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The primary benefit of a metallic stabilization/shunt in high temperature superconductor (HTS) coated conductors (CCs) is to prevent joule heating damage by providing an alternative path for the current flow during the HTS normal state transition (i.e., quench). However, the shunt presence in combination with unavoidable fluctuations in the critical current (I c) of the HTS film can develop a localized quench along the CC's length if the operational current is kept close to I c. This scenario, also known as the hot-spot regime, can lead to the rupture of the CC if the local quench does not propagate fast enough. The current flow diverter (CFD) is the CC architecture concept that has proven to increase the conductor's robustness against a hot-spot regime by simply boosting the quench velocity in the CC, which avoids the shunt compromise in some applications. This work investigates a practical manufacturing route for incorporating the CFD architecture in a reel-to-reel system via the preparation of yttrium oxide (Y2O3) as an insulating thin nanolayer (∼100 nm) on top of a GdBa2Cu3O7 (GdBCO) superconductor. Chemical solution deposition (CSD) using ink jet printing (IJP) is shown to be a suitable manufacturing approach. Two sequences of the experimental steps have been investigated, where oxygenation of the GdBCO layer is performed after or before the solution deposition and the Y2O3 nanolayer thermal treatment formation step. A correlated analysis of the microstructure, in situ oxygenation kinetics, and superconducting properties of the Ag/Y2O3/GdBCO trilayer processed under different conditions shows that a new customized functional CC can be prepared. The successful achievement of the CFD effect in the case of the preoxygenated customized CC was confirmed by measuring the current transfer length, thus demonstrating the effectiveness of the CSD-IJP as a processing method., We acknowledge the funding of this research by FASTGRID Project (EU-H2020, 721019); the Projects COACHSUPENERGY (MAT2014-51778-C2-1-R) and SUMATE (RTI2018-095853-BC21 and RTI2018-095853-B-C22) from the Spanish Ministry of Economy and Competitiveness, which were cofunded by the European Regional Development Fund; and the Project 2017-SGR 753 from Generalitat de Catalunya and the COST Action NANOCOHYBRI (CA16218). ICMAB authors also acknowledge the Center of Excellence awards Severo Ochoa SEV-2015-0496 and CEX2019-000917-S, With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000917-S).

High-temperature superconductors (HTSs) are used in a growing number of applications. Technical HTSs usually consist of superconducting and metallic parts. HTS conductors are characterized by their critical current density and critical temperature defined by the superconducting layer, but other quantities such as the current transfer length (CTL) and the interfacial resistance between the superconducting part and surrounding metals are also important characteristics. Since the CTL and the interfacial resistance cannot be measured directly, a method is known to evaluate these parameters indirectly from the characterization of the spatial variation of the surface voltage of the metallic surrounding that is in direct contact with the superconducting material. In this article, we present the details of the experimental method developed to determine the CTL and the interfacial resistance of commercial second-generation HTS conductors of any type of architecture. We apply this method to quantify the interfacial resistance of ten HTS tapes from six major tape manufacturers. Also, since the architecture of a commercial HTS tape is usually more complicated than an 'idealized' superposition of two flat layers (i.e., a metallic layer and a superconducting layer), recourse to three-dimensional numerical modeling has been required in order to understand in details the current transfer mechanisms taking place within the tape. We also show that the method can be applied directly to more complicated structures encountered in HTS cables, namely to determine the barrier resistance between a metallic structure in contact with a superconducting tape, providing important information required in numerical modeling when designing superconducting devices.

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 $I>I_{\rm {c}}$ , 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.

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.

The H-formulation, used abundantly for the simulation of high-temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well-known H- $\phi$ formulation in COMSOL multiphysics in order to compare the numerical performance of the H and H- $\phi$ formulations in the context of computing the magnetization of bulk superconductors. We show that the H- $\phi$ formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H- $\phi$ formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H- $\phi$ formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL.

The aerospace industry uses 200-h sustained-load test (SLT), described in ASTM F-519, to evaluate hydrogen embrittlement (HE) of their 4340 steel electroplated parts. The cadmium plating used in ASTM F-519 suggest that the coating density may affect HE in an important manner. Therefore, in this work, 4340 steel notched bars were plated with five different cadmium coating densities. Then, the SLT was combined with thermal desorption spectroscopy (TDS) to evaluate: (i) the degree of HE, and (ii) the hydrogen content of the cadmium-plated 4340 steel samples. The results show strong evidences that the major factor causing HE of cadmium-plated 4340 steel is the coating density. Moreover, an advanced analysis of TDS curves using the Hertz–Knudsen equation allows distinguishing hydrogen in steel from hydrogen in the cadmium coating. The advanced analysis also gives an estimation of the coating density, and therefore indicates if the baking will be effective at relieving embrittlement. Finally, TDS could be a good complementary tool to the SLT in evaluating HE.

