A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

Finite-element method modeling of superconductors: from 2-D to 3-D

Within the German project CURL 10 a full scale three-phase resistive current limiter was developed and successfully tested up to the nominal voltage and power (10 kV, 10 MVA). This is up today the largest HTS current limiter world wide. The device is based on bifilar coils of MCP-BSCCO 2212 bulk material and operates at T=66 K. Per phase 30 components are connected in series in order to obtain the required resistance. The electrical stabilization is based on a metallic shunt contacted continuously to the superconductor and allows electrical fields up to 0.6 V/cm. We report on the development of the superconducting components and their large-scale manufacturing processes including material, contacts, mechanical stabilization, high voltage insulation and quality control. In a series of preliminary small scale tests at different temperatures as well as in the final tests with the full scale prototype reliable current limitation could be demonstrated in the full range of prospective fault currents, also in the particular dangerous small load regime. Since April 2004 the demonstrator has been installed within a field test in the grid of RWE.

CURL 10: development and field-test of a 10 kV/10 MVA resistive current limiter based on bulk MCP-BSCCO 2212

Design, parameters, and application areas of a superconducting fault current limiter (FCL) are analyzed on the basis of the requirements of power systems. The comparison of resistive and inductive designs is carried out. An example of the effective application of FCLs in distribution substations is considered and the gain from the FCL installation is discussed. It is shown that an FCL not only limits a fault current but also increases the dynamic stability of the synchronous operation of electric machines. The calculation procedure of the parameters of an inductive FCL for a specific application case is described.

Superconducting FCL: design and application

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.

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

Europe celebrated last year (2008) the 100-year anniversary of the first liquefaction of helium by H. Kammerling Onnes in Leiden. It led to the discovery of superconductivity in 1911. Europe is still active in the development of superconducting (SC) devices. The discovery of high critical temperature materials in 1986, again in Europe, has opened a lot of opportunities for SC devices by broking the 4 K cryogenic bottleneck. Electric networks experience deep changes due to the emergence of dispersed generation (renewable among other) and to the advances in ICT (Information Communication Technologies). The networks of the future will be “smart grids”. Superconductivity will offer “smart” devices for these grids like FCL (Fault Current Limiter) or VLI (Very Low Inductance) cable and would certainly play an important part. Superconductivity also will participate to the required sustainable development by lowering the losses and enhancing the mass specific powers. Different SC projects in Europe will be presented (Cable, FCL, SMES, Flywheel and Electrical Machine) but the description is not exhaustive. Nexans has commercialized the first two FCLs without public funds in the European grid (UK and Germany). The Amsterdam HTS cable is an exciting challenge in term of losses for long SC cables. European companies (Nexans, Air Liquide, Siemens, Converteam, …) are also very active for projects outside Europe (LIPA, DOE FCL, …).

Development of superconducting power devices in Europe

A melting zone processing has been developed to texture long bars of YBCO (10 cm length and 5 mm diameter). The misorientation of ( a , b ) planes with the sample long axis is weak. The transport current is produced by a capacitor discharge with period varying between 1.25 and 20 ms. Pulsed transport currents reaching 3000 A (15000 A/cm 2 ) and 6000 A (30000 A/cm 2 ) could cross resistanceless samples at 77 K over several centimeters length. These results show that YBCO can transport high nominal currents even up to its critical current thanks to high quality of contancts. Above the critical current, the material has been protected against the development of the magnetothermal transition.

High critical transport currents of melt textured YBCO up to 6000 A

The superconducting current limiter could bring a solution to a problem not satisfactory solved: the limitation of fault currents under high voltages. We carry out a research and development program based on bulk bismuth materials. They are attractive due to their homogeneous quench into the resistive state and after the normal state even if their critical current densities are not very high (several MAm/sup -2/ at 77 K, self field). They limit efficiently currents without any risk of burning (no hot spots) even under high electrical fields. These materials are elaborated in the form of Bi-2223 bars formed by an isostatic pressure and classical sintering. Sixty bars (/spl phi/=4 mm, /spl Lscr/=120 mm, I/sub c/=35 A) were assembled. This assembling was tested up to 1100 V at 1080 A instead of a theoretical value of 5000 A. The superconductor was exposed to a maximum power density of 12 GW/m/sup 3/ without damage. We present the measurements obtained on the bars and their assembly.

Current limitation at 1080 A under 1100 V with bulk Bi-2223

In the present work a YBa2Cu3O7- delta melt-textured growth (MTG) sample was used to achieve grain orientation in a thermal gradient over a large domain using 211 bars as support. Starting from a YBa2Cu3O7- delta precursor sintered at 950 degrees C, the authors were able to obtain unidirectional orientation over a large area, 22*8*7 mm, using a 20 degrees C cm-1 gradient and a very slow cooling rate, 1 degrees C h-1. The so-obtained microstructure has been characterized. The study of cleaved surfaces using diffraction and Laue patterns shows widespread development of a-b planes parallel to the thermal gradient and to the bar axis. Moreover, microstructural observations point out that the texturization may extend to the 211 support. Polarized optical microscopy observations show large twinning domains all over the sample which confirm orthorhombicity and thus good reoxygenation of the sample. Magnetic and electrical characteristic were investigated. Large magnetic hystereses were obtained, even at 77 K, revealing the presence of strong pinning centres. Transport critical current density higher than 3.5*104 A cm-2 at 77 K in zero field and 2.6*104 A cm-2 at 77 K in a 7 T magnetic field were measured.

High performance in a bulk melt-textured YBa2Cu3O7- delta ceramic

We analyze the potential for using Bi:2223 material obtained by hot forging process in power applications. Current–voltage characteristics have been investigated at 77 K using pulsed currents with an amplitude several times greater than the critical current of the samples. The objective of the present work is the fault current limiter application (FCL). For this application, high performance materials with a predetermined critical current and a homogeneous morphology are necessary. Here, we present measurements obtained on short textured samples. A shaped meander textured sample, connected in series of 0.21 m, has also been measured in current limitation application. According to the magnitude of the pulsed current injected through the sample, different regimes are observed (inductive behavior, recovery and normal state). The E – I curves reveal that the transition to normal state is very rapid for a high critical current density. An electric field of 1600 V/m has been measured and reproducibly repeated. The feasibility to obtain long length samples is demonstrated and results show the possibility to use these materials for FCL devices.

Possible application of bulk textured Bi:2223 for current limitation

Experiments are reported in which single-crystal grains of rare earth-Ba2Cu3O7- delta (R-123) have been aligned in liquid silver by a magnetic field. They demonstrate that there exists a significant anisotropy in the paramagnetic susceptibility of many R-123 superconducting oxides close to their peritectic decomposition temperature. A magnetic field has also been used to induce and control the direction of alignment within bulk Y-123 and Er-123 material. The authors report magnetization versus field measurements, and observations made using X-ray spectroscopy and scanning electron microscopy which have been used to characterize the nature and degree of alignment obtained. Magnetic field texturing offers an alternative technique for producing bulk textured high-Tc superconductors, in which the direction of preferred orientation can be easily controlled.

J.M. Barbut

Papers

High critical transport currents of melt textured YBCO up to 6000 A

Current limitation at 1080 A under 1100 V with bulk Bi-2223

High performance in a bulk melt-textured YBa2Cu3O7- delta ceramic

Possible application of bulk textured Bi:2223 for current limitation

Bulk textured rare earth-Ba2Cu3O7- delta prepared by solidification in a magnetic field