Quench behavior of high-temperature superconductor tapes for power applications: a strategy toward resilience

High-Temperature Superconductors (HTS) can be superconducting in liquid nitrogen 77 K, holding immense promises for our future. They can enable disruptive technologies such as nuclear fusion, lossless power transmission, cancer treatment devices, and technologies for future transportation. In the past years, the numerical models to describe the electrical resistivity of REBCO commercial tapes for devices working near and above the critical current, have been shown to be not accurate or very empirical. The resistivity in this regime, in fact, is not very well known. The lack of this knowledge is a significant issue in developing quality simulation tools. The major challenge in retrieving such properties lies in the fact that when I>Ic, heating effects, and thermal instabilities can quickly destroy the conductor if nothing is done to protect it. Moreover, due to the current sharing between the layers, it is difficult to know the amount of current carried by the superconducting layer and its resistivity. The present work aims to understand better the overcritical current regime combining ultra-fast pulsed current measurements performed on HTS REBCO based coated conductors with Finite Element Modeling. The experimental activities were carried out mostly at EPFL and in part at PM and KIT. The modeling activities were carried out between EPFL and KIT. The major result is a resistivity relationship describing the overcritical current regime to be used in numerical simulations of REBCO tapes. The first part of the thesis illustrates a post-processing method based on the so-called Uniform Current (UC) model to estimate the REBCO material's resistivity in the overcritical from experimental measurements. Pulsed current measurements as short as 15 us and with current magnitude up to 5 Ic were performed in liquid nitrogen bath 77 K on samples from various manufacturers, without damaging the tapes. The second part of the thesis discusses a post-processing method based on regularization of data to treat the experimental measurements extracted in the overcritical current regime. The output of this technique is a look-up table that can be shared with interested partners and used in numerical modeling afterward. The third part of the thesis presents the overcritical current model (rho-\eta\beta): a mathematical relationship of the overcritical current regime based on measurements performed between 77 K and 90 K and in self-field conditions. We compare such models with the power-law model, and we provide a short discussion of the fitting parameters and their typical values. The last part of the thesis discusses the overcritical current model, based on experimental measurements obtained as outlined above. The model was validated experimentally and used to show that for the case of a superconducting fault current limiter when the power-law model is used to model its electro-thermal response, the device quenches faster than with the overcritical model. In conclusion, this work can help optimize the use of superconductors and, consequently, the stabilizer. More interestingly, it opens the study of the overcritical current regime, a new exciting aspect of REBCO commercial tapes. This project has received funding from the Swiss Federal Office of Energy SFOE under grant agreement SI/500193-02.

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

Modelling the E-J relation of high-Tc superconductors in an arbitrary current range

Joseph Duron, Bertrand Dutoit, Francesco Grilli

For describing the E-J relation of high-Tc superconductors (HTS) in power applications, where the applied current I is generally limited by Ic, the critical state model, a piecewise linear generalization, or a simple power-law of the type E=Ec(J/Jc)^n are most often used. The power-law cannot be used for modelling the E-J relation with I>>I_c due to the unbound exponential increase of the electric field for currents above Ic, while in reality the non-linear HTS resistivity is limited by its normal state value. This paper presents a modified E-J model for describing the V-I characteristic of HTS tapes with applied currents largely exceeding Ic. This model is based on the power-law in combination with a parallel metallic branch and has a limited resistivity - the HTS one in the normal state. It can be used for black-box modelling of superconductors in a unlimited current range, as well as for numerical modelling of superconducting devices, which can be operated at currents far exceeding Ic; for example fault-current limiters or cables with over-critical current excursions. The model has been tested in a simple numerical implementation and the modified power-law has been implemented in finite element method simulations. It is shown that for bulk material with currents above 1.3-2Ic$ (depending on the n-value), the usual power-law results in excessive AC loss estimation.

2004

Modeling and Characterization of Coated Conductors Applied to the Design of Superconducting Fault Current Limiters

François Roy

The Superconducting Fault Current Limiter (SFCL) appears to be a device of great interest to efficiently build the electrical grid of tomorrow. With the recent progress made by the superconducting wires manufacturers, there are needs coming from the industry to evaluate the potential of such devices. In the present thesis work, the behavior under external field and transport current of the last generation of wire is investigated. This study is conduct both experimentally and numerically in order to link the physics occurring at the wires level to the design of SFCLs as a whole. From the nature of the material, the resistance appears non-uniformly in high temperature superconductors. For the purpose of building SFCLs it is important to obtain a fast and uniform resistive transition (quench) when a fault occurs through those conductors. This in order to reduce the local heat generation that may damage the device. This fast quenching property is related to the Normal Zone Propagation Velocity (NZPV). In this work the NZPV is measured using a localized magnetic field to initiate quenches in commercial coated conductors. Those velocities have been measured to be larger than 14 cm/s for pulsed currents above the critical value. The NZPV experiments have demonstrated that the superconductor non-uniformity (generated by the localized field) helps to reduce the initial delay before the quench initiation for transport currents in the range of the critical value. However, for larger transport currents the effect of the non-uniformity on the delay is less important since, with increasing transport current amplitudes, the normal state transition has shown to occur more as a consequence of the heat generated in the stabilizer than as the unique consequence of the advancement of the normal zone in the superconductor. From the experimental measurements, it has been shown that a reduction of the liquid-nitrogen temperature (subcoooled) increases the NZPV. This effect has been observed taking into account of the increase of the critical current associated with the temperature reduction. Nevertheless, it is not clear if it is the heat transfer or the estimation of the critical current that is responsible for this effect. In order to validate the numerical models, time-resolved voltage traces obtained from the experiments have been compared to the outputs of the models. Those are based on the thermal- and electrical-diffusion equations. From the simulations, it has been demonstrated that the NZPV can be increased by three methods: by using a thick diffusive substrate, by inserting a resistive interface between the superconductor and the stabilizer as well as by increasing the heat generation in the stabilizer. In light of those results, it seems that the insertion of a resistive layer is the most promising approach to improve the NZPV in coated conductors. As a matter of fact, a resistive interface increases the normal-zone size and keeps an acceptable temperature level along the conductor during quenches. The present work allowed to simulate the flux-flow regime in coated conductors. Comparing those simulations to experimental data have shown that the power-law may be inappropriate to simulate this regime under weak external magnetic fields. In addition, it appears that the role of transient heat transfer with the surroundings needs to be studied in more details to determine the specifications of a prospected SFCL made of coated conductors.