Thermal desorption spectroscopy (TDS) and sustained-load tests were used to investigate hydrogen embrittlement (HE), hydrogen profiles and the impact of the baking delay of cadmium-plated 4340 steel-notched bars. The results show a tremendous concentration of hydrogen in the cadmium coatings (200 to 1500 ppma) that does not contribute to HE. Hydrogen in manganese sulfide (MnS) traps was also found not to contribute to HE. The total hydrogen concentration measured by TDS is thus not suitable to determine an embrittlement threshold. Subtracting hydrogen in cadmium and MnS traps from total hydrogen allowed finding a true critical hydrogen concentration threshold of 0.6 ppma (0.01 ppmm). No impact of the baking delay was found.

This paper presents a new time-domain finite-element approach for modeling thin sheets with hyperbolic basis functions derived from the well-known steady-state solution of the linear flux diffusion equation. The combination of solutions at different operating frequencies permits the representation of the time-evolution of field quantities in the magnetic field formulation. This approach is here applied to solve a planar shielding problem in harmonic and time-dependent simulations for materials with either linear or nonlinear characteristics. Local and global quantities show good agreement with the reference solutions obtained by the standard finite element method on a complete and representative discretization of the region exposed to a time-varying magnetic field. ispartof: Ieee Transactions On Magnetics vol:57 issue:11 pages:1-10 status: Published online

Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite-element method, the use of vector-dependent variables in nonconducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the nonconducting domains must be made simply connected in order to obey Ampere's law. In this article, we use thin cuts to apply a discontinuity in $\phi$ and make the nonconducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite-element program, already widely used by the applied superconductivity community. We simulate three different models in two dimensions and three dimensions using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H- $\phi$ -formulation can be up to seven times faster than the standard H-formulation in certain applications of interest.

Two dielectric barrier discharge (DBD) reactors, one small, the other about 40 times larger, associated equipment, and a dedicated MATLAB code have been used to carry out precise determinations of electrical energy, $E_{g}$ , dissipated per discharge cycle of the applied a.c. voltage, $V_{a}$ . In the smaller reactor, this was done over the frequency range $5 \le f\le 50$ kHz and using twin pairs of several different insulating materials (2.54-cm-diameter disks) with relative permittivities between $2.1 \le \kappa _{\text {die}}^{\prime }\le 9.5$ as dielectric barriers in DBDs for four different gases: He, Ne, Ar, and N2. In the large reactor, $f$ was restricted to 20 kHz in Ar and He; this latter system primarily serves for plasma polymerization experiments in which organic “monomers” are admixed with the flow of Ar as carrier gas. We report the method for exactly evaluating $E_{g}$ , and then present and compare values measured under different conditions. To the extent possible, these are compared between the small and large reactors, and with results published in the literature. The reliability of the method is confirmed, for example, by reproducing published breakdown fields of the gases examined, and by several other original results.

This paper uses both experimental and numerical approaches to revisit the concept of current transfer length (CTL) in second-generation high-temperature superconductor coated conductors with a current flow diverter (CFD) architecture. The CFD architecture has been implemented on eight commercial coated conductors samples from THEVA. In order to measure the 2-D current distribution in the silver stabilizer layer of the samples, we first used a custom-made array of 120 voltage taps to measure the surface potential distribution. Then, the so-called "static" CTL ($\lambda_s$) was extracted using a semi-analytical model that fitted well the experimental data. As defined in this paper, the static CTL on a 2-D domain is a generalization of the definition commonly used in literature. In addition, we used a 3-D finite element model to simulate the normal zone propagation in our CFD samples, in order to quantify their "dynamic" CTL ($\lambda_d$), a new concept introduced in this paper and defined as the CTL observed during the propagation of a quenched region. The results show that, for a CFD architecture, $\lambda_d$ is always larger than $\lambda_s$, whereas $\lambda_d = \lambda_s$ when the interfacial resistance between the stabilizer and the superconductor layers is the same everywhere. We proved that the cause of these different behaviors is related to the shape of the normal zone, which is curved for the CFD architecture, and rectangular otherwise. Finally, we showed that the NZPV is proportional to $\lambda_d$, not with $\lambda_s$, which suggests that the dynamic CTL $\lambda_d$ is the most general definition of the CTL and should always be used when current crowding and non-uniform heat generation occurs around a normal zone., Comment: 11 pages, 10 figures

