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Although the H-formulation has proven to be one of the most versatile formulations used to accurately model superconductors in the finite element method, the use of vector-dependent variables in nonconducting regions leads to unnecessarily long computation times. Additionally, in some applications of interest, the combination of multiple magnetic components interacting with superconducting bulks and/or tapes leads to large domains of simulation. In this article, we separate the magnetic field into a source and reaction field and use the H– $\phi$ formulation to efficiently simulate a superconductor surrounded by magnetic bodies. We model a superconducting cube between a pair of Helmholtz coils and a permanent magnet levitating above a superconducting pellet. In both cases, we find excellent agreement with the H-formulation while the computation times are reduced by factors of nearly three and four in 2-D and 3-D, respectively. Finally, we show that the H– $\phi$ formulation is more accurate and efficient than the H–A formulation in 2-D. [ABSTRACT FROM AUTHOR]

Previous studies of test coils have demonstrated the high thermal and electrical stability of no-insulation (NI) high temperature superconducting (HTS) coils thanks to the presence of turn-to-turn current paths. These turn-to-turn current paths in a NI coil are significantly influenced by the contact resistivity. In practice, it is very challenging to measure the contact resistivity of a NI coil by direct experiments of short samples, since the contact resistivity of superconducting tapes is influenced by surface roughness and tolerance, stress, temperature etc. A proper simulation model is needed to investigate the contact resistivity of the NI coils with dedicated experiments. Hence, in this paper a distributed circuit model is employed. This model, implemented in Matlab 2018a, considers the local contact resistivity, self and mutual inductance, and HTS resistance, which depends on the supplied current, magnetic field and temperature. To validate the model, experimental results from literature, including sudden discharge, and charge–discharge processes, are employed and the results from simulations are consistent with experimental results. Then the model is used to investigate the equivalent contact resistivity of a 157-turn NI coil. Through the comparison of simulated and experimental results, it is found that the contact resistivity of the NI coil has an inhomogeneous distribution. When the current changes with different speeds, ramping rates or frequency, a different number of turn-to-turn contacts carries radial current. Since the turn-to-turn contacts have different contact resistivity, the equivalent contact resistivity calculated from sudden discharge cannot be used in simulations to reproduce all the experimental data. [ABSTRACT FROM AUTHOR]

When exposed to time-dependent magnetic fields, REBCO Roebel cables generate AC loss resulting from both magnetic hysteresis and induced inter-strand coupling currents. Until now, the AC loss has been computed in a two-dimensional approximation assuming fully coupled or decoupled strands, and a finite inter-strand resistance could be simulated only with three-dimensional models. In this work, we propose a homogenization procedure that reduces the three-dimensional geometry of the Roebel cable to two dimensions, without ignoring connections between the strands. The homogenized cable consists of two parallel 'monoblocks' with an anisotropic resistivity. The proposed model enables computation of AC coupling loss without the need for complex three-dimensional simulations. For experimental validation, a Roebel cable with soldered strands was prepared. The inter-strand resistance was determined by applying a transverse current and measuring the voltage profile. Additionally, the AC magnetization loss of the cable was measured in fields of 1 to 50 mT with frequencies of 1 to 2048 Hz using a calibration-free technique. With the measured inter-strand resistance as input parameter, the monoblock model gives a good estimate for the AC loss, even for conditions in which the coupling loss is dominant. [ABSTRACT FROM AUTHOR]

We report on the effects of different multifilamentary geometries on the dynamic current and field distributions in YBa2Cu3O7-δ thin films. Finite-element model simulations are presented that allow a direct comparison of the calculated magnetic flux and current profiles with experimental data obtained by time-resolved magneto-optical imaging. We find that increasing the distance between filaments reduces the magnetic coupling and decreases the ac losses. Screening and transport currents also redistribute more evenly between all filaments. The measured transport current density profiles are in good agreement with the modified critical state model. [ABSTRACT FROM AUTHOR]

