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The optimization of a HTS cable design with respect to AC-losses is of crucial importance for the economic viability of the respective concept. However the experimental determination of AC-losses is not straightforward since for short cable samples the distribution of current among the super-conducting tapes is mainly determined by the contact resistances of the individual tapes. The resulting inhomogeneous current distribution definitely falsifies the results. To solve this experimental problem we present a new experimental technique. The setup is a 2m-long three phase concentric cable model for which, within each phase, the superconducting tapes (up to 30) are connected in series. The Cu-braid backwards conductors were assembled in a rotational symmetric cage type arrangement, such that their self fields at the cable cancel. If experimental peculiarities of this setup, as the strong inductive coupling between the phases and the suitable positioning of the voltage contact leads, are correctly taken into account, the currents can be controlled independently and the electrical properties of the cable can be measured unambiguously. In this paper preliminary results are presented. The work is part of the German government funded cable project AMPACITY (1 km / 20 kV/ 2 kA)

In this paper we develop a method based on the critical state for calculating the current and field distributions and the AC losses in a cable made of curved thin superconducting tapes. The method also includes the possibility of considering spatial variation of the critical current density, which may be the result of the manufacturing process. For example, rare-earth based coated conductors are known to have a decrease of the transport properties in near the edges of the tape: this influences the way current and field penetrate in the sample and, consequently, the AC losses. We demonstrate that curved tapes arranged on a cylindrical former behave as an infinite horizontal stack of straight tapes, and we compare the AC losses in a variety of working conditions, both without and with the lateral dependence of the critical current density. This model and subsequent similar approaches can be of interest for various applications of coated conductors, including power cables and conductor-on-round-core (CORC) cables.

We address the problem of modeling termination resistances which are largely responsible for the uneven distribution of currents in superconducting cables. For such purpose we present three DC models. In a first model a 0D circuit-like approach considering a continuous E-J relationship is presented. A second model uses the 2D H-Formulation of Maxwell's equations, with a new contribution to the electric field term that takes into account the voltage drop due to termination resistances. A third model, based on the 3D H-Formulation of Maxwell's equations, uses a novel technique to simulate both the termination resistances and the superconducting cable within a compact framework that calculates both contributions using two non-connected domains. Advantages and disadvantages of each model are discussed. Particular applications for which a given model is best fitted are also considered. The models' predictions are in good agreement with experimental results for a stacked-tape cable composed of 4 HTS tapes. Overall, this work presents a palette of three different numerical tools for calculating the current distribution in cables composed of multiples tapes, where the termination resistance is also taken into account. The choice of one model over another depends on the particular application and on the degree of precision needed

Roebel cables made of HTS coated conductors can carry high currents with a compact design and reduced AC losses. They are therefore good candidates for manufacturing coils for HTS applications such as motors and generators. In this paper we present the experimental DC and AC characterization of several coils assembled from a 5 meter long Roebel cable built at KIT, which differ in the number of turns and turn-to-turn spacing. Our experiments, supported by finite-element method (FEM) calculations, show that a more tightly wound Roebel coil, despite having a lower critical (and therefore operating) current, can produce a higher magnetic field than a loosely wound one. For a given magnetic field produced at the coil's center, all the coils have similar AC losses, with the exception of the most loosely wound one, which has much higher losses due to the relatively large current needed to produce the desired field. The experiments presented in this paper are carried out on the geometry of pancake coils made of Roebel cables, but they are exemplary of a more general strategy that, coupling experiments and numerical simulations, can be used to optimize the coil design with respect to different parameters, such as tape quantity, size, or AC loss, the relative importance of which is dictated by the specific application.

Striation of HTS coated conductors (CCs) as a way to reduce their magnetization AC losses has been the subject of intense research in the past years by several groups. While the principle of this approach is well understood, its practical application on commercial material to be used in power application is still far to be implemented due to manufacturing and technological constraints. Recent advances in tape quality and striation technology are now enabling systematic investigations of the influence of the number of filaments on AC loss reduction with a consistency that was not available in the past. In this work we demonstrate the technological feasibility of reducing the magnetization losses of commercially available CC by striating them into a high number of filaments (up to 120). The loss reduction exceeds one order of magnitude and does not come at the expense of current-carrying capability: samples with 10 and 20 filaments are unaffected by the striation process, while samples with 80 and 120 filaments still retain 80 and 70% of the current-carrying potential, respectively. We also investigate the transverse resistivity in order to understand the paths followed by the coupling currents: we found that the coupling current prevalently flows in the metallic substrate, rather than in and out of the filaments. Finally, we use oxidation as a method to reduce the coupling currents and losses. The contribution of this work is three-fold: 1) It describes the know-how to produce a large number of high quality striations in commercially available CCs, greatly reducing their losses without extensively degrading their transport properties; 2) It provides a comprehensive characterization of said samples (e.g. measurements in a wide frequency range, transverse resistance profiles, influence of oxidation on DC and AC behavior); 3) It provides new insight on the patterns of the coupling currents.