The normal zone propagation velocity (NZPV) of three families of REBCO tape architectures designed for superconducting fault current limiters and to be used in high voltage direct current transmission systems has been measured experimentally in liquid nitrogen at atmospheric pressure. The measured NZPVs span more than three orders of magnitude depending on the tape architectures. Numerical simulations based on finite elements allow us to reproduce the experiments well. The dynamic current transfer length (CTL) extracted from the numerical simulations was found to be the dominating characteristic length determining the NZPV instead of the thermal diffusion length. We therefore propose a simple analytical model, whose key parameters are the dynamic CTL, the heat capacity and the resistive losses in the metallic layers, to calculate the NZPV., The authors acknowledge the funding of this research by FASTGRID Project (EU-H2020, 721019), the Projects COACHSUPENERGY (MAT2014-51778-C2-1-R), SUMATE (RTI2018-095853-BC21 and RTI2018-095853-B-C22) from the Spanish Ministry of Economy and Competitiveness which were cofunded by the European Regional Development Fund, the Project 2017-SGR 753 from Generalitat de Catalunya and the COST Action NANOCOHYBRI (CA16218). Polytechnique Montréal authors also acknowledge NSERC (Canada), FRQNT (Québec), the RQMP infrastructure and CMC microsystems for financial support. ICMAB authors also acknowledge the Center of Excellence awards Severo Ochoa SEV-2015-0496 and CEX2019-000917-S., With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000917-S).

Hydrogen embrittlement (HE) of high-strength steels has been a long-standing issue in the aerospace industry. Detecting the presence of hydrogen in steel with a low-cost and fast non-destructive method would be useful to avoid wasting parts. In this paper, we evaluate the feasibility of using eddy currents to achieve this goal. At first, we evaluate HE and hydrogen content in a series of chromium-plated 4340 steel notched bar samples (extremely embrittled) using sustained-load tests and thermal desorption spectroscopy. The failure of the notched bars at only 20% of their maximum mechanical load is coherent with the high hydrogen concentration in the samples, which can be as high as 1400 ppm atomic ( $$\sim \,30\%$$ in steel, $$\sim \,70\%$$ in the coating). However, a baking at $$190\,{^{\circ }}\hbox {C}$$ for 23 h can desorb most embrittling hydrogen in the 4340 steel and relieve HE. Therefore, successive bakings are used to progressively desorb hydrogen from the samples and produce various hydrogen concentrations. By using eddy currents after each baking, coupled with a finite element model implemented in COMSOL, we can deduce the electric and magnetic properties of steel and chromium as a function of hydrogen concentration. Unfortunately, no significant variation of these properties can be observed, even for concentration variations as large as $$\sim \,900\,\hbox {ppma}$$ . The only observable changes happen after performing bakings at high temperature, which induce microstructural changes in the samples. However, eddy currents remain a good approach to detect small changes in electromagnetic materials properties resulting from other causes than hydrogen.

This paper presents extensive electrical, microstructural and chemical characterizations of HTS coated conductor samples in which an oxide layer ( CeO x ) has been added between the superconductor (GdBaCuO) and the silver (Ag) layers, in an attempt to increase the interfacial resistance between these two conductive layers. This increase of interfacial resistance is required to realize the current flow diverter (CFD) architecture in HTS tapes. All samples in this paper have been characterized before and after performing an annealing in oxygen atmosphere. The purpose of the annealing was to reduce the interfacial resistance generated by the CeO x layer, in order to achieve a proper value for the CFD architecture. Samples with different thicknesses of CeO x , namely 0, 10, 35 and 100 nm, have been produced and characterized. The critical current and the critical temperature have been measured to determine the quality of the superconducting layers, while cross-section transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS) have been used to monitor the impact of the annealing. The results show a clear degradation of the superconducting layer for samples with a thick layer ( ≥ 35 nm) of CeO x after annealing at 450 °C. According to the EDS results, a reduction of the amount of barium is observed in the superconducting layer, which could explain the observed reduction of the critical current.

Carbon fiber reinforced polymers (CFRPs) are increasingly used in the latest generations of aircraft, but their low electrical conductivity is a concern for lightning strike protection. During the past few years, development of lightning strike protection solutions for CFRP has attracted increasing interest, and cold spray is one coating approach to achieving this. In this work, pure tin coatings and tin–copper composite coatings were cold sprayed on CFRP as possible lightning strike protection materials. The coatings were subjected to various mechanical and electrical characterizations. The effect of annealing on electrical conductivity was also examined. Furthermore, continuous current injection tests, which duplicated component C of a lightning waveform, were performed on the coatings. The results showed that the cold-sprayed coatings can provide effective protection to the CFRP underneath when subjected to currents up to 200 A with 1-s duration.

