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In several cases, substations have become incapable of supporting faults due to short circuit levels increasing. 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 paper presents the impacts of the different kinds of short circuits in the SIC-SFCL device. To reproduce various types of faults, the SIC-SFCL is modeled in a 3D framework considering both ferromagnetic and superconducting non-linearities. Moreover, the proposed 3D FEM 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-biased superconducting coil's normalized current density and the iron cores' magnetic flux density are examined in light of the different short circuits. The simulations are compared with measurements in a bench prototype, showing a maximum error of 16.5~%. Furthermore, different short circuit types were investigated and compared, which is possible only using a 3D model. The highest limitation occurred in the phase-to-phase short circuit case. In the DC circuit of the SIC-SFCL, the highest transient period has happened in the single-phase short circuit. At last, the phase-to-phase fault presented the highest DC current during the transient.

Green Fields are characterized by many static and dynamic uncertainties that mainly impact the decision-making of the full field development phase. The objective of this work is to provide a workflow that considers all the complexities related to all uncertainties, static and dynamic, associated with tight green fields and how these uncertainties are parameterized with the integration of well hydraulic fractures. Uncertainty and optimization workflow has been adopted in a commercial geo-modeler to consider all the associated uncertainties. Structural uncertainty is parameterized using an in-house plug-in inside the geo-modeler tooldeveloped to apply the structural deformation using the concept of elastic gridding. Hydraulic Fractures are modeled using Local Grid Refinements (LGR) created by a plug-in inside the geo-modeler. A sensitivity analysis has been performed to consider the static uncertainty parameters that impact Hydrocarbon volume in place and dynamic uncertainty parameters that impact cumulative hydrocarbon production, including the LGR (extension and permeability). Statistical maps on 100 different geological realizations calculated on mobile hydrocarbon column and permeability thickness showed the optimum locations of the infilling wells to consider the spatial and vertical variability. A representative case (P50) on volumes in place is chosen to define the suited development strategy for the full field development phase. Due to the complexity of the field, a creaming curve approach has been adopted for each level to consider the optimum number of drainage points needed. A final completion scheme with an optimum number of wells and their hydraulic fracture stages is defined. Sensitivity Analysis showed that LGR parameters have a considerable impact on the cumulative hydrocarbon production, and to overcome the limitation of the LGR plug-in, which does not allow to change the completion for every realization, a dedicated study has been performed to define the optimum extension of perforations needed to consider the structural and petrophysical changes over realizations. Three representative cases (P10 – P50 – P90) on the cumulative hydrocarbon production were selected to represent an uncertainty range of the field volumes and production in the next step of integrated asset modeling. An automatic strategy and related implementation have been developed for wells with LGR simulation to adapt well completions in the context of hydraulic fracturing and uncertainty quantification.

The estimation and measurement of AC losses in coils based on high-temperature superconductors (HTS) are relevant aspects of HTS applications. They influence the cooling power requirement, operating temperature and efficiency, which can be decisive in the construction and implementation of superconducting equipment, such as superconducting electrical machines. The measurement of losses due to AC transport current (without external magnetic field) is not an easy task. Several efforts have been made to measure these AC transport losses in superconducting coils with a calorimetric approach by trying to minimize the influence of the environment, improve the accuracy and ensure the reproducibility of the results. This work presents the design and construction of a setup to measure transport AC losses in high-temperature superconducting coils based on a calorimetric approach (boil-off method). The evaporated cryogen (nitrogen) related to the dissipation of energy is collected by using a 3D printed bubble collector that guides the gas into a flow sensor. A box-inside-a-box approach is used to surround the measurement chamber with a cryogenic environment. This approach allows re-directing the heat transfer from the surroundings into an intermediate zone (space between external and internal box). Since this intermediate zone operates under cryogenic temperatures, the noise and the heat transfer in the internal part of the setup are reduced. A statistical analysis of the results based on a standard load cycle, average value, and standard deviation calculations allows assessing the variability in the measurements and expressing the results as average value and uncertainty range. The calibration and reproducibility of the measurements are verified with a set of resistors under different conditions and during different weeks. Finally, the AC transport losses in a racetrack coil for an electrical machine application are measured and compared with 3D simulation results based on the homogenization of the T-A formulation.