Energy applications employing high-temperature superconductors (HTS), such as motors/generators, transformers, transmission lines and fault current limiters, are usually operated in the alternate current (AC) regime. In order to be efficient, the HTS devices need to have a sufficiently low value of AC loss, in addition to the necessary current-carrying capacity. Most applications are operated with currents beyond the current capacity of single conductors and consequently require cabled conductor solutions with much higher current carrying capacity, from a few kA to up to 20-30 kA for large hydro-generators. A century ago, in 1914, Ludwig Roebel invented a low-loss cable design for copper cables, which was successively named after him. The main idea behind Roebel cables is to separate the current in different strands and to provide a full transposition of the strands along the cable direction. Nowadays, these cables are commonly used in the stator of large generators. Based on the same design concept of their conventional material counterparts, HTS Roebel cables from REBCO coated conductors were first manufactured at the Karlsruhe Institute of Technology (KIT) and have been successively developed in a number of varieties that provide all the required technical features such as fully transposed strands, high transport currents and low AC losses, yet retaining enough flexibility for a specific cable design. In the past few years a large number of scientific papers have been published on the concept, manufacturing and characterization of such cables. Times are therefore mature for a review of those results. The goal is to provide an overview and a succinct and easy-to-consult guide for users, developers, and manufacturers of this kind of HTS cables.

Numerical models for computing the effective critical current of devices made of HTS tapes require the knowledge of the Jc(B,theta) dependence, i.e. of the way the critical current density Jc depends on the magnetic flux density B and its orientation theta with respect to the tape. In this paper we present a numerical model based on the critical state with angular field dependence of Jc to extract the Jc(B,theta) relation from experimental data. The model takes into account the self-field created by the tape, which gives an important contribution when the field applied in the experiments is low. The same model can also be used to compute the effective critical current of devices composed of electromagnetically interacting tapes. Three examples are considered here: two differently current rated Roebel cables composed of REBCO coated conductors and a power cable prototype composed of Bi-2223 tapes. The critical currents computed with the numerical model show good agreement with the measured ones. The simulations reveal also that several parameter sets in the Jc(B,theta) give an equally good representation of the experimental characterization of the tapes and that the measured Ic values of cables are subjected to the influence of experimental conditions, such as Ic degradation due to the manufacturing and assembling process and non-uniformity of the tape properties. These two aspects make the determination of a very precise Jc(B,theta) expression probably unnecessary, as long as that expression is able to reproduce the main features of the angular dependence. The easiness of use of this model, which can be straightforwardly implemented in finite-element programs able to solve static electromagnetic problems, is very attractive both for researchers and devices manufactures who want to characterize superconducting tapes and calculate the effective critical current of superconducting devices.

Use of 2G HTS coated conductors in several power applications has become popular in recent years. Their large current density under high magnetic fields makes them suitable candidates for high power capacity applications such as stacks, coils, magnets, cables and current leads. For this reason, modeling and simulation of their electromagnetic properties is very desirable in the design and optimization processes. For many applications, when symmetries allow it, simple models consisting of 1D or 2D representations are well suited for providing a satisfying description of the problem at hand. However, certain designs such as racetrack coils and finite-length or non-straight stacks, do pose a 3D problem that cannot be easily reduced to a 2D configuration. Full 3-D models have been developed, but their use for simulating superconducting devices is a very challenging task involving a large-scale computational problem. In this work, we present a new method to simulate the electromagnetic transient behavior of 2G HTS stacks and coils. The method, originally used to model stacks of straight superconducting tapes or circular coils in 2D, is now extended to 3D. The main idea is to construct an anisotropic bulklike equivalent for the stack or coil, such that the geometrical layout of the internal alternating structures of insulating, metallic, superconducting and substrate layers is reduced while keeping the overall electromagnetic behavior of the original device. Besides the aforementioned interest in modeling and simulating 2G HTS coated conductors, this work gives a further step towards efficient 3D modeling and simulation of superconducting devices for large scale applications.

In this contribution we develop a refined numerical model of pancake coils assembled from a coated conductor Roebel cable, which includes the angular dependence of the critical current density $J_c$ on the magnetic field and the actual (three-dimensional) shape of the current lead used to inject the current. Previous works of ours indicate that this latter has an important influence on the measured value of the AC losses. For the simulation of the superconductor, we used two alternative models based on different descriptions of the superconductor's properties and implemented in different mathematical schemes. For the simulation of the current lead we use a full three-dimensional finite-element model. The results of the simulation are compared with measurements and the main issues related to the modeling and the measurement of Roebel coils are discussed in detail.

