© 2018 IOP Publishing Ltd. The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as 'dynamic resistance.' Dynamic resistance is relevant to many potential higherature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H -formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30° and 60° to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire's superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, I c( B ), of the wire. It is shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until J c is exceeded and flux-flow resistance occurs.

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Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires

Electrodynamic suspension (EDS) train has the unique advantages of excellent levitation and guidance stabilities, large levitation gap, and so on. All of these merits make it a promising candidate for the future ultra-high-speed transportations, in which the high-temperature superconducting (HTS) linearly synchronous driving motor (LSM) plays an important role because of the decrease of energy consumption of HTS magnet. This paper, which serves as a fundamental study on the HTS synchronous driving system of EDS train, is aimed to calculate the propulsion force of LSM and optimize the propulsion fluctuation. First, in order to define the operating current of LSM, the critical current of a real-scale REBCO coil was numerically estimated using the so-called T-A model. Second, based on the Neumann formula and virtual displacement method, an analytic model to estimate the propulsion force of LSM was established and verified by comparing results with a finite-element method (FEM) numerical model. Finally, by resorting to the validated analytic model, the geometric parameters of propulsion coil were optimized, and then using the optimal parameters, the maximum electromagnetic forces of LSM under different operating conditions of EDS train were calculated. It was found that the linearly driving system inherently keeps robust driving stability to the lateral and normal displacements.

Calculation and Optimization of Propulsion Force of a Real-Scale REBCO Magnet for EDS Train

Superconducting Magnetの特性(低温)

In the measurement of the levitation force between a vertically magnetized permanent magnet (PM) and a bulk high-temperature superconductor (HTS), PM domains with horizontal components of magnetization are shown to produce a nonnegligible contribution to the levitation force in most systems. Such domains are typically found in all PMs, even in those that exhibit zero net horizontal magnetic moment. Extension of this analysis leads to an HTS analog of Earnshaw's theorem, in which at the field-cooling position the vertical stiffness is equal to the sum of the horizontal stiffnesses, independent of angular distribution of magnetic moments within the PM.

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Effect of permanent-magnet irregularities in levitation force measurements.

Considering the need for cost/performance prediction and optimization of superconducting maglev vehicles, we develop and validate here a 3D finite element model to simulate superconducting linear magnetic bearings. Then, we reduce the 3D model to a 2D model in order to decrease the computing time. This allows us to perform in a reasonable time a stochastic optimization considering the superconductor properties and the vehicle operation. We look for the permanent magnet guideway geometry that minimizes the cost and maximizes the lateral force during a displacement sequence, with a constraint on the minimum levitation force. The displacement sequence reproduces a regular maglev vehicle operation with both vertical and lateral movements. For the sake of comparison, our reference is the SupraTrans prototype bearing. The results of the optimization suggest that the bearing cost could be substantially reduced, while keeping the same performances as the initial design. Alternatively, the performances could be significantly improved for the same original cost.

Optimization of the superconducting linear magnetic bearing of a maglev vehicle

It is important and complicated to model and optimize the levitation behavior of superconducting magnetic bearing (SMB). That is due to the nonlinear constitutive relationships of superconductor and ferromagnetic materials, the relative movement between the superconducting stator and PM rotor, and the multi-parameter (e.g., air-gap, critical current density, and remanent flux density, etc.) affecting the levitation behavior. In this paper, we present a theoretical calculation and optimization method of the levitation behavior for radial-type SMB. A simplified model of levitation force calculation is established using 2D finite element method with H-formulation. In the model, the boundary condition of superconducting stator is imposed by harmonic series expressions to describe the traveling magnetic field generated by the moving PM rotor. Also, experimental measurements of the levitation force are performed and validate the model method. A statistical method called Taguchi method is adopted to carry out an optimization of load capacity for SMB. Then the factor effects of six optimization parameters on the target characteristics are discussed and the optimum parameters combination is determined finally. The results show that the levitation behavior of SMB is greatly improved and the Taguchi method is suitable for optimizing the SMB.