Funding Information: Financial support was provided by the Swiss National Science Foundation (Grant No. 200021_184940). Funding Information: Networking support provided by the European Cooperation in Science and Technology, COST Action CA19108 (Hi-SCALE) is acknowledged. Funding Information: Supported by Fundação para a Ciência e a Tecnologia, Portugal, with reference UIDB/00066/2020. Funding Information: A part of this work was supported by the Russian National Technology Initiative Foundation (Grant ID 0000000007418QR20002). Funding Information: The research was also supported by the European Synchrotron Radiation Facility (Grant No. MA-2767). Funding Information: This work was supported in part by the New Zealand Ministry of Business, Innovation and Employment (MBIE) by the Strategic Science Investment Fund ‘‘Advanced Energy Technology Platforms’’ under Contract RTVU2004. Funding Information: Y Wang acknowledges support from the National Science Foundation (NSF) Award DMR-2132338. R P Camata and C-C Chen are supported by the FTPP Program funded by NSF EPSCoR RII Track-1 Cooperative Agreement OIA-2148653. C-C Chen also acknowledges support from the NSF Award DMR-2142801. Publisher Copyright: © 2023 The Author(s). Published by IOP Publishing Ltd. This paper presents a roadmap to the application of AI techniques and big data (BD) for different modelling, design, monitoring, manufacturing and operation purposes of different superconducting applications. To help superconductivity researchers, engineers, and manufacturers understand the viability of using AI and BD techniques as future solutions for challenges in superconductivity, a series of short articles are presented to outline some of the potential applications and solutions. These potential futuristic routes and their materials/technologies are considered for a 10-20 yr time-frame. publishersversion published

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.

This article presents a numerical model based on the definition of the scalar and vector potentials to calculate the ac losses generated in a high-temperature superconductor coated conductor tape by an ac transport current and by an ac external magnetic field applied with a generic orientation. The material characteristics of the different layers of a reference tape are included in the model equations, which allow analyzing the differences between a model including only the superconducting layer or all layers of the coated conductor. The model is applied to study the dependence of ac losses on the amplitude of the transport current and magnetic field (applied individually or combined) and their frequency. The numerical results are compared with analytical formulations, with a second numerical model based on the H -formulation, and with experimental results. The conditions at which the contribution of the nonsuperconducting layers to the total ac losses of the tape become relevant are analyzed. In particular, the dependence of losses on the frequency of the ac external magnetic field applied at different orientations, is investigated. The current density distribution computed on the conductor cross-section is used to explain the trend of the calculated losses.

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.

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.

With recent advances in second-generation high temperature superconductors (2G HTS) and cable technologies, various numerical models based on finite-element method (FEM) have been proposed to help interpret measured AC loss and assist cable design. The T-A formulation, implemented in COMSOL, shows great potential for reducing the overall computation costs. In this paper, the performance of the T-A formulation for calculating the AC loss of coated superconductors and cables were assessed and compared against the widely accepted H formulation, with benchmark model of a single REBCO tape in 2D/3D and a 14-strand Roebel cable. Evaluation and comparison on key metrics including the computation time, the number of degrees of freedom and the numerical accuracy were presented, which could provide a reference for researchers in applying the T-A formulation for AC loss calculation.

Screening currents have long been known to impact the stress state in tape-wound superconducting coils. In recent years the advent of REBCO tape has led to the development of tape-wound coils by a number of organizations. While several groups have been computing screening currents and ac losses in REBCO tape in a variety of applications for several years, little has been published about the stress due to the screening currents. This problem is challenging due to the need to analyze thousands of REBCO turns which are not bonded together. The T-A formulation of Maxwell's equations employing a homogenization technique enables efficient estimation of the current distribution while structural calculations employing contact elements allow conservative estimation of stresses. Computational results are compared with observed degradation in a test coil. Future coil designs that include the effects of screening current strains are proposed.

The 32 T all-superconducting magnet of the National High Magnetic Field Laboratory (NHMFL) was successfully tested in December 2017 and it is expected to be soon available for users. This all-superconducting magnet, comprised of a high-temperature superconducting (HTS) insert and a low-temperature superconducting (LTS) outsert, is the first superconducting magnet reaching more than 30 T. One of the challenges facing this new magnet technology is the estimation of the screening currents, and the corresponding hysteresis losses in the two HTS coils. These coils are made of more than 20,000 turns of insulated REBCO conductor connected in series. The modelling of such system represents a significant challenge due to the huge computational load imposed by the size of the system. Up to now, only medium size magnets (made of units of thousands of turns/tapes) have been successfully modelled with methods based on the well-known H formulation of the Maxwell's equations. In the present work, a new model based on the T-A formulation and a homogeneous technique is proposed. This new approach greatly reduces the computational load and allows performing real-time simulations of large-scale HTS magnets on personal computers.

