Finite-element modelling of YBCO fault current limiter with temperature dependent parameters

In this paper we present a numerical model in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite element method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the materials when the current exceeds Ic. A thermal dependence of the electrical parameters, like the critical current density Jc, has been introduced. This model has been used to analyse the behaviour of strip lines of a YBCO/Au fault current limiter (FCL) on a sapphire substrate. Simulations with currents largely exceeding Ic have been performed, showing that the current limitation phase can be correctly reproduced. Such modelling can be used to study the influence of the geometry on the performance of the FCL. It is designed to replace experiments with currents far exceeding Ic which may damage or destroy HTS samples or devices.

Finite-element modelling of superconductors in over-critical regime with temperature dependent resistivity

Joseph Duron, Bertrand Dutoit, Francesco Grilli

In this paper, we present a new numerical model, in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite-element-method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the superconductor when the current exceeds

I_{c}

. This model has been applied for studying the behaviour of strip lines of an YBCO/Au FCL with a sapphire substrate. Simulations with currents largely exceeding

I_{c}

have been performed, showing that the total current limitation occurs only when the temperature dependence of the electrical parameters is taken into consideration. Such modelling can replace experiments with currents far exceeding

I_{c}

which may damage or destroy the studied sample or HTS device.

2006

Numerical modelling of high temperature superconducting tapes and cables

Francesco Grilli

This Ph.D. thesis is focused on the numerical modelling of high-Tc superconductors (HTS) at the operating temperature of 77 K (liquid nitrogen). The purpose of numerical modelling is to precisely calculate the current and field distributions inside HTS devices (tapes, cables) and the corresponding AC losses, which are one of the most important limiting factors for a large-scale application of such materials. From the electrical point of view, superconductors are characterized by a strongly non-linear voltage-current relation, which defines the transition from superconducting to normal state. In the case of HTS, the steepness of this transition is smoother than for low-Tc superconductors (LTS), so that the commonly used critical state model (CSM) gives a too simplified representation of their electromagnetic behaviour and can be used for a qualitative description only. In this thesis the finite element method (FEM) has been used for precisely computing the current and field distributions as well as for evaluating the AC losses in HTS devices. The superconducting transition is modelled with a power-law relation, E(J) = Ec(J/Jc)n, which is derived from the fit of transport measurements. Firstly, the results obtained with the software package FLUX3D on multi-filamentary tapes have been validated by means of a comparison with the ones obtained by another software package (FLUX2D). The results from FLUX2D, having already been successfully compared with experimental measurements within the framework of two previous Ph.D. theses at LANOS, have been used as reference. Secondly, two power-law models, which take into account the spatial variation of the critical current density inside HTS tapes and its strongly anisotropic dependence on the magnetic field, have been implemented in FLUX3D. In most cases, this latter dependence is extremely important, since the transport capacity of the superconductor is considerably reduced (and its power loss sensibly increased) by the presence of a magnetic field. Afterwards, FEM modelling of HTS tapes has been extended to cables. HTS cables are in general composed by different layers of several tapes and have a quite complex three-dimensional structure: in fact, the layers are wound around a central cylindrical support with different pitch lengths and relative winding orientations, in order to obtain a uniform repartition of the transport current among the layers, which minimizes the total AC losses. For overcoming the difficulties of a direct 3D FEM simulation, a simple electrical model, which allows to find the optimal pitch lengths and whose results are the input data for a 2D FEM evaluation of the AC losses, has been developed. FEM computations have also been used to investigate the influence of the non-uniformity of the tape properties (contact resistance, critical current, power index) on the global loss performance of a single-layer HTS cable. As an alternative to FEM computations, an equivalent circuit model of HTS cables has been utilized. It describes the cable from the macroscopic point of view and allows to compute the current repartition among the layers and the corresponding AC losses, without the necessity of having detailed information about individual tapes. In the framework of the European project BIG-POWA, I have collaborated to the assembling process of a HTS power-link at the Pirelli Labs, in the Milan region, Italy. Finally, 3D simulations have been performed to extensively study the coupling effect between two superconducting filaments via the resistive matrix, which is a typical case where analytical solutions exist for very peculiar geometries and physical conditions only. FEM simulations have been utilized to study the dependence of the filament coupling on the physical and geometrical parameters of the conductors.

EPFL2004