A numerical method is proposed to analyse the electromagnetic behaviour of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current. The E–J constitutive law together with an H-formulation is used to calculate the current distribution and electromagnetic fields in HTSCs, and the magnetization of HTSCs; then the forces in the interaction between the electromagnet and the superconductor and the AC loss of the superconducting cable can be obtained. This numerical method is based on solving the partial differential equations time dependently and is adapted to the commercial finite element software Comsol Multiphysics 3.2. The advantage of this method is to make the modelling of the superconductivity simple, flexible and extendable.

https://iopscience.iop.org/article/10.1088/0953-2048/19/12/004/pdf

Numerical solution of critical state in superconductivity by finite element software

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms, and predicting the performance of high-temperature-superconductor (HTS) tapes, wires, and devices. This is particularly true for ac loss calculation since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, which are based on different techniques and implementations, has been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This paper presents a literature review of the methods for computing ac losses in HTS tapes, wires, and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy-current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications.

Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents

This paper presents a topical review of the current state of the art in modelling the magnetization of bulk superconductors, including both (RE)BCO (where RE?=?rare earth or Y) and MgB2 materials. Such modelling is a powerful tool to understand the physical mechanisms of their magnetization, to assist in interpretation of experimental results, and to predict the performance of practical bulk superconductor-based devices, which is particularly important as many superconducting applications head towards the commercialization stage of their development in the coming years. In addition to the analytical and numerical techniques currently used by researchers for modelling such materials, the commonly used practical techniques to magnetize bulk superconductors are summarized with a particular focus on pulsed field magnetization (PFM), which is promising as a compact, mobile and relatively inexpensive magnetizing technique. A number of numerical models developed to analyse the issues related to PFM and optimise the technique are described in detail, including understanding the dynamics of the magnetic flux penetration and the influence of material inhomogeneities, thermal properties, pulse duration, magnitude and shape, and the shape of the magnetization coil(s). The effect of externally applied magnetic fields in different configurations on the attenuation of the trapped field is also discussed. A number of novel and hybrid bulk superconductor structures are described, including improved thermal conductivity structures and ferromagnet?superconductor structures, which have been designed to overcome some of the issues related to bulk superconductors and their magnetization and enhance the intrinsic properties of bulk superconductors acting as trapped field magnets. Finally, the use of hollow bulk cylinders/tubes for shielding is analysed.

/pdf/modelling-of-bulk-superconductor-magnetization-iet0fuf1ew.pdf

Modelling of bulk superconductor magnetization

A three-dimensional (3D) numerical model is proposed to solve the electromagnetic problems involving transport current and background field of a high-Tc superconducting (HTS) system. The model is characterized by the E?J power law and H-formulation, and is successfully implemented using finite element software. We first discuss the model in detail, including the mesh methods, boundary conditions and computing time. To validate the 3D model, we calculate the ac loss and trapped field solution for a bulk material and compare the results with the previously verified 2D solutions and an analytical solution. We then apply our model to test some typical problems such as superconducting bulk array and twisted conductors, which cannot be tackled by the 2D models. The new 3D model could be a powerful tool for researchers and engineers to investigate problems with a greater level of complicity.

https://iopscience.iop.org/article/10.1088/0953-2048/25/1/015009/pdf

3D modeling of high-Tc superconductors by finite element software

In this paper, we present a general review of the status of numerical modelling applied to the design of high temperature superconductor devices. The importance of this tool is emphasized at the beginning of the paper, followed by formal definitions of the notions of models, numerical methods and numerical models. The state-of-the-art models are listed, and the main limitations of existing numerical models are reported. Those limitations are shown to concern two aspects: on the one hand, the numerical performance (i.e. speed) of the methods themselves is not good enough yet; on the other hand, the availability of model file templates, material data and benchmark problems is clearly insufficient. Paths for improving those elements are indicated in the paper. Besides the technical aspects of the research to be further pursued, for instance in adaptive numerical methods, most recommendations command for an increased collective effort for sharing files, data, codes and their documentation.

https://iopscience.iop.org/article/10.1088/0953-2048/28/4/043002/pdf

Potential and limits of numerical modelling for supporting the development of HTS devices

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

Finite-element method modeling of superconductors: from 2-D to 3-D

A new three-dimensional (3-D) finite element formulation based on the use of the magnetic scalar potential is proposed. It allows the description of multiply connected solid conductors coupled to electric circuits and to take into account the nonlinearities. Like the solutions using the magnetic vector potential, it is a general formulation and offers powerful solutions but at a lower cost.

A nonlinear circuit coupled t-t/sub 0/-/spl phi/ formulation for solid conductors

This paper intends to compare the many different solutions available to design a busbar interconnection. Starting from a single copper plate and going to multilayer busbars, the influence of the external shape of the sheet, of the number and the nature of holes and apertures are considered. Simulations and measurements are used to determine the stray inductance of the different busbars. Design rules are deduced from the many case studies, based on industrial examples

Busbar Design: How to Spare Nanohenries ?

This paper presents the theory and the validation of a new finite-element formulation to realize the coupling between electrical circuits and multiply connected magnetic circuits, using a magnetic scalar potential as state variable. For this purpose, we used formulations in reduced magnetic scalar potential versus T/sub 0/ taking into account electrical circuits and a total magnetic scalar potential taking into account cuts.

Coupled problem computation of 3-D multiply connected magnetic circuits and electrical circuits

This paper deals with the modeling of eddy currents generated by arc motion during opening phases of low voltage circuit breakers. Two kinds of modeling are tested. While the first one consists in determining eddy currents in splitter plates, the second one is devoted to the calculation of eddy currents in electrodes. All simulations are carried out with a T-/spl Phi/ finite-element method formulation and no new mesh at each time step is required.

/pdf/eddy-current-effects-in-circuit-breakers-during-arc-mgw5marxoi.pdf

Y. Le Floch

Papers

Finite-element method modeling of superconductors: from 2-D to 3-D

A nonlinear circuit coupled t-t/sub 0/-/spl phi/ formulation for solid conductors

Busbar Design: How to Spare Nanohenries ?

Coupled problem computation of 3-D multiply connected magnetic circuits and electrical circuits

Eddy-current effects in circuit breakers during arc displacement phase