnetic scalar potential in non-conducting regions to improve the efficiency of the model. This leads to a significant reduction in the number of degrees of freedom, particularly in 3-D applications. The proposed models are verified on two frequency-domain benchmark problems: a 2-D axisymmetric problem and a 3-D problem. They reproduce results obtained with magnetic flux density conforming formulations and with resolved conductor models that explicitly discretize all turns. Moreover, the models are applied in the transient simulation of a high-temperature superconducting coil. In all investigated configurations, the proposed models provide reliable results while considerably reducing the size of the numerical problem to be solved.

Problem

• Extend foil winding homogenization to magnetic field conforming formulations
• Reduce degrees of freedom in 3-D magnetic field modeling
• Verify models on 2-D and 3-D frequency-domain benchmark problems

Innovation

• Extends foil winding homogenization method
• Introduces magnetic scalar potential
• Reduces degrees of freedom significantly