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.
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 c…
Superconducting bulk (RE)Ba$_2$Cu$_3$O$_{7-x}$ materials (RE-rare earth elements) have been successfully used to generate magnetic flux densities in excess of 17 T. This work investigates an alternative approach by trapping flux in stacks of second generation high temperature superconducting tape from several manufacturers using field cooling and pulsed field magnetisation techniques. Flux densities of up to 13.4 T were trapped by field cooling at ~5 K between two 12 mm square stacks, an improvement of 70% over previous value achieved in an HTS tape stack. The trapped flux approaches the recor…
The project of superconducting magnetic system (SMS) for the magnetic refrigerator machine is proposed. The second-generation high-temperature superconducting tapes for SMS are developed, fabricated and tested in NRC Kurchatov Institute. The magnet consists of 12 non-insulated double pancake coils. The SMS is installed in the vacuum chamber and cooled by a cryo refrigerator.
Dynamic voltage-current characteristics of an HTS Ag/BiSCCO composite tape are studied both experimentally and theoretically. The tape is subjected by pulsed currents with different shapes and magnitude and voltage traces are measured using the four-point method with different location of potential taps on the sample surface. Clockwise and anticlockwise hysteresis loops are obtained for the same sample depending on location of the potential taps. The dynamic characteristics deviate substantially from the DC characteristic, especially in the range of low voltages where a criterion for the criti…
Numerical models are powerful tools to predict the electromagnetic behavior of superconductors. In recent years, a variety of models have been successfully developed to simulate high-temperature-superconducting (HTS) coated conductor tapes. While the models work well for the simulation of individual tapes or relatively small assemblies, their direct applicability to devices involving hundreds or thousands of tapes, as for example coils used in electrical machines, is questionable. Indeed the simulation time and memory requirement can quickly become prohibitive. In this article, we develop and …
In this work we present a modeling tool designed to estimate the hysteretic losses in the coils of an electric generator with coils made of coated conductor tapes during transient operation. The model is based on a two-stage segregated model approach that allows simulating the electric generator and the current distribution in the superconducting coils using a one-way coupling from the generator to the HTS coils model. The model has two inputs: the rotational speed and the electric load signal. A homogeneous anisotropic bulk model for the coils allows computing the current distribution in the …
Bending-like stress induced by solder joint under uniaxial tensile testing in 2G-HTS tapes: Impact and optimization approach
School of Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电气工程学院）；State key Laboratory of High-Efficiency special cable technology, Shanghai Jiao Tong University（上海交通大学高效特种电缆技术国家重点实验室）；Key Laboratory of Applied Superconductivity, Institute of Electrical Engineering, Chinese Academy of Sciences（中国科学院电气工程技术研究所超导应用重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Numerical models based on the finite-element method (FEM) are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the $T$-$A$ formulation for modeling HTS coils in 2D with different coupling scenarios between the turns. First we consider a racetrack coil wound from one piece of superconducting tape. Then we consider a coil obtained by winding a cable composed of different HTS tapes. In the latter case, the tape turns are either electrically connected along their entire length or just at…
A compact HTS cable that is able to carry large current density is crucial for developing high field accelerator magnets. We are reporting a novel HTS cable (named X-cable) that could achieve a high current density as the Roebel cable, but is implemented by in-plane bending stacked HTS tapes directly to realize the transposition. The cable is jointly developed with an industrial company on a production line: ready for large scale production from the beginning. Recently, a prototype cable with REBCO coated conductor has been successfully fabricated. Test results show no significant degradation,…
The current-voltage (I-V) curve is the basic characteristic of a superconducting wire or tape. Measuring I-V curves is generally problematic when samples have poor stabilization. Soldering voltage taps to an active part of the conductor affects the effectiveness of the local cooling and/or can be difficult to do in certain devices such as fault current limiters and cables where the tapes are closely packed. In order to overcome these problems, voltage taps can be placed outside the active area of the superconductor. We proved both by simulations and experiments that this arrangement leads to t…
High-temperature superconductors (HTS) are finding use as high - current wires for potential application in power devices. The dependence of their basal-plane critical current properties on orientation in a magnetic field can pose important design problems. Here we report material and operating parameter conditions where prototype HTS tape conductors exhibit critical current characteristics that are essentially field-orientation independent. The novel phenomenon is observed for specific magnetic field intensities that depend on the operating temperature, and in materials having strong flux pin…
