arXiv subjects

Francesco Grilli

Publications and source records attributed to Francesco Grilli.

At least 19 recordsLinked to original sources

arXiv2026

Current patterns and loss contributions in CORT cables carrying AC current

Conductor-on-round-tube (CORT) cables are a potential solution for carrying AC power in a small cross-section. Due to the geometry of the cable and the helical arrangement of the coated conductors (CC), the current follows a non-trivial pattern inside each CC. For instance, for the case of a single-layer cable, the current flow is mostly axial along the outer face of the CCs and mostly azimuthal along their inner face. Such a current distribution, known as the Garber current pattern, affects the transport AC losses. In numerical models, commonly adopted simplifications are either based on straight conductors or infinitely thin CCs. Such approaches neglect the Garber current pattern and thus misrepresent both the detailed current flow within the CC and the resulting 3D distribution of the fields. In this work, the detailed 3D current distribution in the CCs is investigated in a one-layer CORT cable, as a function of the cable geometrical parameters such as the conductor thickness, the pitch angle, and the gap between adjacent CCs. In particular, the impact of the Garber current pattern is studied on the two largest contributions to the AC losses, namely the surface losses (associated with the penetration of the component of the magnetic field parallel to the wide faces of the superconducting layer) and the edge losses (associated with the penetration of the perpendicular component of the magnetic field occurring in the vicinity of the gaps between the CCs). The detailed distribution of the currents in the CCs is examined and its relationship with the different AC loss mechanisms is established. This study is carried out by means of an effective 2D model that uses a system of coordinates conforming with the helical structure of the cable.

cond-mat.supr-con↗

arXiv2023

The Garber Current Pattern: An Additional Contribution to AC Losses in Helical HTS Cables?

Conductors made of high-temperature (HTS) wires helically wound in one or more layers on round tubes (CORT) are compact, flexible, and can carry a large amount of current. Although these conductors were initially developed for DC applications, e.g. in magnets, it is worth considering their use for AC, e.g. in underground cables for medium voltage grids and with currents in the kA-range. In these cases, the major challenge is reducing AC losses. In contrast to a straight superconducting wire, in a helical arrangement, due to superconducting shielding, the current does not follow the direction of the wires, but takes a non-trivial zig-zag path within the individual HTS wires (Garber pattern). This includes current components across the thickness of the superconducting layers, so that the often used thin-shell approximation does not hold. In this contribution, we studied a one-layer three-wire CORT by means of fully three-dimensional simulations, based on the H-formulation of Maxwell's equations implemented in the commercial software package COMSOL Multiphysics. As a result of our simulations, the peculiar current profiles were confirmed. In addition, the influence of current, pitch angle, and frequency on the AC losses was studied. We found an optimum for the pitch angle and that the current profiles strongly depend on frequency.

cond-mat.supr-con↗

arXiv2022

3D homogenization of the T-A formulation for the analysis of coils with complex 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.

cond-mat.supr-con↗

arXiv2022

2D Modeling of HTS Coils with $T$-$A$ Formulation: How to Handle Different Coupling Scenarios

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.

cond-mat.supr-con↗

arXiv2021

The eta-beta model model: an alternative to the power-law model for numerical simulations of REBCO tapes

When modeling superconducting devices based on REBCO tapes andworking near or above the critical current value (i.e. I> Ic), the power-law model is not always accurate. In our previous works, we proposed the overcritical current model, based on a combination of fast pulsed current measurements and finite elementan alysis. The overcritical current model was provided in the form of look-up tables and was validated experimentally. We showed that the overcritical current model could better reproduce experimental measurements than the power-law model, and that the power-law model predicts a faster quench than the overcritical current model. In this contribution, we propose the eta-beta model, a mathematical expression to model analytically the overcritical current model, based on measurements performed between 77 K and 90 K in self-field conditions. The proposed model is verified by comparing DC fault measurements with the results of numerical simulations using the eta-beta model to represent the electrical resistivity of the superconducting layer of REBCO tapes.

cond-mat.supr-con↗

arXiv2021

Efficient modeling of high temperature superconductors surrounded by magnetic components using a reduced H-$\phi$ formulation

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 non-conducting 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 work, 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.

cond-mat.supr-con↗

arXiv2021

3D Homogenized T-A Formulation for Modeling HTS Coils

The estimation of losses in high-temperature superconductors (HTS) is fundamental during the design of superconducting devices 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 T-A homogenization in 3D for the analysis of superconducting coils. This allows simulating complex geometries such as racetrack coils. We show that this approach has lower computation time than the currently available 3D homogenization of the H formulation. The approach is first validated against measurements and 2D axisymmetric solutions. Then, it is used to estimate losses and study the electromagnetic behavior of a racetrack coil.

cond-mat.supr-con↗

arXiv2021

Influence of Coil Position on AC Losses of Stator Superconducting Windings of a Synchronous Machine for a 10 MW Wind Turbine

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 publication, we focus on the dissipation in the stator superconducting coils of a synchronous machine for a wind turbine application. The T-A formulation of Maxwell's equations is used in a 2D finite element model to analyse the behaviour 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.

cond-mat.supr-con↗

arXiv2020

Implementation of the H-$\phi$ formulation in COMSOL Multiphysics for simulating the magnetization of bulk superconductors and comparison with the H-formulation

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.

physics.comp-ph↗

arXiv2020

A new benchmark problem for electromagnetic modelling of superconductors: the high-Tc superconducting dynamo

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.