Lightning strike protection (LSP) offered by two different classes of conductive coatings deposited on carbon fiber-reinforced polymer (CFRP) panels was studied in three stages: (i) emulated lightning impulse strikes, (ii) conducted continuous currents, and (iii) physical aspects of lightning-coating interaction. Two types of coatings, hybrid and metallic were studied. Hybrid (multi-material) coatings consisted of silver nanoparticles dispersed in conducting polymer PEDOT:PSS, and silver-coated carbon-nanofiber transferred onto an epoxy surfacing film. For metallic coatings, continuous coatings of silver, and a composite of 10% copper in tin were considered. We evaluate the material design schemes of these two classes of materials based on the degree of protection offered to the composite substrates from emulated lightning strikes. Two additional cases, CFRP with an epoxy surfacing film and a continuous coating of tin were also studied, while expanded copper foil (ECF)-protected and unprotected CFRP formed the reference materials. Continuous metallic coatings outperformed their hybrid counterparts, although none of the materials was comparable to ECF in terms of LSP performance. This work demonstrates the limitations of electrical resistivity and/or sheet resistance measurements to provide a reliable estimate about the performance of conductive coatings and that emulated lightning strikes are crucial for assessment of lightning protection. Keywords: Coatings, Composites, Current, Damage analysis, Lightning, Resistance, Resistivity, Thermography, Ultrasonic

This paper presents a novel finite-element (FE) approach for the electromagnetic modeling of superconducting coated conductors with transport currents. We combine a thin-shell (TS) method to the H-φ-formulation to avoid the meshing difficulties related to the high aspect ratio of these conductors and reduce the computational burden in simulations. The interface conditions in the TS method are defined using an auxiliary 1-D FE discretization of N elements along the thinnest dimension of the conductor. This procedure permits the approximation of the superconductor’s nonlinearities inside the TS in a time-transient analysis. Four application examples of increasing complexity are discussed: (1) single coated conductor, (2) two closely packed conductors carrying anti-parallel currents, (3) a stack of 20 superconducting tapes and (4) a full representation of a high-temperature superconducting tape comprising a stack of thin films. In all these examples, the profiles of both the tangential and normal components of the magnetic field show good agreement with a reference solution obtained with the standard 2-D H-φ-formulation. Results are also compared with the widely used T-A-formulation. This formulation is shown to be dual to the TS model with a single FE (N = 1) in the auxiliary 1-D systems. The increase of N in the TS model is shown to be advantageous at small inter-tape separation and low transport current since it allows the tangential components of the magnetic field to penetrate the thin region. The reduction in computational cost without compromising accuracy makes the proposed model promising for the simulation of large-scale superconducting applications.

Purpose Surface heat treatment by induction heating (10-100 kHz) requires precise prediction and control of the depth of the induced phase transformation. This paper aims at identifying common issues with the measurement and modeling of magnetic properties used in induction heating simulations, and it proposes ways to improve the situation. Design/methodology/approach In particular, it is demonstrated how intrinsic magnetic properties (i.e. the B-H curve) of a sample can change during the magnetic characterization process itself, due to involuntary annealing of the sample. Then, for a B-H curve that is supposed perfectly known, a comparison is performed between multiple models, each one representing the magnetic properties of steel in time-harmonic (TH) finite element method simulations. Finally, a new model called “power-equivalent model” is proposed. This model provides the best possible accuracy for a known nonlinear and hysteretic B-H curve used in TH simulations. Findings By carefully following the guidelines identified in this paper, reduction of errors in the range of 5-10 per cent can be achieved, both at the experimental and modeling levels. The new “power-equivalent model” proposed is also expected to be more generic than existing models. Originality/value This paper highlights common pitfalls in the measurement and modeling of magnetic properties, and suggests ways to improve the situation.

High voltage direct current super-grids are one attractive solution for the transmission of bulk power of renewable electricity over long distances. Their protection is still an issue and superconducting fault current limiters (SCFCL) offer attractive perspectives. However, the actual superconducting tapes are not yet properly designed for operation at high voltages (>100 kV): The electric field developed during the current limitation is still too low (approximately 50 V/m for 50 ms) and the limiter requires too long lengths of tape. The European project FASTGRID aims at improving the properties of the REBCO tapes to enhance significantly (by 2-3 times) the electric field limit and so the economical SCFCL attractiveness. We use advanced THEVA tapes. Substantial improvements are also planned on the stabilizer (shunt) layer. Several shunt ways are under investigations. Other improvement on the tape properties will be carried out, namely the increase of the normal zone propagation velocity by at least one order of magnitude, with the help of the innovative current flow diverter architecture. The optimized conductor will be used in a SCFCL module (≈1.5 kA-50 kV) tested at 65 K. We will monitor the temperature along the conductor using an attached optical fibre. FASTGRID will also develop innovative tapes based on sapphire substrate, which can tolerate very high electric fields, in the range of kilovolts per meter. Validated on the laboratory scale, this game-changing technology needs to be implemented at long lengths with an industrial process. We will provide an overview of the project and its first results., This work was supported by the European Union's Horizon 2020 research and innovative programme under Grant 721019.

