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High-temperature superconducting (HTS) coils are generally operated in a closed-loop persistent current mode, which is crucial for ensuring long-term stability and minimizing heat generation in various applications. However, factors such as joint resistance, flux creep, and losses due to external fields can lead to accelerated decay of the coil's current, making it challenging to achieve an effective persistent current mode. To gain insight into the current decay characteristics of HTS coils, we built a finite element method based model coupled with a lumped parameter electric circuit model. The model is initially verified against the experiment of an inductive magnetized HTS coil subject to a magnetic field perpendicular to the tape surface. The results indicate that the proposed model is highly effective in predicting the current decay behavior of this magnetized HTS coil and is able to provide high accuracy. With the help of this model, we have experimentally and numerically studied the behavior of a current-carrying closed-loop HTS coil subject to external alternating fields. The HTS coil is charged by a DC power supply and then shorted using a thermally-controlled persistent current switch. The current decay behavior of the HTS coil is examined under various scenarios. The simulation results show excellent agreement with experimental data, further validating the effectiveness and versatility of the modeling strategy. The influence of both local and global screening currents on the current decay performance of the closed-loop HTS coils has been investigated. For every case examined, rapid demagnetization occurred in the initial cycle of the applied alternating field. Furthermore, the current decay rate demonstrated a slight dependence on the frequency of the applied fields. Additionally, the resulting resistance has been thoroughly characterized. These insights contribute to the knowledge of the behavior and performance of closed-loop HTS coils, facilitating their practical application. [ABSTRACT FROM AUTHOR]

Flux pumps provide a promising solution for contactless charging of high-temperature superconducting (HTS) coils, eliminating the need for bulk current leads and reducing the heat burden for the cryogenic system. Characterizing the nonlinear effects of an HTS coil charged by a flux pump and understanding the dynamics of the charging process is essential for promoting the practical application of flux pumps. Numerical models provide a fast and cost-effective way of achieving this. In this study, we propose a methodology for coupling HTS coil and flux pump models using an electrical circuit, resulting in reduced computation costs. We validate the effectiveness of our approach against the experimental results of an HTS coil charged by a dynamo-type flux pump. Specifically, we obtain the voltage produced by the HTS dynamo using a 3D model based on the minimum electromagnetic entropy production method and apply this voltage to the load HTS coil using a T − A formulation finite-element method model coupled via an electrical circuit. The simulated charging current shows good agreement with experimental observations, validating our modeling strategy. The results demonstrate that the flux flow state in the HTS coil is the primary factor limiting the charging performance of the HTS dynamo as the charging current approaches the coil's critical current. Furthermore, based on the simulation, we demonstrate that, when using flux pumps, it is advisable to leave a margin between the operating current and the critical current of the coil. Overall, our approach has the potential to be applied to HTS coils charged by any device. [ABSTRACT FROM AUTHOR]

One of the main tasks during the design of a superconducting electrical machine is the estimation of losses in the superconducting coils. These losses can be decisive in such applications since they influence the cooling power requirements and the overall efficiency of the machine. In this article, we focus on the dissipation in the stator superconducting coils of a synchronous machine. The calculations are done within the framework of the SupraGenSys project, which aims to develop a new superconducting generator for the wind energy sector. A detailed study of the ac losses in the stator coils is carried out based on a basic design that considers the main constraints of this application. The objective is to look for an optimum solution for the level and distribution of losses as a second step in the design process. The T-A formulation of Maxwell's equations is used in a 2-D finite-element model to analyze the behavior of the magnetic field around the coils and calculate losses. Particular attention is given to the position of the coils inside a slot and several coil configurations are presented. It is shown that certain coil arrangements lead to a significantly lower total loss, a more uniform loss distribution, which ultimately leads to the possibility of increasing the operating temperature. [ABSTRACT FROM AUTHOR]

Modeling 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 article presents a 2-D time dependent model to assess the ac losses of superconducting motors based on the new T–A-formulation, which by using the finite-element method, 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 approximation i.e., the HTS tapes are modeled as infinitely thin lines. The model is then expected to tackle the high aspect ratio of the HTS as well as decreasing both the mesh complexity and the computing time. The first objective of the article is to validate the method in 2-D by evaluating the ac losses of a specific synchronous motor called superconducting torque motor; the computed results are compared with good agreements to those assessed with the minimum electromagnetic entropy production method, already validated. In a second part, the same losses are computed, taking into account the field anisotropy of Jc with the implementation of a dataset based on experimentally measured Ic at 65 and 77 K. With the model proposed in this article, it is possible to calculate the magnetic field of a whole electrical machine cross section and compute the ac losses in the individual tapes of its windings within the same numerical model. [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]

Rare earth-based coated conductors have large ac magnetization losses, which hinder their use in a variety of applications. A common way to reduce these losses is by striating the superconductor into narrow filaments by means of laser ablation. Practical superconductors also need a sufficiently thick copper stabilization. The best way of creating copper-stabilized filamentized coated conductors is still to be found. In this paper, the ac magnetization losses of differently prepared 12 mm wide coated conductors manufactured by SuperOx were measured. The samples differ in terms of thicknesses of copper stabilization (5 and 10 \mu \textm), number of filaments (from 10 to 60), and order for copper deposition (filaments produced before or after electroplating the tape). The ac loss measurements were performed at 77 K in a wide range of frequencies of the external magnetic field, which allows determining the onset of coupling currents and the importance of the coupling losses. Complementary dc measurements of the transverse resistivity between filaments help to understand the path of the coupling currents. Thanks to the variety of tested samples and operating conditions, this paper provides a direct comparison of the two striation processes in commercially available high-temperature superconductor coated conductors. [ABSTRACT FROM PUBLISHER]

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]

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]

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 order to successfully integrate superconducting fault current limiters (SFCL) into electric power system networks, accurate and fast simulation models are needed. This led us to develop a generic electric circuit model of an inductive SFCL, which we implemented in the EMTP-RV software. The selected SFCL is of shielded-core type, i.e. a HIS hollow cylinder surrounds the central leg of a magnetic core, and is located inside a primary copper winding, generating an AC magnetic field proportional to the line current. The model accounts for the highly nonlinear flux diffusion phenomenon across the superconducting cylinder, governed by the Maxwell equations and the non-linear E-J relationship of HIS materials. The computational efficiency and simplicity of this model resides in a judicious 1-D approximation of the geometry, together with the use of an equivalent electric circuit that reproduces accurately the actual magnetic behavior for the flux density (B) inside the walls of the HTS cylinder. The HTS properties are not restricted to the simple power law model, but instead, any resistivity function depending on J, B and T can be used and inserted directly in the model through a non-linear resistance appearing in the equivalent circuit. [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 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]

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]

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]

The finite element method has been employed in order to simulate the behavior of a HTS cable for transport current applications. The E - J model includes an anisotropic dependence of the critical current density J[sub c] and power index n on the local magnetic field, whose magnitude is nonnegligible and determines the effective critical current of the cable. The cable consists of four electrically insulated layers, each of them composed by 20 superconducting tapes, providing a total critical current of about 4 kA. In order to obtain a uniform repartition of the current among the layers, a sufficiently high contact resistance has been inserted in the electric circuit. The ac losses and the field distribution have been computed. A comparison is also made with a simple electric model of a HTS cable. [ABSTRACT FROM AUTHOR]

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 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 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. Therefore it is timely 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 cable. [ABSTRACT FROM AUTHOR]