This article presents a review of the finite element method (FEM) model based on the $H$ formulation of Maxwell's equations used to calculate AC losses in high temperature superconductor (HTS) tapes, cables and windings for different applications. This model, which uses the components of the magnetic field as state variables, has been gaining a great popularity and has been in use in tens of research groups around the world. This contribution first reviews the equations on which the model is based and their implementation in finite element method programs for different cases, such 2D longitudi…
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 lo…
The estimation of the critical current ($I_c$) and AC losses of high-temperature superconductor (HTS) devices through modeling and simulation requires the knowledge of the critical current density ($J_c$) of the superconducting material. This $J_c$ is in general not constant and depends both on the magnitude ($B_{loc}$) and the direction ($θ$, relative to the tape) of the local magnetic flux density. In principle, $J_c(B_{loc},θ)$ can be obtained from the experimentally measured critical current $I_c(B_a,θ)$, where $B_a$ is the magnitude of the applied magnetic field. However, for applications…
The current-voltage characteristics of superconductors are commonly determined by means of a standard 4-probe DC measurement technique. In coated conductors, however, one often encounters problems due to weak or no stabilization and in such case, when the risk of burning the tape is high, the 4-probe approach can fail. In other cases such as in HTS cable structures, besides vulnerability and high risk of damage, it may also be difficult to achieve a high critical current level with a power supply that is normally used to characterize single strands. We therefore investigated an alternative met…
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 …
The electromagnetic properties of a pancake coil in AC regime as a function of the number of turns is studied theoretically and experimentally. Specifically, the AC loss, the coil critical current and the voltage signal are discussed. The coils are made of Bi2Sr2Ca2Cu3O10/Ag (BiSCCO) tape, although the main qualitative results are also applicable to other kinds of superconducting tapes, such as coated conductors. The AC loss and the voltage signal are electrically measured using different pick up coils with the help of a transformer. One of them avoids dealing with the huge coil inductance. Be…
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 …
Striating HTS coated conductor (CC) tapes into narrow filaments offers the possibility of reducing the tapes' magnetization losses without unreasonably decreasing their current-carrying capability. However, realizing well-separated striations presents technological challenges, especially if the number of filaments is large and/or if a thick layer of metallic stabilizer is present. In these situations, the filaments can be easily coupled and their effectiveness to reduce magnetization losses is strongly diminished or eliminated. While the onset of coupling is well visible from magnetization los…
Fluorescent Microthermographic Imaging, a method using rare-earth fluorescent coatings with temperature-dependent light emission, was used for quench investigation in high temperature superconductors (HTS). A fluorophore was embedded in a polymer matrix and used as a coating on top of an HTS tape, while being excited with UV light and recorded with a high-speed camera. Simultaneously, the tape was pulsed with high amplitude, short duration DC current, and brought to quench with the help of a localized defect. The joule heating during a quench influences the fluorescent light intensity emitted …
This paper presents the alternating current (AC) loss analysis on high-temperature superconductor (HTS) Cross-Conductor (CroCo) cables, in order to evaluate whether they could be utilized for electrical power transmission. The modeling of HTS CroCo cables was based on a cable assembled at the Karlsruhe Institute of Technology (KIT) and the AC loss calculation was based on the H-formulation model implemented in the finite-element method (FEM) software package COMSOL Multiphysics. The AC loss calculations have been carried out for isolated single-phase CroCo cable and three-phase CroCo cables. T…
High temperature superconducting (HTS) tape can be cut and stacked to generate large magnetic fields at cryogenic temperatures after inducing persistent currents in the superconducting layers. A field of 17.7 T was trapped between two stacks of HTS tape at 8 K with no external mechanical reinforcement. 17.6 T could be sustained when warming the stack up to 14 K. A new type of hybrid stack was used consisting of a 12 mm square insert stack embedded inside a larger 34.4 mm diameter stack made from different tape. The magnetic field generated is the largest for any trapped field magnet reported a…