We have wound a 157-turn, non-insulated pancake coil with an outer diameter of 85 mm and we cooled it down to 77 K with a combination of conduction and gas cooling. Using high-speed fluorescent thermal imaging in combination with electrical measurements we have investigated the coil under load, including various ramping tests and over-current experiments. We have found that the coil does not heat up measurably when being ramped to below its critical current. Two over-current experiments are presented, where in one case the coil recovered by itself and in another case a thermal runaway occurred. We have recorded heating in the bulk of the windings due to local defects, however the coil remained cryostable even during some over-critical conditions and heated only to about 82–85 K at certain positions. A thermal runaway was observed at the center, where the highest magnetic field and a resistive joint create a natural defect. The maximum temperature, ∼100 K, was reached only in the few innermost windings around the coil former.

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.

WOS:000468607600001; International audience; A new formulation of the Preisach-Mayergoyz model was developed to radically improve its numerical performance. This new computationally efficient vector hysteresis model was incorporated in a 3-D finite element software. Many improvements to the transient nonlinear solver were made in order to obtain a good convergence of the TEAM problem 32 while using only 125 time steps per cycle. The results of this simulation show good agreement with the experimental data.

Lightning strike emulator was employed for evaluating the response of copper electroless coatings on epoxy-CFRP laminates under these high demanding electrical events. Samples were coated for 15 and 30 min producing 0.6 and 1.2 µm thick layers, respectively, and their performances were compared with commercially protected and naked laminates. Data show that a thin copper layer can improve the performance of CFRP under 40 kA discharges by absorbing part of the electrical energy, as a sacrificial protection. The surface of delaminated composite was lower whereas the coating area affected was larger for samples treated at longer times. An interesting relationship was found between the charge transfer and the damaged area, for all samples. In addition, sustained 30 A injection tests were performed and both electrical data and thermal imaging showed a better tolerance to continuous currents and a better heat dissipation of 30 min versus 15 min coated samples.

The complete penetration magnetic field $B_{P}$ is the main feature of a superconducting pellet submitted to an axial applied magnetic field. The electric $E{-}J$ characteristics of HTS bulk is generally described by a power law $E(J) = E_{C}(J/J_{C})^{n}$ . The influence of the $n$ -value and applied magnetic field rise rate $V_{b}$ on the $B_{P}$ of a HTS cylindrical pellet has been presented in a previous paper. The numerical results presented come from a numerical resolution of a nonlinear diffusion problem. With the help of these simulations, a linear relationship between $B_{P}$ , ln $V_{b}$ , and $n$ -value has been deduced. This comparison allows determining the critical current density $J_{C}$ and the $n$ -value of the power law based on direct measurement of $B_{P}$ in the gap between two bulk HTS pellets. In this paper, an improvement of this method is presented. The influence of geometric parameters $R$ and $L$ is studied to give generality to the relationship between $B_{P}$ , $V_{b}$ , and $n$ -value. A previous $B_{P}$ formula is confirmed by these new simulations. To correctly connect simulation and experimental results, the influence of spacing $e$ between bulks is studied and presented. A relationship between $B_{P}$ and measured complete penetration magnetic field $B_{PM}$ is determined.

A volume integral formulation for solving electromagnetic problems in the frequency domain is proposed. First, it is based on a magnetic flux and current density face element interpolation for representing the electromagnetic problem through an equivalent circuit. Second, magnetic vector potentials $A$ and electric vector potential $T$ are considered, thanks to the use of finite element mesh connectivity matrices. The formulation is particularly well adapted to solving electromagnetic problems with large air domains, in the presence of thin electric regions and magnetic materials.

AC losses in superconductors are generated every time a time-varying current/field is present. Engineers must be able to predict these losses as accurately as possible during the design phase of power applications. The electrodynamics of superconductors can be formulated as a nonlinear eddy current problem in which the resistivity of the superconducting region is a highly nonlinear function of the current density. In 3-D finite-element simulations, it leads to time-consuming simulations and convergence issues. In this paper, we compare two different $E$ – $J$ constitutive equations, namely: 1) power law model and 2) the percolation model (PM), programmed within both the $H$ – $\phi $ and $T$ – $\phi $ formulations. Based on the 3-D case of a three-filament twisted superconducting wire, the numerical performance of all these formulations/material models is compared in terms of accuracy, computation times, number of time steps, and number of Newton iterations for different relaxation methods. It is shown that the combination of the $T$ – $\phi $ formulation and the $E$ – $J$ PM works fine and should be further developed, as it seems to constitute the best modeling option from both a numerical and physical point of view.

