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.

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, as for example coils used in electrical machines, is questionable. Indeed the simulation time and memory requirement can quickly become prohibitive. In this article, 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 Hformulation finite element model that includes all the tapes. Both approaches allow speeding-up simulations of large number of HTS tapes by 1-3 orders of magnitudes, while keeping a good accuracy of the results. Such models could be used to design and optimize large-scale HTS devices. I.

The modeling of superconducting magnetic bearing (SMB) is of great significance for predicting and optimizing its levitation performance before construction. Although lots of efforts have been made in this area, it 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 SMB is summarized. Then its effectiveness for simulating SMBs in 2-D, 2-D axisymmetric and 3-D 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 2-D model for a stack-type SMB modeling the tapes real thickness, implementation of a 2-D axisymmetric SMB model, implementation of a 3-D SMB model, 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 proved, it has now 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.

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.

The energy conversion chain in a photovoltaic water pumping system was modelled.  Water collection by the inhabitants was included as a model input.  The model was validated by using data acquired on a system in rural Africa.  The accuracy of the model is higher than 95 % when using local climatic data.  Accuracy drops of 1 to 3 % when replacing local climatic data by satellite ones.

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We present a step-by-step method for the design and control of a full-scale back-to-back converter for wind energy conversion systems using direct-drive electrically excited synchronous generators. First the system modeling is described in details. Then the converter controllers are designed and their PI parameters are systematically calculated using the symmetrical optimum method. Finally, the performances of a 2 MW class generator connected to the grid through the obtained converter are evaluated through simulations.

The high-T c superconducting (HTS) dynamo exploits the nonlinear resistivity of an HTS tape to generate a DC voltage when subjected to a varying magnetic field. This leads to the so-called flux pumping phenomenon and enables the injection of DC current into a superconducting coil connected to the dynamo without current leads. In this work, the process of charging a coil by an HTS dynamo is examined in detail using two numerical models: the minimum electromagnetic entropy production and the segregated -formulation finite element model. The numerical results are compared with an analytical method for various airgaps and frequencies. Firstly, the I–V curves of the modeled HTS dynamo are calculated to obtain the open-circuit voltage, short-circuit current and internal resistance. Afterward, the process of charging a coil by the dynamo including the charging current curve and its dynamic behavior are investigated. The results obtained by the two models show excellent quantitative and qualitative agreement with each other and with the analytical method. Although the general charging process of the coil can be obtained from the I–V curve of the flux pump, the current ripples within a cycle of dynamo rotation, which can cause ripple AC loss in the HTS dynamo, can only be captured via the presented models.