Yttrium barium copper oxide (YBCO) coated conductors are now the most promising high-temperature superconducting tapes in terms of current capacity and price. One form of these conductors utilizes YBCO films on Ni–W metallic tapes and is being considered for a number of power engineering applications. In these applications, the conductor will carry an ac current, leading to energy losses, which are the focus of significant technical and experimental efforts. Our measurements of the ac losses of YBCO/Ni–W conductors carrying ac currents in applied dc magnetic fields have revealed a complex interaction between the magnetic materials present, the geometry of the conductor, the ac and dc magnetic fields, and the electromagnetic “history” of the sample. The investigation of this interaction is the main subject of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the conditions of use and the equivalence of various constitutive laws used to model the electromagnetic behavior of high-temperature superconductors: two versions of the critical state model (CSM), the power law model, and a so-called percolation model. All these models can be used to represent the same superconducting material with some limit of accuracy. The CSM and the power law model are well known in the literature. The percolation model can be seen as a generalization of the power law model that includes also a CSM-like behavior at very low electric fields. The investigation has been carried out for three types of operating conditions: the sudden application of a dc excitation, a pure ac excitation, and combined dc and ac excitations. The equivalence between the different constitutive laws is shown to be a function of the magnitude of the electric fields and of the time scales involved. In the dc case, long time scales and very small electric fields are predominant; thus, the superconductor requires a model that is accurate at low electric fields, such as the percolation model. The losses then arise from the relaxation of the magnetic field in the sample. In the ac case, the power law and percolation models are nearly identical when considering power frequencies, so choosing the simpler power law model is fully acceptable in practice. In addition, the CSM coincidentally provides good predictions of the losses in the power frequency range. In the dc+ac case, when time scales in the range of minutes to hours are considered, it is shown that ac losses dominate over relaxation losses, and the same conclusions as for the ac case apply. [ABSTRACT FROM AUTHOR]

In view of high-temperature superconductor (HTS) magnet applications, the concept of Twisted Stacked Tape Cable (TSTC) made of HTS coated conductors is very promising because of the easy manufacturing process and of the very high tape length usage efficiency. For the use of these cables in magnet applications, where the cables carry high current while subjected to the strong magnetic field generated by the rest of the magnet, the possibility of being able to calculate in detail current and field distributions is very welcome, particularly for evaluating the cable’s performance during the charge of the magnet. The numerical modeling of this kind of cable is particularly challenging because of the twisted geometry. In this paper, we use a 3-D finite element model to compute the magnetization AC losses of a twisted superconductor and current repartition among the tapes in a cable composed of four HTS coated conductor tapes. The utilized model is able to simulate not only twisted geometries, but also the contact resistance of the electrical terminations used to inject the current. The latter can importantly influence the current repartition between the tapes, especially in short samples. The model is also able to take into account the angular dependence of the critical current on the local magnetic field, whose relative orientation with respect to the tape needs to be locally evaluated as a consequence of the twisted geometry. [ABSTRACT FROM AUTHOR]

Roebel cables made of high temperature superconducting (HTS) coated conductors can carry high currents with a compact design and reduced ac losses. Therefore, they are 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-m-long Roebel cable built at Karlsruhe Institute of Technology, which differ in the number of turns and turn-to-turn spacing. Our experiments, which are supported by finite-element-method 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, based on coupling experiments and numerical simulations, that 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. [ABSTRACT FROM PUBLISHER]

In HTS Roebel cables for low-field applications the tightly packed strands produce a substantial self-field, which can be comparable to the background field the cable operates in. As a result, the self-field critical current ( I c ) of a cable is lower than the value obtained by multiplying the self-field I c of the strands by the number of strands. In addition, the in-field reduction of the superconducting material plays an important role for a cable's I c . Numerical models can accurately calculate the magnetic field distribution inside a cable and estimate its I c . In this contribution we employ a recently developed open-source model to estimate the I c of Roebel cables. In particular, we investigate the influence of the spacing between the superconducting layers, of the J c ( B , θ) dependence, and of the presence of an external magnetic field. For the present analysis, we consider tapes from two manufactures, whose properties were characterized in our group. [ABSTRACT FROM AUTHOR]