In this paper, a critical review of existing methods to couple magnetic circuits to electric circuits is provided and explained using a two-port element called mutator. In order to couple magnetic circuits in electromagnetic transients-type programs, a new implementation of mutators is described, which uses the commonly available coupled series R-L branches. The practical case of a single-phase two-winding transformer is studied, and the results show that the new method is equivalent to the dual (inductive) model. However, it is concluded that the new method is more interesting than duality to couple large 3-D topological models (transformers, lines, motors, etc.), because it avoids difficulties of duality associated with nonplanar magnetic circuits.

While the storage properties and the anticipation potential of many classes of power system loads (such as thermal loads) can be exploited to mitigate renewable sources variability, the challenge to do so in an optimal and coherentmanner is significant. This is due to the sheer number and dynamic diversity of the loads that can be involved in any large-scale application. The smartDESC concept is a control architecture that was developed for this purpose. It builds on the more pervasive communication means currently available (such as Advanced Metering Infrastructures), as well as the mathematical tools of (i) aggregate load modeling, (ii) renewable energy forecasting, (iii) optimizationtheory, deterministic or stochastic, and (iv) some recent developments in control of large-scale systems based ongame theory, and so-called mean-field (MF) control theory, which allow a scalable yet optimal approach to thedecentralized control of large pools of loads. This paper presents the building blocks of the smartDESC architecture,together with an associated simulator and simulation results.

A detailed knowledge of the resistivity of high-temperature superconductors in the overcritical current regime is important to achieve reliable numerical simulations of applications such as superconducting fault current limiters. We have previously shown that the combination of fast pulsed current measurements and finite element analysis allows accounting for heating effects occurring during the current pulses. We demonstrated that it is possible to retrieve the correct current and temperature dependence of the resistivity data points of the superconductor material. In this contribution, we apply this method to characterize the resistivity vs. current and temperature of commercial REBCO tapes in the overcritical current regime, between 77 and 90 K and in self-field conditions. The self-consistency of the overcritical resistivity model ρ O C ( I , T ) is verified by comparing DC fault measurements with the results of numerical simulations using this model as input. We then analyze by numerical simulation to what extent using the ρ O C ( I , T ) model instead of the widely used power-law model ρ P W L ( I , T ) affects the thermal and electrical performance of the tapes in the practical case of a superconducting fault current limiter. A remarkable difference is observed between the measured overcritical current resistivity model ρ O C ( I , T ) and the power-law resistivity model ρ P W L ( I , T ) . In particular, the simulations using the power-law model show that the device quenches faster than with the overcritical resistivity model. This information can be used to optimize the architecture of the stabilizer in superconducting fault current limiters.

This work presents a generalization of the concept of current transfer length (CTL) between the stabilizer and the superconducting layer of high temperature superconductor (HTS) coated conductor tapes with a current flow diverter (CFD) architecture. The CFD architecture consists in a non-uniform interfacial resistance between the two layers, namely a high interfacial resistance in the middle of the tape and a low interfacial resistance on its sides. With this architecture, when the current transfers from the stabilizer to the superconductor to circumvent a normal zone or a crack, a current density component along the width of the tape appears, required for the current to circumvent the high interfacial resistance. This current component does not exist in a classical tape architecture. To describe quantitatively this current transfer, we developed a quasi-analytical formula that computes the electric potential in the stabilization layer, from which we can derive the current density components. The model is then used to determine the current transfer length (CTL) in tapes with a CFD architecture, using a generalized definition of the CTL. The model is simple and quick to run and allows deepening our understanding of the dependence of the CTL with different geometric and materials parameters, and clearly shows that the CFD architecture is very effective in increasing the CTL of HTS tapes while keeping the effective interfacial resistance to very low values. The model is quasi-analytical because it requires the numerical evaluation of a transcendental equation for determining one set of coefficients, but otherwise, it takes the form of a double summation of analytical functions (series solution). The exactness of the model has been verified by comparisons with finite element simulations.

