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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]

In several cases, substations have become incapable of supporting faults due to increase in short-circuit levels. Fault current limiters (FCLs) are a potential solution for this problem. Among several FCL topologies presented in the literature, the saturated iron core superconducting fault current limiter (SIC-SFCL) has shown promising results in real tests in substations. In this context, this article presents the impacts of different kinds of short circuit on the SIC-SFCL device. To reproduce various types of fault, the SIC-SFCL is modeled in a 3-D framework considering both ferromagnetic and superconducting nonlinearities. Moreover, the proposed 3-D finite-element method model can couple the SIC-SFCL to the electric power system, also representing the electrical grid and the protection systems. For this investigation, the dc-bias superconducting coil’s normalized current density and the iron cores’ magnetic flux density are examined in light of different kinds of short circuit. The simulations are compared with measurements in a bench prototype, showing a maximum error of 16.5%. Furthermore, different types of short circuit are investigated and compared, which is possible only using a 3-D model. The highest limitation occurs in the phase-to-phase short-circuit case. In the dc circuit of the SIC-SFCL, the highest transient period happens in the single-phase short circuit. Finally, the phase-to-phase fault presents the highest dc current during the transient. [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]

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]

A good knowledge of material properties is a critical aspect for modeling high-temperature superconductor (HTS) devices. However, the knowledge of the electrical resistivity of coated conductors above the critical current is limited. The major challenge in characterizing this regime lies in the fact that for I > Ic, heating effects and thermal instabilities can quickly destroy the conductor if nothing is done to protect it. In previous work we extracted overcritical current data, obtained by combining fast pulsed current measurements with finite element analysis (Uniform Current (UC) model). In this work, we assessed the impact of the uncertainties of the input parameters on the quantities calculated with the UC model (temperature, current in each layer of the tape and resistivity of HTS). Firstly, sensitivity and uncertainty analyses were performed and it was found that the input parameters that mostly affect the accuracy of the UC model are the electrical resistivity and the thickness of the silver layer. Afterwards, an optimization method was developed to correctly estimate the geometry and the resistivity of the silver layer. This method combines experimental measurements of resistance R(T) of the tape and pulsed current measurements. The development of this strategy allowed us to determine the parameters that significantly impact the results of the UC model and helped to minimize their uncertainties. This enables a more accurate estimation of the resistivity in the overcritical current regime. [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]

In recent years, the $H$ formulation of Maxwell's equations has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where other formulations are desirable, for example for modeling superconducting turns in electrical machines or situations where the superconductor is better described by the critical state than by a power-law resistivity. In order to accurately and efficiently handle these situations, here we consider two approaches based on the magnetic vector potential: the $T$ - $A$ formulation of Maxwell's equations (with power-law resistivity) and the implementation of a quasi critical state model (QCSM) with a steep $E$ - $J$ relationship limited at $J_{\rm c}$. In this article, we extend the $T$ - $A$ formulation to thick conductors so that large coils with different coupling scenarios between the turns can be considered. We also discuss the QCSM in terms of its ability to calculate ac losses: in particular, we investigate the dependence of the calculated ac losses on the frequency of the ac excitation and the possibility of using quick one-step (instead of full-cycle) simulations to calculate the ac losses. [ABSTRACT FROM AUTHOR]

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H -formulation-based methods, coupled H - A and T - A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. Finally, a critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom, tolerance settings and the approximate time taken per cycle for each model. This benchmark and the results contained herein provide researchers with a suitable framework to validate, compare and optimise their own methods for modelling the HTS dynamo. [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]

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]

A numerical model implemented in the open-source finite-element method FreeFEM program is presented, with the aim of introducing students to the calculation of AC losses in superconductors. With this simple approach, students can learn about the critical state model used to describe the macroscopic electromagnetic behavior of superconductors and the importance of different factors influencing the AC losses of superconductors. [ABSTRACT FROM AUTHOR]

The current distribution in a superconductor is commonly calculated by solving the Maxwell's equations in differential form. An alternative method based on an integral form of Maxwell's equations was proposed by E. H. Brandt. Since the integral formulation needs to be solved in the conductor volume only, this method can be easily implemented in a programming language such as MATLAB. Brandt's approach has been used by several authors over the years, but no ready-to-use implementations are available. In this article, we present a step-by-step derivation of the method for a thin strip, a rectangular bar, and a cylindrical bulk. The results are validated using a comparison with exact solutions of the critical state model and a finite element solution of the $H$ -formulation. [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]

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 calculations for predicting the performance of high-temperature superconducting (HTS) cables, uniform physical and geometrical properties of the tapes are usually assumed. However, commercially available coated conductor tapes present a certain nonuniformity of their transport capability—namely their critical current—along the length. In addition, when coated conductor strands are compactly assembled to form a Roebel cable, their arrangement is far from the ideal one. In this work, we calculate the influence of Ic nonuniformities and of nonperfect strand alignment on the critical current of Roebel cables made of an HTS-coated conductor tape. For this purpose, we perform a statistical analysis using a recently developed and freely available open-source code to calculate the critical current of Roebel cables. We find that, for the considered cases, the nonuniformity of the strands’ Ic can have a significant impact on the final critical current of the cable, whereas the influence of the misalignment of the strands is rather low. [ABSTRACT FROM PUBLISHER]

