T. A. Coombs

Numerical solution of critical state in superconductivity by finite element software

A numerical method is proposed to analyse the electromagnetic behaviour of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current. The E–J constitutive law together with an H-formulation is used to calculate the current distribution and electromagnetic fields in HTSCs, and the magnetization of HTSCs; then the forces in the interaction between the electromagnet and the superconductor and the AC loss of the superconducting cable can be obtained. This numerical method is based on solving the partial differential equations time dependently and is adapted to the commercial finite element software Comsol Multiphysics 3.2. The advantage of this method is to make the modelling of the superconductivity simple, flexible and extendable.

An improved FEM model for computing transport AC loss in coils made of RABiTS YBCO coated conductors for electric machines

AC loss can be a significant problem for any applications that utilize or produce an AC current or magnetic field, such as an electric machine. The authors investigate the electromagnetic properties of high temperature superconductors with a particular focus on the AC loss in superconducting coils made from YBCO coated conductors for use in an all-superconducting electric machine. This paper presents an improved 2D finite element model for the cross-section of such coils, based on the H formulation. The model is used to calculate the transport AC loss of a racetrack-shaped coil using constant and magnetic field-dependent critical current densities, and the inclusion and exclusion of a magnetic substrate, as found in RABiTS (rolling-assisted biaxially textured substrate) YBCO coated conductors. The coil model is based on the superconducting stator coils used in the University of Cambridge EPEC Superconductivity Groups all-superconducting permanent magnet synchronous motor design. To validate the modeling results, the transport AC loss of a stator coil is measured using an electrical method based on inductive compensation by means of a variable mutual inductance. Finally, the implications of the findings on the performance of the motor are discussed.

Study of second generation, high-temperature superconducting coils: Determination of critical current

This paper presents the modeling of second generation (2 G) high-temperature superconducting (HTS) pancake coils using finite element method. The axial symmetric model can be used to calculate current and magnetic field distribution inside the coil. The anisotropic characteristics of 2 G tapes are included in the model by direct interpolation. The model is validated by comparing to experimental results. We use the model to study critical currents of 2 G coils and find that 100 μV/m is too high a criterion to determine long-term operating current of the coils, because the innermost turns of a coil will, due to the effect of local magnetic field, reach their critical current much earlier than outer turns. Our modeling shows that an average voltage criterion of 20 μV/m over the coil corresponds to the point at which the innermost turns’ electric field exceeds 100 μV/m. So 20 μV/m is suggested to be the critical current criterion of the HTS coil. The influence of background field on the coil critical current ...

3D modeling of high-Tc superconductors by finite element software

A three-dimensional (3D) numerical model is proposed to solve the electromagnetic problems involving transport current and background field of a high-Tc superconducting (HTS) system. The model is characterized by the E?J power law and H-formulation, and is successfully implemented using finite element software. We first discuss the model in detail, including the mesh methods, boundary conditions and computing time. To validate the 3D model, we calculate the ac loss and trapped field solution for a bulk material and compare the results with the previously verified 2D solutions and an analytical solution. We then apply our model to test some typical problems such as superconducting bulk array and twisted conductors, which cannot be tackled by the 2D models. The new 3D model could be a powerful tool for researchers and engineers to investigate problems with a greater level of complicity.

A model for calculating the AC losses of second-generation high temperature superconductor pancake coils

A model is presented for calculating the AC losses of a stack of second-generation high temperature superconductor tapes. This model takes as a starting point the model of Clem and co-workers for a stack in which each tape carries the same current. It is based on the assumption that the magnetic flux lines lie parallel to the tapes within the part of the stack where the flux has not penetrated. In this paper we allow for the depth of penetration of field to vary across the stack, and use the Kim model to allow for the variation of Jc with B. The model is applied to the cases of a transport current and an applied field. For a transport current the calculated result differs from the Norris expression for a single tape carrying a uniform current and it does not seem possible to define a suitable average Jc which could be used. Our method also gives a more accurate value for the critical current of the stack than other methods. For an applied field the stack behaves as a solid superconductor with the Jc averaged locally over several tapes, but still allowed to vary throughout the stack on a larger scale. For up to about ten tapes the losses rise rapidly with the number of tapes, but in thicker stacks the tapes shield each other and the losses become that of a slab with a field parallel to the faces.

Superconducting magnetic bearings for energy storage flywheels

We are investigating the use of flywheels for energy storage. Flywheel devices need to be of high efficiency and an important source of losses is the bearings. In addition, the requirement is for the devices to have long lifetimes with minimal or no maintenance. Conventional rolling element bearings can and have been used, but a noncontact bearing, such as a superconducting magnetic bearing, is expected to have a longer lifetime and lower losses. We have constructed a flywheel system. Designed to run in vacuum this incorporates a 40 kg flywheel supported on superconducting magnetic bearings. The production device will be a 5 kW device storing 5 kWh of retrievable energy at 50000 rpm. The Cambridge University system is being developed in parallel with a similar device supported on a conventional bearing. This will allow direct performance comparisons. Although superconducting bearings are increasingly well understood, of major importance are the cryogenics and special attention is being paid to methods of packaging and insulating the superconductors to cut down radiation losses. The work reported here is part of a three-year program of work supported by the EPSRC.

System Studies of the Superconducting Fault Current Limiter in Electrical Distribution Grids

A superconducting fault current limiter (SFCL) in series with a downstream circuit breaker could provide a viable solution to controlling fault current levels in electrical distribution networks. In order to integrate the SFCL into power grids, we need a way to conveniently predict the performance of the SFCL in a given scenario. In this paper, short circuit analysis based on the Electromagnetic Transient Program was used to investigate the operational behavior of the SFCL installed in an electrical distribution grid. System studies show that the SFCL can not only limit the fault current to an acceptable value, but also mitigate the voltage sag. The transient recovery voltage (TRV) could be remarkably damped and improved by the presence of the SFCL after the circuit breaker is opened to clear the fault.

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields : Experiment and model

Crossed-magnetic-field effects on bulk high-temperature superconductors have been studied both experimentally and numerically. The sample geometry investigated involves finite-size effects along both (crossed-)magnetic-field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O single domains that had been premagnetized with the applied field parallel to their shortest direction (i.e., the

Design and Test of a Superconducting Magnetic Energy Storage (SMES) Coil

c

Alternating current loss of second-generation high-temperature superconducting coils with magnetic and non-magnetic substrate

axis) and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample