This paper reviews the modeling of high-temperature superconductors (HTS) using the finiteelement method (FEM) based on the H-formulation of Maxwell's equations. This formulation has become the most popular numerical modeling method for simulating the electromagnetic behavior 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.

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Overview of H -Formulation: A Versatile Tool for Modeling Electromagnetics in High-Temperature Superconductor Applications

When the electromagnetic suspension (EMS) type maglev vehicle is traveling over a track, the airgap must be maintained between the electromagnet and the track to prevent contact with that track. Because of the open-loop instability of the EMS system, the current must be actively controlled to maintain the target airgap. However, the maglev system suffers from the strong nonlinearity, force saturation, track flexibility, and feedback signals with network time-delay, hence making the controller design even more difficult. In this article, the minimum levitation unit of the maglev vehicle system has been established. An amplitude saturation controller (ASC), which can ensure the generation of only saturated unidirectional attractive force, is thus proposed. The stability and convergence of the closed-loop signals are proven based on the Lyapunov method. Subsequently, ASC is improved based on the radial basis function neural networks, and a neural network-based supervisor controller (NNBSC) is thus designed. The ASC plays the main role in the initial stage. As the neural network learns the control trend, it will gradually transition to the neural network controller. Simulation results are provided to illustrate the specific merit of the NNBSC. The hardware experimental results of a full-scale IoT EMS maglev train are included to validate the effectiveness and robustness of the presented control method as regards to time delay.

RBF Neural Network-Based Supervisor Control for Maglev Vehicles on an Elastic Track With Network Time Delay

Vehicle dynamics and the need to satisfy ride quality requirements have long been recognized as crucial to the commercial success of passenger carrying transportation systems. Design concepts for maglev systems are no exception. The work reported here was undertaken with the intention of summarizing information that has been accumulated worldwide and that is relevant to dynamic stability of repulsive-force maglev systems, assimilating that information, and gaining an understanding of the factors that influence that stability. Included in the paper is a discussion and comparison of results acquired from some representative tests of large-scale vehicles on linear test tracks, together with analytical and laboratory-scale investigations of stability and dynamics of EDS systems. The paper also summarizes the R and D activities at Argonne National Laboratory since 1991 to study the nature of the forces that are operative in an EDS system and the dynamic stability of such systems.

Review of dynamic stability of repulsive-force maglev suspension systems

When the electromagnetic suspension (EMS) type maglev vehicle is traveling over a track, the airgap must be maintained between the electromagnet and the track to prevent contact with that track. Because of the open-loop instability of the EMS system, the current must be actively controlled to maintain the target airgap. However, the maglev system suffers from the strong nonlinearity, force saturation, track flexibility, and feedback signals with network time-delay, hence making the controller design even more difficult. In this article, the minimum levitation unit of the maglev vehicle system has been established. An amplitude saturation controller (ASC), which can ensure the generation of only saturated unidirectional attractive force, is thus proposed. The stability and convergence of the closed-loop signals are proven based on the Lyapunov method. Subsequently, ASC is improved based on the radial basis function neural networks, and a neural network-based supervisor controller (NNBSC) is thus designed. The ASC plays the main role in the initial stage. As the neural network learns the control trend, it will gradually transition to the neural network controller. Simulation results are provided to illustrate the specific merit of the NNBSC. The hardware experimental results of a full-scale IoT EMS maglev train are included to validate the effectiveness and robustness of the presented control method as regards to time delay. 

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.

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Superconducting magnetic bearings simulation using an H-formulation finite element model

The nonlinear vibration of high temperature superconducting (HTS) bulks in an applied permanent magnetic array (Halbach array) field, as a precondition for commercial application to HTS maglev train and HTS bearing, is systematically investigated. This article reports the actual vibration rules of HTS bulks from three aspects. First, we propose a new numerical model to simplify the calculation of levitation force. This model could provide precise simulations, especially the estimation of eigenfrequency. Second, an approximate analytic solution of the vibration of the HTS bulks is obtained by using the method of harmonic balance. Finally, to verify the results mentioned above, we measure the vertical vibration acceleration signals of an HTS maglev model, consisting of eight YBaCuO bulks, oscillating freely above a Halbach array with large displacement excitation. Higher order harmonic components, which indicate the nonlinear vibration phenomenon, are detected in the responses. All the three results are com...

Nonlinear vibration behaviors of high-Tc superconducting bulks in an applied permanent magnetic array field

https://iopscience.iop.org/article/10.1088/1361-6668/aac860/pdf

Lateral motion stability of high-temperature superconducting maglev systems derived from a nonlinear guidance force hysteretic model

In this paper, we built a high-temperature superconducting (HTS) maglev vehicle-bridge coupled system model by Universal Mechanism (UM) software, and analyzed the vertical dynamics. The UM model is composed of two parts, the train subsystem involved three vehicles, and the flexible bridge with simple-supports. In the UM modeling system, the expression of levitation force and the parameters related to the maglev vehicle-bridge were indispensable. The levitation force of maglev vehicle was described by an exponential analytical expression simplified by the experimental results of four YBCO bulks above a Halbach permanent magnetic guideway. The parameters related to the maglev vehicle-bridge are based on experimental prototype. Based on the UM model, the vertical dynamic was simulated and analyzed with different bridge spans under different operating velocities. This subject is a basic study for understanding the unique dynamic characteristic of the HTS maglev vehicle-bridge system. The simulation results provided reference for the further design of the HTS maglev vehicle-bridge coupled system in different speed ranges.

Dynamic Simulation of the HTS Maglev Vehicle-Bridge Coupled System Based on Levitation Force Experiment

This paper presents the design process and test results of a high-temperature superconducting pulsed-power transformer (HTSPPT). The primary winding of the HTSPPT is constructed out of several double-pancake-type coils connected in series. Every double-pancake-type coil is made of Bi2223/Ag tapes. The secondary winding is constructed out of several single-pancake-type coils made of normal conductors. The configuration of the HTSPPT is designed such that the primary and secondary coils are arranged in interleaving. The testing experiments show that a high-current impulse could be achieved with a small current in the primary, which proves that the designed test circuit and the configuration of HTSPPT are feasible.

Design and Testing of a High-Temperature Superconducting Pulsed-Power Transformer

https://iopscience.iop.org/article/10.1088/1361-6668/ab7845/pdf

Haitao Li

Papers

Nonlinear vibration behaviors of high-Tc superconducting bulks in an applied permanent magnetic array field

Lateral motion stability of high-temperature superconducting maglev systems derived from a nonlinear guidance force hysteretic model

Dynamic Simulation of the HTS Maglev Vehicle-Bridge Coupled System Based on Levitation Force Experiment

Design and Testing of a High-Temperature Superconducting Pulsed-Power Transformer

Modeling and identification of the hysteresis nonlinear levitation force in HTS maglev systems