This article presents a review of the finite-element method (FEM) model based on the H formulation of Maxwell’s equations used to calculate AC losses in high-temperature superconductor (HTS) tapes, cables and windings for different applications. This model, which uses the components of the magnetic field as state variables, has been gaining a great popularity and has been in use in tens of research groups around the world. This contribution first reviews the equations on which the model is based and their implementation in FEM programs for different cases, such as 2D longitudinal and axis-symmetric geometries and 3D geometries. Modeling strategies to tackle large number of HTS tapes, such as multi-scale and homogenization methods, are also introduced. Then, the second part of the article reviews the applications for which the H formulation has been used to calculate AC losses, ranging from individual tapes to complex cables and large magnet windings. Afterwards, a section is dedicated to the discussion of the H formulation in terms of computational efficiency and easiness of implementation. Its pros and cons are listed. Finally, the last section draws the main conclusions.

This paper reviews the modelling of high-temperature superconductors (HTS) using the finite-element method (FEM) based on the H-formulation of Maxwell’s equations. This formulation has become the most popular numerical modelling method for simulating the electromagnetic behaviour of HTS, especially thanks to the easiness of implementation in the commercial finite-element program COMSOL Multiphysics. Numerous studies prove that the H-formulation is able to simulate a wide scope of HTS topologies, from simple geometries such as HTS tapes and coils, to more complex HTS devices, up to large superconducting magnets. In this paper, we review the basics of the H-formulation, its evolution from 2D to 3D, its application for calculating critical currents and AC losses as well as magnetization of HTS bulks and tape stacks. We also review the use of the H-formulation for large-scale HTS applications, its use to solve multi-physics problems involving electromagnetic-thermal and electromagnetic-mechanical couplings, and its application to study the dynamic resistance of superconductors and flux pumps.

This paper presents a comprehensive alternating current (AC) loss study of a circular high temperature superconductor (HTS) coated conductor coil. The AC losses from a circular double pancake coil were measured using the electrical method. A 2D axisymmetric H -formulation model using the FEM package in COMSOL Multiphysics has been established to match the circular geometry of the coil used in the experiment. Three scenarios have been analysed: Scenario 1 with AC transport current and DC magnetic field (experiment and simulation); Scenario 2 with DC transport current and AC magnetic field (simulation); and Scenario 3 with AC transport current and AC magnetic field (simulation and experimental data support). The angular dependence analysis on the coil under a magnetic field with different orientation angle θ has been carried out for all three scenarios. For Scenario 3, the effect of the relative phase difference Δ φ between the AC current and the AC field on the total AC loss of the coil has been investigated. In summary, a current/field/angle/phase dependent AC loss ( I , B , θ , Δ φ ) study of a circular HTS coil has been carried out. The obtained results provide useful indications for the future design and research of HTS AC systems.

This paper presents a roadmap to the application of AI techniques and big data (BD) for different modelling, design, monitoring, manufacturing and operation purposes of different superconducting applications. To help superconductivity researchers, engineers, and manufacturers understand the viability of using AI and BD techniques as future solutions for challenges in superconductivity, a series of short articles are presented to outline some of the potential applications and solutions. These potential futuristic routes and their materials/technologies are considered for a 10–20 yr time-frame.