Numerical models based on the finite-element method (FEM) are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the $T$-$A$ formulation for modeling HTS coils in 2D with different coupling scenarios between the turns. First we consider a racetrack coil wound from one piece of superconducting tape. Then we consider a coil obtained by winding a cable composed of different HTS tapes. In the latter case, the tape turns are either electrically connected along their entire length or just at the two ends of the coil: in the model, these two different types of electrical connection are implemented with the help of the electrical circuit module. The current density distributions and the AC losses of the coils in the different coupling scenarios are compared and discussed. The limits of applicability of the presented approach are pointed out. The model is developed for the straight section of racetrack coils, but can be easily adapted to axisymmetric geometries.

The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing improvements, and computing quantities that are not easy to calculate with an analytical approach. For instance, the estimation of losses in HTS is fundamental during the design stage since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D finite element analysis is used to calculate AC losses in HTS, due to the lack of analytical solutions that can accurately represent complex operating conditions such as AC transport current and AC external applied magnetic field in coils. These 2D models are usually a representation of an infinitely long arrangement. Therefore, they cannot be used to analyze end effects and complex 3D configurations. In this publication, we use the homogenization of the T-A formulation in 3D for the analysis of superconducting coils with complex geometries where a 2D approach can not provide accurate analyses and verification of assumptions. The modeling methodology allows an easier implementation in commercial software (COMSOL Multiphysics) in comparison with the currently available 3D H homogenization, despite the complexity of the geometry. This methodology is first validated with a racetrack coil (benchmark case) by comparing the results with the well-established H formulation. Then, the electromagnetic behavior of coils with more complex geometries is analyzed., arXiv admin note: text overlap with arXiv:2103.06590

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.

Oral presentation at the Applied Superconductivity Conference 2020

Numerical simulation is an effective tool for predicting the electromagnetic behavior of superconductors. Recently, a finite element method-based model coupling the T-A formulation with an electrical circuit has been proposed: the model presents the superconducting constituent as a global voltage parameter in the electrical circuit. This allows assessing the overall behavior of complex high-temperature superconductor (HTS) systems involving multiple power items, while keeping a high degree of precision on the presentation of local effects. In this work, the applicability of this model has been extended to large-scale HTS applications with hundreds or thousands of tapes by referring to two widely recognized methodologies, multi-scale and homogenization, to improve the computation efficiency. Based on the two approaches, three different models were developed and their effectiveness was assessed using the case study of a 1000 turn cylindrical HTS coil charged by a DC voltage source. The comparison of the calculated global circuit parameters, local field distributions, losses, and computation time proves that the computation efficiency can be improved with respect to a model simulating all HTS tapes, without compromising accuracy. The results indicate that the developed models can therefore be efficient tools to design and optimize large-scale HTS devices used in electrical machines and power grids. It is also found that the inductance of an HTS coil is varied according to the transport current and can be even higher than that of a normal conductor coil with the same geometry. We attribute this result to the superconductor’s non-uniform current distribution and relaxation effect during the dynamic process.

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.

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.

The growing interest in modeling superconductors has led to the development of increasingly effective numerical models and software. Alongside this interest, the question of how to teach and to explain the operation of superconductors to students has arisen. Ecole Polytechnique Federale de Lausanne (EPFL) and Karlsruhe Institute of Technology (KIT) have created a series of web applications based on COMSOL Multiphysics that are publicly accessible through a web server called AURORA. Users can change the values of several parameters of the applications and observe the influence on the results. This article describes part of the currently available applications and some exercises that can be done with them.

Too high loss levels can severely limit the efficiency and the safe operation of several high-temperature superconductor (HTS) AC applications. A reliable estimation of AC losses, which includes the observed field-dependence of the superconductor’s critical current density on the magnetic field, is therefore paramount. In this contribution, we use numerical simulations to evaluate the AC losses of HTS coated conductors in a variety of working scenarios: individual wires carrying AC transport current and/or subjected to AC magnetic fields, and wire assemblies like stacks and arrays carrying AC transport current. Numerical results are compared to the corresponding analytical models and to experimental results. This work presents some general guidelines regarding the extent to which the dependence of the critical current density J c on the magnetic flux density B modifies the AC loss characteristics with respect to a constant-J c model based on the superconductor’s self-field critical current.