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 Jc 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. [ABSTRACT FROM PUBLISHER]

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 of tapes, 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 3D 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 bulk-like 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 provides a further step towards efficient 3D modeling and simulation of superconducting devices for large-scale applications. [ABSTRACT FROM AUTHOR]

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 Ic, 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Finite-element models are a powerful and widely used tool for evaluating the ac losses of HTS tapes and wires as well as of assemblies such as cables and coils. The H-formulation, which uses the magnetic field components as state variables, has proved to be an efficient implementation to solve 2-D problems, involving infinitely long or axially-symmetric geometries; an excellent agreement with experimental data has been found in many cases. However, the simulation of certain applications requires a full 3-D model. In this paper we report on the development of a 3-D model based on the H-formulation. We describe the implementation of Maxwell equations, the imposition of current constraints and we discuss the issues related to meshing 3-D volumes. The model is validated by comparing the results with those obtained with 2-D models in cases that can be investigated in 2-D; then, it is used to simulate cases that can be handled only in 3-D. [Copyright &y& Elsevier]

In this paper, we derive 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 nonlinear 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. [ABSTRACT FROM PUBLISHER]

In the past few years the Roebel technique has been established as a method for cabling of coated conductor tapes to achieve high current carrying capabilities for low ac-loss applications. We have successfully developed Roebel cables consisting of up to 50 tapes and with current carrying capabilities up to 2.6 kA (77 K, self-field). However, for applications like busbars or fusion magnets current carrying capabilities of more than 10 kA are required. Such high current carrying capabilities cannot be reached by a simple scale-up with additional tapes. [ABSTRACT FROM AUTHOR]

In this paper we present a new model for computing the current density and field distributions in superconductors by means of a finite element (FE) periodic space-time (PST) formulation. By considering the time as a space dimension, and considering periodic excitations for the applied field or transport current, we can use a static model to solve this time dependent problem. This approach has the potential to overcome one of the major problems of FE modeling of superconductors: the length of simulations, even for relatively simple cases. In this paper we show our first results for different cases of superconductors with AC magnetic fields and currents. Results are compared with those of standard time-dependent methods and analytical solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influence of various numerical parameters on the precision and the speed of ac loss computations in high-temperature superconductors using the finite-element method. The case considered here is an infinite slab subjected to an external ac magnetic field. This problem can be modeled by a 1-D partial differential equation (diffusion equation). This relatively simple case allowed investigating the influence of the various parameters in a reasonable time. The findings of this work can be used as a starting point for optimizing the numerical settings of more complex models. As the main results, it is shown that choosing first-order elements for approximating the flux density (13) is the most stable option, and that using high order adaptive time-stepping methods provides good accuracy and fast simulations. A new and simple self-check test for validating the computed ac losses is also proposed. Finally, a detailed analysis about the behavior of the numerical solution near flux/current fronts is provided. [ABSTRACT FROM AUTHOR]

In superconducting coils tapes are often closely packed in a configuration similar to a ‘z-stack’, which strongly influences the AC losses with respect to when tapes can be considered as separate objects: losses are reduced in the presence of externally applied AC magnetic field, but are increased in the presence of AC transport current. In this paper, we quantify the magnitude of the tape interaction and the AC losses of these two cases, both experimentally and by means of finite-element method simulations. We also discuss the experimental issues arisen with the utilized AC loss measurement technique. [ABSTRACT FROM AUTHOR]

In this paper we present a new 2D numerical model for AC loss computation in high-temperature superconductors, based on the use of edge finite elements. These elements are curl conforming by construction and involve the continuity of the tangential component of the magnetic field between adjacent elements. In this way they do not require the imposition of the zero divergence of the magnetic field at each time step, which, with standard nodal elements, increases the null space of the matrix and the risks of divergence of the algorithm. The model, implemented in the software package COMSOL, uses the two magnetic field components as state variables. It has been tested for computing the losses of YBCO coated conductor tapes in two cases of practical interest, which cannot be investigated by analytical models. [ABSTRACT FROM AUTHOR]