Optimization of radial-type superconducting magnetic bearing using the Taguchi method

The magnetism of substrate has significant influence on the transport loss in high temperature superconducting (HTS) coated conductors (CCs). Taking three types of substrates (i.e., nonmagnetic, weakly magnetic, and strongly magnetic) into account, a study on the frequency dependence (in the range of 10–1000 Hz) of transport loss in HTS CCs with these substrates is performed numerically and experimentally. Different loss components and magnetic field profile are calculated individually to clarify the effect of substrate magnetism. Results show that HTS CCs with magnetic substrate exhibit higher transport loss than CCs with nonmagnetic substrate. Both hysteresis loss in HTS layer and eddy current loss in conventional metal increase with the enhancement of substrate magnetism.

Influence of Substrate Magnetism on Frequency-Dependent Transport Loss in HTS-Coated Conductors

The numerical study on the transport loss reduction in REBCO double pancake (DP) coil is presented in this paper. An axisymmetric finite element model based on H formulation and E-J power law is established. The influence of the gap between two pancakes on the transport losses of DP coils is investigated. The use of magnetic flux diverters to reduce the ac loss of the DP coil by decreasing the perpendicular magnetic field applied to the tape surface is also studied. It is found that the perpendicular magnetic field is decreased clearly by attaching the flux diverter in the middle and end positions of DP coil. Compared with the ac losses of DP coils without flux diverters, the use of flux diverters can decrease the ac losses by 70% when the applied current is at half the critical current of DP coil.

Study on the AC Loss Reduction of REBCO Double Pancake Coil

A 2 kW/28.5 kJ superconducting flywheel energy storage system (SFESS) with a radial-type high-temperature superconducting (HTS) bearing was set up to study the electromagnetic and rotational characteristics. The structure of the SFESS as well as the design of its main parts was reported. A mathematical model based on the finite element method (FEM) was established to research the electromagnetic characteristics of the HTS bearing during the levitation process, which show that a part of the magnetic flux penetrates into the edge of the HTS bulks and then goes back to the opposite pole of the permanent magnet rotor (PMR). The induced current mainly distributes in the edge of the HTS bulks, indicating that larger force acts on the edge part of the HTS bulks and probably causes them to crack. The free rotations of the rotor at different steady-state speeds of 2500–5000 rpm and its radial vibration were displayed. The induced voltage of the stator winding of the motor in this process was analyzed. The rotational characteristics are related to the vibration of the rotor. Below the resonant frequency, the vibration increases significantly with the speed. Enhancing the radial stiffness to limit the vibration amplitude of the rotor is an effective approach to improve the speed.

Electromagnetic and Rotational Characteristics of a Superconducting Flywheel Energy Storage System Utilizing a Radial-Type High-Temperature Superconducting Bearing

There are some disadvantages in conventional cryogenic liquid pumps (CLPs) with mechanical bearings, such as difficult lubrication and short working life. In this paper, we propose a new structure of CLP-submerged cryogenic disk motor-pump with superconducting magnetic bearing (SMB). The impeller and the rotor of the disk motor are combined as the suspension rotor of the disk motor-pump. The suspension rotor which is supported by SMB system, rotates frictionlessly with self-stabilized. The SMB system includes a radial-type SMB, an axial-type permanent magnet bearing, and an axial flux disk motor. Theoretical calculations and experimental measurements of levitation forces in the SMB system are carried out. The levitation force of radial-type SMB is calculated by using H -formulation finite-element model in COMSOL. The kinetic model of the suspension rotor is established to ensure the force balance and torque balance. The results demonstrate the feasibility of the proposed submerged cryogenic disk motor-pump with SMB.

Wanjie Li

Papers

Optimization of radial-type superconducting magnetic bearing using the Taguchi method

Influence of Substrate Magnetism on Frequency-Dependent Transport Loss in HTS-Coated Conductors

Study on the AC Loss Reduction of REBCO Double Pancake Coil

Electromagnetic and Rotational Characteristics of a Superconducting Flywheel Energy Storage System Utilizing a Radial-Type High-Temperature Superconducting Bearing

Research on a Superconducting Magnetic Bearing System for Submerged Cryogenic Disk Motor-Pump