physics.comp-ph↗

arXiv2020

Electromagnetic modeling of large-scale high-temperature superconductor systems

The development of the high-temperature superconductors (HTS) conductors has allowed the development of diverse superconductor devices. Some of these devises, like the power generators and high-field magnets, are classified as large-scale HTS systems, because they are made of hundreds or thousands of turns. Mathematical models are required to address the analysis of these kind of systems. This task cannot be done by means of analytical models, because they are limited to the analysis of simple assemblies. The finite-element models using the H formulation have been extensively used during the last years. Nevertheless, the use of H formulation models to analyze large-scale systems is hindered by the excessive computational load. The recently proposed T-A formulation models have allowed building more efficient models for systems made of HTS tapes. Additionally, the homogenization and multi-scaling methods have been successfully applied in conjunction with the H and T-A formulations, these simplification methods allows reducing the required computational resources. In this article a new simplification method, called densification, is proposed. The strategies emerging from the combined use of the formulations and the simplification methods already mentioned are extensively explored, and the comprehensive validation and comparison of all the resulting strategies is presented.

physics.app-ph↗

arXiv2020

Electromagnetic Modeling of Superconductors with Commercial Software: Possibilities with Two Vector Potential-Based Formulations

In recent years, the $H$ formulation of Maxwell's equation 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 those situations, here we consider two published approaches based on the magnetic vector potential: the $T$-$A$ formulation of Maxwell's equations (with power-law resistivity) and Campbell's implementation of the critical state model. In this contribution, 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 revise Campbell's model and discuss it 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.

cond-mat.supr-con↗

arXiv2019

Non-twisted stacks of coated conductors for DC magnets: analysis of inductance and AC losses

In the last 10-15 years, the most common strategy in the development of High Temperature Superconducting (HTS) cable for magnets has been to imitate Low Temperature Superconducting (LTS) cable designs. However, requirements for LTS materials are not valid for HTS materials, which are extremely stable. For example, non-twisted multifilamentary Bi-2223 tapes have been successfully used in several magnets. This paper review stability and analyse inductance and AC losses in non-twisted stack of HTS tapes. Numerical calculations show that twisting has negligible effect on inductance variations in a stack of tapes. Regarding AC losses, any magnet built with coated conductors have larger losses than LTS ones, because of the aspect ratio and large width of the tape. If a wide tape is replaced by a non-twisted stack of narrow tapes, losses and residual magnetisation could be reduced. In contrast with multifilamentary wires, twisting a stack of tapes reduces losses only marginally. Therefore, cables composed of non-twisted stack could be designed to have losses comparable to the one of twisted stack concepts. Few examples of large cables for fusion applications are discussed. Designs based on non-twisted stacks can be simpler, more robust and cost effective than twisted ones.

cond-mat.supr-con↗

arXiv2019

Cross-field demagnetization of stacks of tapes: 3D modelling and measurements

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.

physics.app-ph↗

arXiv2019

Screening Current-Induced Field and Field Drift Study in HTS coils using T-A homogenous model

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 the most successful and 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 real-time simulations of slow ramping cycles of large-scale systems are possible. The T-A homogeneous model also allows systematically investigating the screening current using numerical simulations.

physics.app-ph↗

arXiv2019

Review of the AC Loss Computation for HTS using the H-formulation

This article presents a review of the finite element method (FEM) model based on the $H$ formulation of Maxwell's equations used to calculate AC losses in high temperature superconductor (HTS) tapes, cables and windings for different applications. This model, which uses the components of the magnetic field as state variables, has been gaining a great popularity and has been in use in tens of research groups around the world. This contribution first reviews the equations on which the model is based and their implementation in finite element method programs for different cases, such 2D longitudinal and axis-symmetric geometries, 3D geometries. Modeling strategies to tackle large number of HTS tapes, such as multi-scale and homogenization methods, are also introduced. Then, the second part of the article reviews the applications for which the $H$ formulations has been used to calculate AC losses, ranging from individual tapes, to complex cables and large magnet windings. Afterwards, a section is dedicated to the discussion of the $H$ formulation in terms of computational efficiency and easiness of implementation. Its pros and cons are listed. Finally, the last section draws the main conclusions.

cond-mat.supr-con↗

arXiv2019

T-A Formulation to Model Electrical Machines with HTS Coated Conductor Coils

Modelling high temperature superconductor (HTS) motors remains challenging mainly due to the high aspect ratio of these conductors but also because of the properties of the magnetic materials. This paper presents a 2D time dependent model to assess the AC losses of superconducting motors based on the new T-A formulation, which by using Finite Element Methods (FEM), allows its implementation in commercial software. The T-A formulation computes the magnetic flux density with different Maxwell's equations depending on the areas of the motor and makes it possible to use the thin strip approximation i.e. the HTS tapes are modelled as infinitely thin lines. The model is then expected to tackle the high aspect ratio of the HTS as well as decreasing both the mesh complexity and the computing time. The first objective of the paper is to validate the method in 2D by evaluating the AC losses of a specific synchronous motor called SUTOR; the computed results are compared with good agreements to those assessed with the MEMEP method, already validated. In a second part, the same losses are computed, taking into account the anisotropy of Jc with the implementation of a data set based on experimentally measured Ic at 65 K and 77 K.

cond-mat.supr-con↗

arXiv2018

AC loss modelling in superconducting coils and motors with parallel tapes as conductor

Many superconducting power applications contain REBCO coils. Superconducting motors are very interesting for mobile applications like aviation, thanks to their high power per unit weight. In order to reduce the inductance, multi-tape conductors are often used in windings but parallel tapes present coupling AC loss. In this article, we analyze the AC loss of single coils and a full stator of a motor made of windings of parallel tapes, taking several coupling situations into account. Our computer modeling method combines self-programmed and commercial finite-element methods to calculate the current density and AC loss. We found that isolating the tapes along the length provides almost the same AC loss reduction as that obtained by full transposition. This reveals that there are still many unexploited strategies to reduce the AC loss in multi-tape conductors.

cond-mat.supr-con↗