In this paper we present initial results on growing YBCO/IBAD-MgO/YBCO stacks. Amorphous Y2O3 layers, deposited by sol-gel, are used to level the YBCO surface. Since the YRCO films prepared by pulsed laser deposition are relatively rough, preparing a smooth surface on top of YBCO for IBAD texturing is a major challenge for this structure. For all substrates studied-polished and unpolished metal tape and YBCO—we were able to reduce the roughness of the substrate using the sol-gel layer, with multiple coatings being more effective. First it is demonstrated that high quality YBCO films can be deposited on sol-gel-Y2 O3/IBAD-MgO templates. Second it is shown that the sol-gel and the IBAD process do not affect the superconducting properties of the underlying YBCO film. Finally, a superconducting YBCO bilayer stack is demonstrated. Improvements in the properties of the top YBCO layer is expected when the surface roughness is reduced further for deposition of subsequent IBAD-textured layers. This new technology should enable novel designs of coated conductors for reduced AC losses and increased Je. [ABSTRACT FROM AUTHOR]

The performance of HTS devices is strongly influenced by local values of the current and field distributions. In this paper, we investigate the influence of the magnetic field and the geometrical configuration on the loss behavior of a 200 kVA FCL prototype, composed by 111-2223/Ag tapes wound around a cylindrical support. The investigation is performed by means of finite element computations, with the use of an axisymmetric 2D A-V formulation for taking into account the cylindrical geometry. The electrical behavior of the superconductor is described by means of a B-dependent E-J power-law relation, derived from experimental measurements with a field of different orientation. Several geometrical configurations are analyzed and compared, in order to find the ones with the lowest AC loss. [ABSTRACT FROM AUTHOR]

The magnetic field profile on the surface of Bi-2223/Ag tapes has been dynamically measured across the width of the samples. The experimental technique uses a flail-probe array with 7 sensors connected to a multiple channel lock-in amplifier especially programmed for fast and synchronous data acquisition measurements. The speed of the system is high enough to measure real-time profiles with 7 probes and 50 Hz sine current through the sample. A numerical method to estimate the current distribution inside the tapes using the measured field profile data is proposed. The inverse problem has been solved using certain assumptions on the current distribution in the superconductor. Validation of the results has been done by comparison with finite element method simulations. [ABSTRACT FROM AUTHOR]

To reach large current carrying capability and mechanical flexibility, superconducting cables consist of many single conductors connected in parallel. Distribution of ac current into these parallel paths is controlled by their impedances, which often are not identical. We have found that, even in the case of a cable model made from straight Bi-2223 tapes placed in just one single layer, the nonuniformity of contact resistances causes a dispersion in the amplitudes and phases of acts in individual tapes. Two models, one analytical and other a Finite Element Model, were used to predict the influence of phase shifts on ac loss and its measurement by an electrical method. Due to phase shifts of local magnetic fields, the purely inductive component of voltage taken by an arbitrary pair of taps is not exactly out-of-phase regarding the total cable current. Then, its product with the cable current is evaluated as a false loss-contributing component Fortunately, with the use of voltage taps and wires regularly distributed around the cable, true value of ac loss can be recovered. [ABSTRACT FROM AUTHOR]

A three-dimensional (3-0) 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 3.0, 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. [ABSTRACT FROM AUTHOR]

