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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]

Finite-element method is used for examining the influence of various numerical parameters on the precision and the speed of ac loss computations in high-temperature superconductors. A new and simple self-check test is proposed for validating the computed ac losses and the behavior of the numerical solution near flux/current fronts is analyzed.

A new finite-element model is developed to study the electromagnetic and thermal behavior of high-temperature superconductor (HTS) for resistive fault current limiter applications. This model is simpler to use and fast due to coupling of electromagnetic and thermal equations in a single process.

A new method for the deposition of stacks of YBCO layers on the same substrate is studied using the multiple ion beam-assisted deposition (IBAD) templates. The analysis reveals that the resetting of the surface texture helps in the manufacture of new types of structures in the coated conductors.

The study presents the quantification of the tape interaction and the AC losses that are observed in the YBCO coated conductor coils. The losses are found to decrease in the presence of an externally applied magnetic field.

The study describes a new model, which is based on the use of edge finite elements and is generally used for calculating the AC losses in high-temperature superconducting (HTS) tapes.

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents.

A study of the effects of the magnetic self-filed on the transport properties of a multilayer high T(sub c) superconducting (HTS) cable with the help of a two dimensional finite-element method (FEM) simulations is presented. A simple electrical model of the cable would give optimal winding pitches, leading to a uniform current repartition and also overcome the difficulties of the direct three-dimensional FEM computations.

The influence of self-field and geometry effects in transport current applications of multifilamentary Bi-2223/Ag conductors is examined and reported.

The finite element method is employed for simulating the behavior of a high temperature superconducting (HTS) cable.

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]

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]

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]

In this paper we refer to a specific class of Dynamic Channel Allocation (DCA) strategies, namely the interference-free, timid, not-conditioned class. The main concern of this work is to verify if and to what extent strategies belonging to this class can offer better performance than Fixed Channel Allocation (FCA). The interest in this kind of strategies is motivated by their feasibility with current TDM technologies, the limited amount of information required to carry out channel assignments and their intrinsic stability. In this framework we present a simple, but very attractive DCA strategy, the so-called Geometric DCA (GDCA). A performance evaluation is carried out to compare some representative DCA strategies of the considered class, by using a user mobility model that accounts for the large fluctuations of the number of users in a cell coverage area expected in a microcellular environment. The effect of the non-null propagation time required by the information exchange in the DCA strategies is also taken into account. It emerges that the proposed GDCA allows better performance than more sophisticated strategies already proposed, at the expense of a frequency planning carried out only at network configuration. This is due to the ability of GDCA to exploit the a priori information to maintain a tight geometric packing of used carriers. The reported results also show that DCA strategies in the considered class cope with large and sudden traffic fluctuations remarkably better than the FCA scheme does and that the advantage becomes more evident as the burstiness of the user mobility process (hence of the offered traffic) increases.

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]

The effects of different multifilamentary geometries on the dynamic current and field distributions in Y[Ba.sub.2][Cu.sub.3][O.sub.7-[delta]] thin films are studied. The studies have shown that increasing the distance between filaments has reduced the magnetic coupling and has decreased the ac losses.

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]

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]