Invited talk at the International Symposium of Superconductivity 2020, Tsukuba, Japan

Second-generation high-temperature superconducting (2G HTS) tapes are considered to be the main candidates for the development of future ultra-high DC magnetic field magnets. In such applications, the usability of the HTS magnets can be strongly impaired by large screening currents developed in the flat strip of the tapes. These currents lead to the generation of a screening current-induced field (SCIF) that can deteriorate the performance by affecting the stability and the homogeneity of the magnetic field. Besides the SCIF, there is also the likely mechanical degradation of the tapes under the action of large Lorentz forces. The mechanical degradation and the presence of large screening currents intertwine to affect the reliable operation of 2G HTS magnets. To study the combined issues, an electromagneto-mechanical model based on tensile mechanical characterization of short samples was built to simulate the coupled electromagnetic and mechanical behaviors of insert magnets made of 2G HTS tapes under very high magnetic field. The coupling is carried out by considering the dependence of the n index and the critical current density J c on the local relative deformation in addition to the magnetic flux density. The case study is the Little Big Coil (LBC, version 3) which broke the world record of the strongest continuous magnetic field achieved to this date. An analysis of the electromagneto-mechanical behavior of the LBC is conducted on the basis of information extracted from the literature to show that the proposed model can assess the current magnitude at which the insert magnet quenched. Additionally, it is shown that the model can also provide some insights on the impact of the mechanical degradation of the tape on the SCIF hysteresis loop. The studies are conducted on the original LBC and on versions that include additional modifications such as harnessing and co-winding with rigid metallic tapes. These modifications are employed to limit the mechanical degradation of the HTS insert magnet under ultra-high magnetic field. They are expected to deliver an extra safety margin to 2G HTS insert magnets.

In recent years, the T-A formulation has emerged as an efficient approach for modelling the electromagnetic behaviour of high-temperature superconductor (HTS) tapes in the form of coated conductors (CCs). HTS CCs are characterized by an extremely large width-to-thickness ratio of the superconducting layer, normally up to 1000 ∼ 6000, which in general leads to a very large number of degrees of freedom. The T-A formulation considers the superconducting layer to be infinitely thin. The magnetic vector potential A is used to calculate the magnetic field distribution in all simulated domains. The current vector potential T is used to calculate the current density in the superconducting layer, which is a material simulated with a highly nonlinear power-law resistivity. This article presents a review of the T-A formulation. First, the governing equations are described in detail for different cases (2D and 3D, cartesian and cylindrical coordinates). Then, the literature on the implementation of T-A formulation for simulating applications ranging from simple tape assemblies to high field magnets is reviewed. Advantages and disadvantages of this approach are also discussed.

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. 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 (DOFs), tolerance settings and the approximate time taken per cycle for each model., 22 pages, 7 figures, 2 tables

The European Union-funded Advanced Superconducting Motor Experimental Demonstrator (ASuMED) project started in May 2017 with the purpose of demonstrating the benefits of a new, fully superconducting motor for reaching the targets established by the Flightpath 2050 plan. The project aims at a motor power density of 20kW kg−1 using a high-temperature superconducting (HTS) stator. The rotor will use HTS stacks operating like permanent magnets. A highly efficient cryostat for the motor combined with an integrated cryogenic cooling system and associated power converter will be used. This article provides a general overview of the prototype that is currently being assembled and that will be tested soon.

Stacks of superconducting tapes can trap much higher magnetic fields than conventional magnets. This makes them very promising for motors and generators. However, ripple magnetic fields in these machines present a cross-field component that demagnetizes the stacks. At present, there is no quantitative agreement between measurements and modeling of cross-field demagnetization, mainly due to the need of a 3D model that takes the end effects and real micron-thick superconducting layer into account. This article presents 3D modeling and measurements of cross-field demagnetization in stacks of up to 5 tapes and initial magnetization modeling of stacks of up to 15 tapes. 3D modeling of the cross-field demagnetization explicitly shows that the critical current density, $J_c$, in the direction perpendicular to the tape surface does not play a role in cross-field demagnetization. When taking the measured anisotropic magnetic field dependence of $J_c$ into account, 3D calculations agree with measurements with less than 4 % deviation, while the error of 2D modeling is much higher. Then, our 3D numerical methods can realistically predict cross-field demagnetization. Due to the force-free configuration of part of the current density, J, in the stack, better agreement with experiments will probably require measuring the Jc anisotropy for the whole solid angle range, including $J$ parallel to the magnetic field., Comment: 36 pages, 20 figures

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.