In this paper, the effects of the magnetic self-field on the transport properties of a multilayer high-T superconducting (HTS) cable are investigated by means of two-dimensional finite-element method (FEM) simulations. Analyzed is a three-layer HTS cable, but the developed methods can be used for a different number of layers. The superconductor is described by the nonlinear power-law relation E = E3(J/Je)n, where the parameters J2 and n depend on the magnetic field experienced by the material. This dependence decreases the global transport capacity of the superconductor, enhancing its AC losses. It is shown that, especially at high transport currents, the AC losses are considerably higher than in the case where the dependence on the magnetic field is neglected. A simple electrical model, considering the cable from macroscopic point of view, has been proposed for finding the optimal winding pitches, leading to a uniform current repartition. The use of this electrical model allows to overcome the difficulties of direct three-dimensional FEM computations. In addition, the rapidity of solutions by the electric model gives the possibility of testing quickly many geometrical configurations in order to find the ones leading to an even current repartition. This optimization process would not be possible with detailed FEM simulations. [ABSTRACT FROM AUTHOR]

Superconductor technology has recently attracted increasing attention in power-generation- and electrical-propulsion-related domains, as it provides a solution to the limited power density seen by the core component, electrical machines. Superconducting machines, characterized by both high power density and high efficiency, can effectively reduce the size and mass compared to conventional machine designs. This opens the way to large-scale purely electrical applications, e.g., all-electrical aircrafts. The alternating current (AC) loss of superconductors caused by time-varying transport currents or magnetic fields (or both) has impaired the efficiency and reliability of superconducting machines, bringing severe challenges to the cryogenic systems, too. Although much research has been conducted in terms of the qualitative and quantitative analysis of AC loss and its reduction methods, AC loss remains a crucial problem for the design of highly efficient superconducting machines, especially for those operating at high speeds for future aviation. Given that a critical review on the research advancement regarding the AC loss of superconductors has not been reported during the last dozen years, especially combined with electrical machines, this paper aims to clarify its research status and provide a useful reference for researchers working on superconducting machines. The adopted superconducting materials, analytical formulae, modelling methods, measurement approaches, as well as reduction techniques for AC loss of low-temperature superconductors (LTSs) and high-temperature superconductors (HTSs) in both low- and high-frequency fields have been systematically analyzed and summarized. Based on the authors' previous research on the AC loss characteristics of HTS coated conductors (CCs), stacks, and coils at high frequencies, the challenges for the existing AC loss quantification methods have been elucidated, and multiple suggestions with respect to the AC loss reduction in superconducting machines have been put forward. This article systematically reviews the qualitative and quantitative analysis methods of AC loss as well as its reduction techniques in superconductors applied to electrical machines for the first time. It is believed to help deepen the understanding of AC loss and deliver a helpful guideline for the future development of superconducting machines and applied superconductivity. [ABSTRACT FROM AUTHOR]

This paper presents a new finite-element simulation model for computing the electromagnetic properties and AC losses in systems of YBCO (yttrium barium copper oxide) conductors on roll assisted biaxially textured substrates (RABiTS). In this model, the magnetic field dependent permeability and ferromagnetic loss of the substrates in RABiTS YBCO tapes are taken into account. The simulations were employed to simulate the AC loss in stacks of two parallel connected YBCO tapes. The simulation results are compared with the experimental data to check the validity of the simulation model. The result reveals an effective way of significantly reducing AC loss in YBCO tapes by stacking two RABiTS YBCO coated conductors with the appropriate relative tape orientation. [ABSTRACT FROM AUTHOR]

Many superconductor applications require cables with a high current capacity. This is not feasible with single-piece coated conductors because their ac losses are too large. Therefore, it is necessary to develop superconducting cables with a high current capacity and low ac losses. One promising solution is given by ROEBEL cables. We assembled three ROEBEL cables from commercial YBCO coated conductors. The cables have the same width but a different number of strands, which results in different aspect ratios and current capacities. We experimentally studied their ac losses under a transport current or a perpendicular magnetic field. In addition, we performed numerical calculations, which agree with the experiments, especially for the transport case. We found that in the cables there is good current sharing between the strands. We also found that stacking the strands reduces the magnetization losses. For a given critical current, thicker cables have lower magnetization ac losses. In addition, a conducting matrix is not required for a good current sharing between strands. [ABSTRACT FROM AUTHOR]