BEST PATHS (acronym for “BEyond State-of-the-art Technologies for rePowering ac corridors and multi-Terminal HVDC Systems”) is a collaborative project of 40 leading European organizations from science and industry, supported by the 7th Research Framework Programme of the European Commission. The project investigates the feasibility of technological innovations that could advance high-capacity transmission links. These innovations include a demonstrator project dedicated to superconducting electric lines, which aims to validate the novel MgB2 technology for GW-level HVDC power transmission. The four-year project will thus demonstrate the operation of a full-scale 320 kV MgB2 monopole cable system that can transfer up to 3.2 GW. This paper focuses on the design and development activities for the 10 kA cable conductor, which were carried out in the first two years of the project. [ABSTRACT FROM PUBLISHER]

In this paper, we describe the critical state of a thin superconducting ring (and of a perfectly conducting ring as a limiting case) as a mixed boundary value problem. The disc is characterized by a three-part boundary division of the positive real axis, so this work is an extension of the procedure used in a previous work of ours for describing superconducting discs and strips, which are characterized by a two-part boundary division of the real axis. Here, we present the mathematical tools to solve this kind of problems-the Erdélyi-Kober operators-in a frame that can be immediately used. Contrary to the two-part problems considered in our previous work, three-part problems do not generally have analytical solutions and the numerical work takes on a significant heaviness. Nevertheless, this work is remunerated by three clear advantages: firstly, all the cases are afforded in the same way, without the necessity of any brilliant invention or ability; secondly, in the case of superconducting rings, the penetration of the magnetic field in the internal/external rims is a result of the method itself and does not have to be imposed, as it is commonly done with other methods presented in the literature; thirdly, the method can be extended to investigate even more complex cases (four-part problems). In this paper, we consider the cases of rings in uniform field and with transport current, with or without flux trapping in the hole and the case without net current, corresponding to a cut ring (washer), as used in some SQUID applications. [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]

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 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]

High temperature superconductor Roebel cables are well known for their large current capacity and low AC losses. For this reason they have become attractive candidates for many power applications. The continuous transposition of their strands reduces the coupling losses while ensuring better current sharing among them. However, since Roebel cables have a true 3D structure and are made of several high aspect ratio coated conductors, modelling and simulation of their electromagnetic properties is very challenging. Therefore, a realistic model taking into account the actual layout of the cable is unavoidably a large scale computational problem. In this work, we present a full 3D model of a Roebel cable with 14 strands. The model is based on the H-formulation, widely used for 2D problems. In order to keep the 3D features of the cable (in particular the magnetization currents near the transpositions), no simplifications are made other than the reduction of the modelled length according to the periodicity of the cable structure. The 3D model is used to study the dependence of AC losses on the amplitude of the AC applied magnetic field or transport current. Beyond the importance of simulating the Roebel cable layout, this work represents a further step into achieving 3D simulation of superconducting devices for real applications. [ABSTRACT FROM AUTHOR]

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]

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 Erdélyi-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-part 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 naïve translation of physics into a consistent mathematical formulation whose possible extension to other cases is self-evident. [ABSTRACT FROM AUTHOR]

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]

A new German government funded project for a resistive fault current limiter has started in September 2009 (ENSYSTROB) and is presented. The consortium includes partners from industry, research centers and utilities. It aims the construction of a 3-phase medium voltage current limiter (12 kV, 800 A) for the protection of the domestic supply in a power plant. A special feature of this application is the presence of large in-rush currents (4100 Ap for 50 ms, 1800 A for 15 s). The superconducting components are bifilar pancake coils consisting of pairs of YBCO-tapes in face to back configuration. Successful limitation experiments on prototype components with prospective currents in the whole range are shown. Also the stability with respect to high voltage could be demonstrated. The AC-losses under normal operation are shown, by simulation and experiment, to be smaller than the heat input of the current leads. The current limiting components are compared with similar elements based on BSCCO 2212 bulk material (Nexans SuperConductors). [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 present a new model to compute the current density distribution and the AC losses in multiple YBCO coated conductors by means of coupled integral equations implemented in a finite-element (FE) environment. The model considers the superconducting tapes as 1D objects and allows overcoming the problem of the mesh of conductors of large aspect ratio, typical of 2D implementations; as a result, it is also much faster. The interaction between the different conductors is taken into account by means of a coupling of the electromagnetic variables. The magnetic field distribution in the space between the conductors is computed by coupling the 1D model with a standard 2D magnetic model, which uses the computed current density distributions as sources for the magnetic field. Results are compared with those obtained with standard 2D implementations and with experimental results. [ABSTRACT FROM AUTHOR]

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]

Coated conductors (CCs) are very promising for the design of novel and efficient resistive fault current limiters (FCLs). However, a detailed knowledge about their thermal and electromagnetic behaviors in the presence of over-critical currents is crucial for their improvement. In this context, we performed finite-element magneto-thermal modeling of CCs under over-critical current on several geometries. Accordingly, we have investigated the influence of the physical properties of stabilizer and substrate on the thermal stability to improve the high-temperature superconductor (HTS)-FCL design. All simulations were performed using COMSOL Multiphysics, a commercial finite-element package, which has a built-in coupling between the thermal and electrical equations, allowing us to compute both quantities simultaneously during the solving process. Our results allow us to determine the current threshold to achieve thermal stability of HTS FCLs made with CCs. [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]

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]

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]

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]

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]

Studies the influence of self-field and cross-sectional geometry on effective current and alternating current losses in transport current applications of non-twisted multifilamentary superconductors. Results of finite-element method simulations; Numerical implementations.

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]

Focuses on a study concerning the development of finite-element method formulations to model the electromagnetic behavior of superconductors. Discussion on the analytical model for superconductors in applied magnetic field; Assessment of alternating and transport current; Methodology and results.

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]