This study presents an HTS electromagnetic model combining the thin-strip, homogeneous and multi-scale methods using T-A formulation. In particular, we build the thin strips as both the analyzed HTS tapes and the boundaries of the homogeneous bulks where the non-analyzed tapes are merged. Thus, the coil geometry is re-constructed with several bulks, but the bulks boundaries and domains are tackled with different electromagnetic properties, and solved by T and A formulations, respectively. Firstly, we introduce the modeling process and highlight the differences and advantages over the previous …
In the last 10-15 years, the most common strategy in the development of High Temperature Superconducting (HTS) cable for magnets has been to imitate Low Temperature Superconducting (LTS) cable designs. However, requirements for LTS materials are not valid for HTS materials, which are extremely stable. For example, non-twisted multifilamentary Bi-2223 tapes have been successfully used in several magnets. This paper review stability and analyse inductance and AC losses in non-twisted stack of HTS tapes. Numerical calculations show that twisting has negligible effect on inductance variations in a…
A noteworthy physical dependence of the hysteresis losses with the axial winding misalignment of superconducting racetrack coils made with commercial \textcolor{black}{Second Generation High Temperature Superconducting (2G-HTS)} tapes is reported. A comprehensive study on the influence of the turn-to-turn misalignment factor on the local electromagnetic properties of individual turns, is presented by considering six different coil arrangements and ten amplitudes for the applied alternating transport current, $I_{a}$, together with an experimentally determined function for the magneto-angular a…
Various applications of superconducting materials require accounting of anisotropy of the current-carrying capacity relative to magnetic field direction - Ic(θ). However, today there is no sufficiently comprehensive model that takes into account the anisotropy, therefore the angular dependences are usually not analysed, but only described using various mathematical formulas. As a result, the fitting parameters have no physical meaning and it is difficult to correlate the picture with the features of the microstructure. In this paper, we propose a method for analysing the critical current angul…
For an accurate estimation of the AC losses of superconducting triaxial cables, we present a 2D model capable to provide a global assessment of multi-layer triaxial cables, validated against the AC-losses on single-phase cables provided by the VNIIKP Cable Institute. Four models are presented, the first being a single-phase cable of 50 tapes and the others being three triaxial cables made of up to 135 coated conductors distributed in up to 9 layers. A systematic study is devised, where the number of layers per phase increases from 1 to 3, with at least 14 tapes distributed across each layer of…
Minimization of ac losses is essential for economic operation of high-temperature superconductor (HTS) ac power cables. A favorable configuration for the phase conductor of such cables has two counter-wound layers of HTS tape-shaped wires lying next to each other and helically wound around a flexible cylindrical former. However, if magnetic materials such as magnetic substrates of the tapes lie between the two layers, or if the winding pitch angles are not opposite and essentially equal in magnitude to each other, current distributes unequally between the two layers. Then, if at some point in …
A homogenization method to model a stack of second generation (2G) High Temperature Superconducting (HTS) tapes under AC applied transport current or magnetic field has been obtained. The idea is to find an anisotropic bulk equivalent for the stack, such that the geometrical layout of the internal alternating structures of insulating, metallic, superconducting and substrate layers is "washed" out while keeping the overall electromagnetic behavior of the original stack. We disregard assumptions upon the shape of the critical region and use a power law E-J relationship allowing for overcritical …
Modelling high temperature superconductor (HTS) motors remains challenging mainly due to the high aspect ratio of these conductors but also because of the properties of the magnetic materials. This paper presents a 2D time dependent model to assess the AC losses of superconducting motors based on the new T-A formulation, which by using Finite Element Methods (FEM), allows its implementation in commercial software. The T-A formulation computes the magnetic flux density with different Maxwell's equations depending on the areas of the motor and makes it possible to use the thin strip approximatio…
Measurements of AC losses in a HTS-tape placed in between of two bulk magnetic shields of high permeability were performed by applying calorimetric techniques for various asymmetrical shielding arrangements. The experiment was supported by analytical calculations and finite-element simulations of the field and current distributions, based on the Bean model of the critical state. The simulated current and field profiles perfectly reproduce the analytic solutions known for certain shielding geometries. The evaluation of the consequent AC losses exhibits good agreement with measurements for the c…