Electroplating of aerospace parts generates hydrogen embrittlement, which is controlled by 200-h sustained-load tests performed on cylindrical notched samples. Those tests are costly and offer only a pass-or-fail assessment, with limited interpretability. In this article, we propose a new fractographic method to obtain a quantitative indication of the embrittlement severity of electroplated samples that failed the sustained-load test. On the fracture surfaces of failed samples, intergranular (IG) zones were observable at fracture initiation sites, surrounded by ductile zones, with intermediate regions containing mixed (ductile+IG) features. Within the framework of the recently proposed Hydrogen-Enhanced Plasticity-Mediated DEcohesion mechanism (HELP-mediated HEDE), we argue that there is a correlation between the intergranular appearance of the fracture surfaces and the subcritical nature of the crack propagation. Using this argument, we computed the stress intensity factor K for each crack and loading condition, with the input of intergranular zone sizes and finite element analysis. Minimum and maximum K values were identified and statistics of the extremes was used to calculate the minimum expected K values for various embrittlement conditions. It is proposed that this value is an estimate of the threshold for embrittlement, Kth. Values of Kth between 9 MPa m0.5 and 30 MPa m0.5 were measured for various plating conditions. Those estimations are more conservative than the thresholds reported in the literature, which were measured using more complex experimental procedures. Moreover, the fracture toughness estimated with the maximum K values was possibly affected by high initial hydrogen concentrations as per the HELP+HEDE embrittlement mechanism.

In this study, copper coatings smaller than 3 &micro, m were created by electroless deposition on epoxy-based carbon fiber-reinforced polymer (CFRP) laminates for enhancing their electrical properties. This well-known method of metallization was employed with a self-designed combination of reagents, and the coatings were studied to evaluate their physical and chemical properties. A five-stage plating strategy was applied to 40 mm &times, 40 mm samples, and three different coatings were produced during the work. The metal layers created were studied and characterized to evaluate their, electrical conductivity, thickness, and adhesion to substrates, among other properties. In addition, the growth mechanisms of the microstructure were analyzed in detail for a better understanding of the process. The results showed that the proposed metallization strategy presents good characteristics and is a strong candidate for enhancing the electrical performance of CFRP.

High temperature superconductors (HTS)-wound coils are being developed for use in motors, generators as well as magnet applications. Determining the stability and safe operating margins of such coils still poses challenges. While the recently introduced no-insulation winding method provides a remedy for many problems, it comes with its own limitations. For comparison, we have wound two pancake coils from HTS coated conductors with the insulated and non-insulated winding techniques. Both coils were coated with a fluorescent, temperature-sensitive coating, which allowed monitoring the surface temperatures during operation. The coils were cooled to 77 K via a combination of conduction and gas cooling, and their electrical and thermal behaviour was observed in operation. Here we present the normal transition of both coils caused by an artificially introduced instability due to a surface-mounted, resistive heater element. In the insulated coil, the localized disturbance caused a local transition of the superconductor to the normal conducting state, triggering a thermal runaway. Merely the turns in contact with the artificial disturbance heated up, while the rest of the coil remained in the superconducting state. In the non-insulated coil—although a much longer heater pulse was required—the normal transition started from the weakest point of the coil (around the bobbin) and the whole coil was heating thereafter, with the centre heating more.

Cadmium-plated high-strength steel parts in aerospace are subject to hydrogen embrittlement (HE). Standard 200-h sustained-load tests (SLT) detect embrittlement on plated parts; however tests relying on fracture mechanics can improve interpretability and reduce testing times. We measured the invariant threshold for the onset of HE on compact tension samples with the incremental step-loading method. No HE was observed after plating conditions deemed embrittling per SLT, unless a 200-h preload was applied. We argue that hydrogen is located in or close to the coating, and that the compact samples are too thick to allow a uniform hydrogen profile across the thickness.

Currently, modelling hysteresis losses in superconductors is most often based on the H-formulation of the eddy current model (ECM) solved using the finite element method (FEM). In the H-formulation, the problem is expressed using the magnetic field intensity H and discretized using edge elements in the whole domain. Even though this approach is well established, it uses unnecessary degrees of freedom (DOFs) and introduces modelling error such as currents flowing in air regions due to finite air resistivity. In this paper, we present a modelling tool utilizing another H-oriented formulation of the ECM, making use of cohomology of the air regions. We constrain the net currents through the conductors by fixing the DOFs related to the so-called cohomology basis functions. As air regions will be truly non-conducting, DOFs and running times of these nonlinear simulations are reduced significantly as compared to the classical H-formulation. This fact is demonstrated through numerical simulations.

Carbon fiber reinforced polymers (CFRPs) have a highly anisotropic electrical resistivity, which limits their use in electrical applications. In this contribution, an electric field was used to align multiwalled carbon nanotubes (MWCNTs) to create preferential conductive pathways within a nanocomposite and a multiscale composite in order to reduce their resistivity. Investigation on epoxy containing MWCNTs have shown that an electric field of 40 V mm−1 or higher applied for 2 h can lead to a reduction of the resistivity parallel to the field up to four orders of magnitude with only 0·01 wt-% loading. In the case of CFRPs reinforced with 0·01 and 0·1 wt-% of MWCNTs, we observed reductions of the through the thickness resistivity of 36 and 99% respectively, when an electric field of 60 V mm−1 was applied for 2 h during the fabrication of the samples.