The current density and field distributions in polygonally arranged thin superconducting tapes carrying AC current are derived under the assumption of the critical state model. Starting from the generic Biot-Savart law for a general polygonal geometry, we derive a suitable integral equation for the calculation of the current density and magnetic field in each tape. The model works for any transport current below $I_c$, which makes it attractive for studying cases of practical interest, particularly the dependence of AC losses on parameters such as the number of tapes, their distance from the center, and their separation.

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms and predicting the performance of high-temperature superconductor (HTS) tapes, wires and devices. This is especially true for ac loss calculation, since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, based on different techniques and implementations, have been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This article presents a literature review of the methods for computing ac losses in HTS tapes, wires and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications., Comment: IEEE Transactions on Applied Superconductivity, 2013

In this paper we derive the integral equations for radially and polygonally arranged high-temperature superconductor thin tapes and we solve them by finite-element method. The superconductor is modeled with a non-linear power law, which allows the possibility of considering the dependence of the parameters on the magnetic field or the position. The ac losses are computed for a variety of geometrical configurations and for various values of the transport current. Differences with respect to existing analytical models, which are developed in the framework of the critical state model and only for certain values of the transport current, are pointed out.

With this paper we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here all the problems are reduced to finding the weight functions for the Green integrals that represent the magnetic field components; these latter must satisfy the mixed boundary value conditions that naturally arise from the critical state assumptions. The use of the Erd\'elyi-Kober operators and of the Hankel transforms (and mostly the employment of their composition properties) is the keystone to unify the method toward the solution. In fact, the procedure consists always of the same steps and does not require any peculiar invention. For this reason the method, here presented in detail for the simplest cases that can be handled in analytical way (two parts boundary), can be directly extended to many other more complex geometries (three or more parts), which usually will require a numerical treatment. In this paper we use the operator technique to derive the current density and field distributions in perfectly conducting and superconducting thin discs and tapes subjected to a uniform magnetic field or carrying a transport current. Although analytical expressions for the field and current distributions have already been found by other authors in the past by using several other methods, their derivation is often cumbersome or missing key details, which makes it difficult for the reader to fully understand the derivation of the analytical formulas and, more importantly, to extend the same methods to solve similar new problems. On the contrary, the characterization of these cases as mixed boundary conditions has the advantage of referring to an immediate and na\"ive translation of physics into a consistent mathematical formulation whose possible extension to other cases is self-evident., Comment: The final publication is available at http://link.springer.com/article/10.1007/s00033-011-0185-5

First experimental observations of the ferromagnetic shielding effect in high-Tc superconducting coated conductors were carried out. Experimental results were compared to simulations calling upon finite-element calculations based on the H-formulation of Maxwell equations to model superconducting strips with ferromagnetic shields. Samples of copper-stabilized coated conductors were electroplated with nickel shields and afterwards characterized. Both externally applied oscillating transverse magnetic fields as well as transport currents were studied. Having observed promising gains with respect to the reduction of ac losses in both cases, we further investigated the potential of ferromagnetic shielding. The numerical model was able to reproduce and also predict experimental results very well and will serve as an indispensable tool to determine the potential of soft ferromagnetic materials to significantly reduce hysteretic losses., Comment: 4 pages, 3 figures, 1 table

The AC loss in ReBCO coated conductors is large in situations when the conductors are subjected to a considerable magnetic field, like in rotating machines, transformers and high-field magnets. Roebel cables can reduce the AC loss in these cases. However, computer simulations are needed to interpret the experiments, understand the loss mechanisms, reduce the AC loss by optimising the Roebel cable and design the cryogenic system. In this article, we simulate and discuss the AC loss due to an applied magnetic field making an arbitrary angle with the cable and taking into account a realistic anisotropic field dependence of the critical current density. We study the AC loss in the superconductor parts for the limits of very high coupling currents and completely uncoupled strands. The simulations for the uncoupled case also describe a double pancake coil with no transport current. For the simulations, we use two different numerical methods with complementary strengths. This serves as a mutual check of the correctness of the simulation results, which agree to each other. Opposite than expected, we found that the AC loss does not only depend on the perpendicular component of the applied magnetic field. We also found that the AC loss for applied fields with an orientation below 7 degrees with the strands surface is reduced more than one order of magnitude comparing to an untransposed cable. Therefore, we recommend to use Roebel cables for windings with important parallel components of the magnetic field, such as transformers and high-field magnets., Comment: 28 pages, 11 figures