High temperature superconducting (HTS) dynamos are promising devices that can inject large DC currents into the winding of superconducting machines or magnets in a contactless way. Thanks to this, troublesome brushes in HTS machines or bulky currents leads with high thermal losses will be no longer required. The working mechanism of HTS dynamo has been controversial during the recent years and several explanations and models have been proposed to elucidate its performance. In this paper, we present the first three-dimensional (3D) model of an HTS flux pump, which has good agreement with experi…
High temperature superconductor (HTS) (RE)Ba2Cu3Ox (REBCO) conductor on round core cable (CORC) has high current carrying capacity for high field magnet and power applications. In REBCO CORC cables, current redistribution occurs among tapes through terminal contact resistances when a local quench occurs. Therefore, the quench behaviour of CORC cable is different from single tape situation, for it is significantly affected by terminal contact resistances. To better understand the underlying physical process of local quenches in CORC cables, a new 3D multi-physics modelling tool for CORC cables …
AC losses in High Temperature Superconductor tapes (HTS) are an important design parameter for large scale power applications. The electrical method is often used for losses measurements on SC tapes and, when the results are to be compared to computed estimations, simple theoretical models like the Norris Brandt are typically used. Electromagnetic dynamic effects are not usually taken into account by the simpler models, but their presence may corrupt the measured data. In this paper, a preliminary study on a conventional copper bar sample has been done to evaluate the effect of the skin curren…
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 t…
In recent years, numerical models have become popular and powerful tools to investigate the electromagnetic behavior of superconductors. One domain where this advances are most necessary is the 3D modeling of the electromagnetic behavior of superconductors. For this purpose, a benchmark problem consisting of superconducting cube subjected to an AC magnetic field perpendicular to one of its faces has been recently defined and successfully solved. In this work, a situation more relevant for applications is investigated: a superconducting parallelepiped bulk with the magnetic field parallel to tw…
In order to transport sufficiently high current, high-temperature superconductor (HTS) tapes are assembled in cable structures of different forms. In such cables, the tapes are tightly packed and have a strong electromagnetic interaction. In particular, the generated self-field is quite substantial and can give an important contribution in reducing the maximum current the cable can effectively carry. In order to be able to predict the critical current of said cable structures, a static numerical model has been recently proposed. In this contribution, we present in detail the implementation of …
Rare-earth-barium-copper-oxide (REBCO) tapes are now available from several industrial manufacturers and are very promising conductors in high field applications. Due to diverging materials and deposition processes, these manufacturers' tapes can be expected to differ in their electro-mechanical and mechanical properties. For magnets designers, these are together with the conductors' in-field critical current performance of the highest importance in choosing a suitable conductor. In this work, the strain and stress dependence of the current carrying capabilities as well as the stress and strai…
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 operatin…
Low AC loss high transport current HTS cables (>1 kA) are required for application in transformers, generators and are considered for future generations of fusion reactors coils. 2G coated conductors are suitable candidates for high field application at quite high operation temperatures of 50-77 K, which is crucial precondition for economical cooling costs. As a feasibility study we present the first ROEBEL bar cable of approx. 35 cm length made from industrial DyBCO coated conductor (THEVA GmbH, Germany). Meander shaped ROEBEL strands of 4 mm width with a twist pitch of 180 mm were cut from 1…
Roebel cables made of HTS coated conductors are regarded as promising cables for winding applications in virtue of their large engineering current density and low losses. The composing meander-shaped strands are assembled very tightly into the cable, which results in a strong electromagnetic interaction between them. This interaction profoundly influences the effective self-field critical current ($I_c$) of the cable, which is much lower than the sum of the $I_c$s of the composing strands. Also the AC losses are influenced by the material's properties and by the geometrical configuration of th…
HTS are feasible for hight power applications because of the smaller consumption demand of the cooling system in comparison to the whole power device. Real industral devices contain superconductors with 2D and 3D geometry (coated conductors tapes represent an example of 2D geometry, since the superconducting layer is very thin). In order to know the feasibility and the optimum design of a certain device, there is a need of software tools. These Numerical tools have hight requirements like fast computation, a physical model for any E(J) relation of the superconductor and any complex geometry su…
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 t…