The emergence of second generation (2G) high-temperature superconductor (HTS) tapes has favored the development of HTS magnets for their applications in areas such as NMR, MRI and high field magnets. The screening current-induced field and the field drift are two major problems hindering the use of HTS tapes in the mentioned areas. Both problems are caused by the screening current, then it is necessary to have a modeling strategy capable to estimate such phenomena. Thus far, the H formulation has been a widely used approach to model medium-size systems (hundreds of tapes). However, its application to large-scale systems is still impaired by excessive computation times and memory requirements. Homogenization and multi-scaling strategies have been successfully implemented to increase the computational efficiency. In this contribution, we show that using the homogenization technique with the recently developed T-A formulation allows reducing the computation time and the amount of memory up to the point that realtime simulations of slow ramping cycles of large-scale systems are possible. At the same time, the T-A homogeneous model provides enough resolution to investigate the screening current using numerical simulations.

The low core losses and high yield strength of amorphous materials are attractive properties for ultra-high-speed rotor applications. This paper proposes an innovative interior permanent-magnet synchronous rotor for ultra-high-speed motors, which takes full advantage of those properties and eliminates the need for sleeves. In order to study the feasibility of the proposed rotor, the electromagnetic properties of the amorphous core are first measured and the challenges for producing such rotors are subsequently discussed. Then, by using numerical methods, the electromagnetic, mechanical, and thermal performances of an example motor with an amorphous rotor core are evaluated and compared to those of a motor with a silicon steel rotor core. Through experimental characterization of the material and multiphysics numerical modeling of an example motor, it is shown that the amorphous material has great potential for producing high power density ultra-high-speed motors.

(RE)BCO commercial coated superconductors have been gaining an increasing interest due to the potentialities of using them in high-field magnets. The leading project is the 32 T user magnet recently tested successfully at full field at the National High Magnetic Field Laboratory (NHMFL), Tallahasee, FL, USA. This state-of-the-art high-field all-superconducting magnet, bath-cooled at 4.2 K, is comprised of a two-nested-coil insert pancake-wound with (RE)BCO tapes supplied by SuperPower Inc. and a multicoil low temperature superconductors (LTS) outsert. To ensure the magnet's reliable operation, it is important to estimate the hysteresis losses. Such an estimate will allow implementing safe operational procedures to avoid premature quenching and, in the worst case scenario, insert failure. The insert coils have thousands of turns with notable variations in the critical current. Therefore, estimating the losses in such a large superconducting magnet presents a significant challenge. We propose here a new approach relying on a multiscale scheme to achieve a high computational efficiency. This new method is flexible enough to simulate different sections of the entire insert with the right level of detail while providing a larger computational speed than other approaches using the finite element method. Estimates of the hysteresis losses in the insert coils for a ramping operation sequence are presented.

A fully superconducting wind generator employs superconductors in stator and rotor to enable high torque density and low weight, that is, enable an ultra-light electric machine for wind application. However, the level of the AC loss of the stator armature coils is a critical issue, which lacks investigations in the design of the fully superconducting generators. In this paper, an in-house model was developed to analyze the potential of a fully superconducting generator by integrating the electromagnetic design with the AC loss estimation. The electromagnetic model was made through analytical equations, which take into consideration the geometry, the magnetic properties of iron, and the nonlinear E–J constitutive law of superconductors. Since the permeability of iron materials and the critical current of the superconductors depend on the magnetic field, an iteration process was proposed to find their operating points for every electromagnetic design. The AC loss estimation was carried out through finite element software based on the T–A formulation of Maxwell’s equations instead of analytical equations, due to the complexity of magnetic fields, currents and rotation. The results demonstrate that the design approach is viable and efficient, and is therefore useful for the preliminary design of the generator. In addition, it is found that smaller tape width, larger distance between the superconducting coils in the same slot, smaller coil number in one slot and lower working temperature can reduce the AC loss of the stator coils, but the reduction of the AC loss needs careful design to achieve an optimum solution.