We develop a quantitative model to calculate the optimal experimental conditions for the etching of the oxide barrier of porous anodic alumina (PAA) membranes. The method is applied to a membrane fabricated at 370 V in a solution of 2% citric acid. The process creates a network of small pores at the bottom of the larger pores, which accelerates the oxide barrier etching relatively to the pore walls of the PAA membranes, when etched in a solution of phosphoric acid. The oxide barrier etching is confirmed by observation of PAA membranes using scanning electron microscopy, revealing the formation of the small pores and the preferential etching of the bottom of the pores rather than the pore walls. The proposed method, which leads to a better control over the fabrication of nanoporous templates, can be adapted to oxide barriers of different PAA membranes formed at different voltages and in different acids.

Numerical models for computing the effective critical current of devices made of high-temperature superconducting tapes require the knowledge of the J c (B,θ) dependence, i.e., of the way the critical current density J c depends on the magnetic flux density B and its orientation θ with respect to the tape. In this paper, we present a numerical model based on the critical state with angular field dependence of J c to extract the J c (B,θ) relation from experimental data. The model takes into account the self-field created by the tape, which gives an important contribution when the field applied in the experiments is low. The same model can be also used to compute the effective critical current of devices composed of electromagnetically interacting tapes. In this paper, we consider three examples: two differently current-rated Roebel cables composed of ten strands from REBCO coated conductors and a power cable prototype composed of 22 Bi-2223 tapes. The critical currents computed with the numerical model show good agreement with the measured ones. The simulations reveal also that several parameter sets in J c (B,θ) give an equally good representation of the experimental characterization of the tapes and that the measured I c values of cables are subjected to the influence of experimental conditions, such as I c degradation due to the manufacturing and assembling process and nonuniformity of the tape properties. These two aspects make the determination of a very precise J c (B,θ) expression probably unnecessary, as long as that expression is able to reproduce the main features of the observed angular dependence. The easiness of use of this model, which can be straightforwardly implemented in finite-element programs able to solve static electromagnetic problems, is very attractive both for researchers and device manufactures who want to characterize superconducting tapes and calculate the effective critical current of superconducting devices.

Today MgB2 superconducting wires can be manufactured in long lengths at low cost, which makes this material a good candidate for large scale applications. However, because of its relatively low critical temperature (less than 40 K), it is necessary to operate MgB2 devices in a liquid or gaseous helium environment. In this context, losses in the cryogenic environment must be rigorously minimized, otherwise the use of a superconductor is not worthy. An accurate estimation of the losses at the design stage is therefore mandatory in order to allow determining the device architecture that minimizes the losses. In this paper, we present a complete a 3D finite element model of a 36-filament MgB2 wire based on the architecture of the Italian manufacturer Colombus. In order for the model to be as accurate as possible, we made a substantial effort to characterize all constitutive materials of the wire, namely the E–J characteristics of the MgB2 filaments and the electric and magnetic properties (B−H curves) of nickel and monel, which are the two major non-superconducting components of the wire. All properties were characterized as a function of temperature and magnetic field. Limitations of the characterization and of the model are discussed, in particular the difficulty to extract the maximum relative permeability of nickel and monel from the experimental data, as well as the lack of a thin conductive layer model in the 3D finite element method, which prevents us from taking into account the resistive barriers around the MgB2 filaments in the matrix. Two examples of numerical simulations are provided to illustrate the capabilities of the model in its current state.

Fluorescent microthermographic imaging, a method using rare-earth fluorescent coatings with temperature dependent light emission, was used for quench investigation in high temperature superconductors (HTS). A fluorophore was embedded in a polymer matrix and used as a coating on top of an HTS tape, while being excited with UV light and recorded with a high-speed camera. Simultaneously, the tape was pulsed with high amplitude, short duration DC current, and brought to quench with the help of a localised defect. The Joule heating during a quench influences the fluorescent light intensity emitted from the coating, and by recording the local variations in this intensity over time, the heating of the tape can be visualised and the developed temperatures can be calculated. In this paper, the fluorophore europium tris[3-(trifluoromethylhydroxymethylene)-(+)-camphorate] (EuTFC) provided sufficient temperature sensitivity and a usable temperature range from 77–260 K. With the help of 2500 image captures per second, the normal zone development was imaged in a 20 μm copper stabilised HTS tape held in a liquid nitrogen bath, and using a calibration curve, the temperatures reached during the quench have been calculated.