Numerical models are powerful tools to predict the electromagnetic behavior of superconductors. In recent years, a variety of models have been successfully developed to simulate high-temperature-superconducting (HTS) coated conductor tapes. While the models work well for the simulation of individual tapes or relatively small assemblies, their direct applicability to devices involving hundreds or thousands of tapes, e.g., coils used in electrical machines, is questionable. Indeed, the simulation time and memory requirement can quickly become prohibitive. In this paper, we develop and compare two different models for simulating realistic HTS devices composed of a large number of tapes: (1) the homogenized model simulates the coil using an equivalent anisotropic homogeneous bulk with specifically developed current constraints to account for the fact that each turn carries the same current; (2) the multi-scale model parallelizes and reduces the computational problem by simulating only several individual tapes at significant positions of the coil’s cross-section using appropriate boundary conditions to account for the field generated by the neighboring turns. Both methods are used to simulate a coil made of 2000 tapes, and compared against the widely used H-formulation finite-element model that includes all the tapes. Both approaches allow faster simulations of large number of HTS tapes by 1–3 orders of magnitudes, while maintaining good accuracy of the results. Both models can therefore be used to design and optimize large-scale HTS devices. This study provides key advancement with respect to previous versions of both models. The homogenized model is extended from simple stacks to large arrays of tapes. For the multi-scale model, the importance of the choice of the current distribution used to generate the background field is underlined; the error in ac loss estimation resulting from the most obvious choice of starting from a uniform current distribution is revealed.

The modeling of superconducting magnetic bearings (SMBs) is of great significance for predicting and optimizing their levitation performance before construction. Although much effort has been made in this area, there still remains some space for improvements. Thus the goal of this work is to report a flexible, fast and trustworthy H -formulation finite element model. First the methodology for modeling and calibrating both bulk-type and stack-type SMBs is summarized. Then its effectiveness for simulating SMBs in 2D, 2D axisymmetric and 3D is evaluated by comparison with measurements. In particular, original solutions to overcome several obstacles are given: clarification of the calibration procedure for stack-type and bulk-type SMBs, details on the experimental protocol to obtain reproducible measurements, validation of the 2D model for a stack-type SMB modeling the tapes’ real thickness, implementation of a 2D axisymmetric SMB model, implementation of a 3D SMB model, and extensive validation of the models by comparison with experimental results for field cooling and zero field cooling, for both vertical and lateral movements. The accuracy of the model being having proven, it now has a strong potential for speeding up the development of numerous applications including maglev vehicles, magnetic launchers, flywheel energy storage systems, motor bearings and cosmic microwave background polarimeters.

The high-T _c superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. Finally, a critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom, tolerance settings and the approximate time taken per cycle for each model. This benchmark and the results contained herein provide researchers with a suitable framework to validate, compare and optimise their own methods for modelling the HTS dynamo.

Three superconducting stacks made of 120 REBCO coated conductor tapes were each fabricated and assembled to obtain several REBCO modules. Their levitation responses over two different permanent magnet (PM) guideways were investigated by experiment and finite element simulation. For the experiment, a test rig was developed that can measure the force in the three directions for any given relative movement between the REBCO stacks and the PM guideway. For the finite element simulation, a 2D H -formulation was adopted. To treat the high aspect ratio of REBCO tapes, an anisotropic homogenization technique was used. The agreement between the measurements and the simulations is good, thus validating the modeling methodology. It was observed from the experiment and simulation results that the perpendicular field contributes to the levitation force whereas the parallel field is responsible for the guidance force, as a result of the existence of anisotropy on the local magnetic stimulation. Based on that, promising REBCO modules including both longitudinal and transverse arrangements of REBCO stacks were proposed and tested, in terms of providing a significant levitation force with the lateral stability preserved. Moreover, a pre-load process able to suppress the relaxation of the levitation force was put forward. To conclude, this study outlines explicit principles to obtain an appropriate layout of coated conductor stacks that could be effective for practical magnetic levitation operation.