Numerical Modeling of AC Loss in HTS Coated Conductors and Roebel Cable Using T-A Formulation and Comparison With H Formulation

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.

[1]  U. Trociewitz,et al.  Practical fit functions for transport critical current versus field magnitude and angle data from (RE)BCO coated conductors at fixed low temperatures and in high magnetic fields , 2015 .

[2]  Min Zhang,et al.  3D modeling of high-Tc superconductors by finite element software , 2011 .

[3]  W. Yuan,et al.  Quench behavior of high-temperature superconductor (RE)Ba2Cu3Ox CORC cable , 2019, Journal of Physics D: Applied Physics.

[4]  H. Kate,et al.  Introduction of CORC® wires: highly flexible, round high-temperature superconducting wires for magnet and power transmission applications , 2017 .

[5]  F. Grilli,et al.  Anisotropic monoblock model for computing AC loss in partially coupled Roebel cables , 2020, Superconductor Science and Technology.

[6]  Francesco Grilli,et al.  Review of the AC loss computation for HTS using H formulation , 2019, Superconductor Science and Technology.

[7]  F. Grilli,et al.  Simple and Fast Method for Computing Induced Currents in Superconductors Using Freely Available Solvers for Ordinary Differential Equations , 2019, IEEE Transactions on Applied Superconductivity.

[8]  D. Larbalestier,et al.  A CORC® cable insert solenoid: the first high-temperature superconducting insert magnet tested at currents exceeding 4 kA in 14 T background magnetic field , 2020, Superconductor Science and Technology.

[10]  Francesco Grilli,et al.  Simulation of ac loss in Roebel coated conductor cables , 2010 .

[11]  T. A. Coombs,et al.  Comparison of first‐ and second‐order 2D finite element models for calculating AC loss in high temperature superconductor coated conductors , 2011 .

[12]  Peng Song,et al.  Numerical Investigation of the Coupling Effect in CORC Cable With Striated Strands , 2020, IEEE Transactions on Applied Superconductivity.

[13]  T. A. Coombs,et al.  Numerical solution of critical state in superconductivity by finite element software , 2006 .

[14]  Luciano Martini,et al.  Development of an edge-element model for AC loss computation of high-temperature superconductors , 2006 .

[15]  Luciano Martini,et al.  Edge and top/bottom losses in non-inductive coated conductor coils with small separation between tapes , 2010 .

[16]  John R. Clem.  Field and current distributions and ac losses in a bifilar stack of superconducting strips , 2008 .

[17]  Naoyuki Amemiya,et al.  Corrigendum: Three-dimensional model for numerical electromagnetic field analyses of coated superconductors and its application to Roebel cables , 2012 .

[18]  F. Grilli,et al.  Numerical Considerations About Using Finite-Element Methods to Compute AC Losses in HTS , 2008, IEEE Transactions on Applied Superconductivity.

[19]  Francesco Grilli,et al.  Numerical Modeling of HTS Applications , 2016, IEEE Transactions on Applied Superconductivity.

[20]  J. Kovac,et al.  AC loss in ReBCO pancake coils and stacks of them: modelling and measurement , 2011, 1109.2526.

[21]  Enric Pardo,et al.  Electromagnetic modelling of superconductors with a smooth current–voltage relation: variational principle and coils from a few turns to large magnets , 2014, 1410.0772.

[22]  Michal Vojenciak,et al.  Numerical Study on Magnetization Characteristics of Superconducting Conductor on Round Core Cables , 2017, IEEE Transactions on Applied Superconductivity.

[23]  Wilfried Goldacker,et al.  Transport and magnetization ac losses of ROEBEL assembled coated conductor cables: measurements and calculations , 2009 .

[24]  Pascal Tixador,et al.  3-D Numerical Modeling of AC Losses in Multifilamentary MgB2 Wires , 2016, IEEE Transactions on Applied Superconductivity.

[25]  Francesco Grilli,et al.  Overview of H-Formulation: A Versatile Tool for Modeling Electromagnetics in High-Temperature Superconductor Applications , 2020, IEEE Access.

[26]  Walter H. Fietz,et al.  HTS CroCo: A Stacked HTS Conductor Optimized for High Currents and Long-Length Production , 2016, IEEE Transactions on Applied Superconductivity.

[27]  Anna Kario,et al.  HTS Roebel Cables: Self-Field Critical Current and AC Losses Under Simultaneous Application of Transport Current and Magnetic Field , 2016, IEEE Transactions on Applied Superconductivity.

[28]  M. Zhang,et al.  Experimental and Numerical Study on the Magnetization Process of Roebel Cable Segments , 2019, IEEE Transactions on Applied Superconductivity.

[29]  F. Grilli,et al.  Numerical modeling of twisted stacked tape cables for magnet applications , 2015 .

[30]  Weijia Yuan,et al.  Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents , 2013, IEEE Transactions on Applied Superconductivity.

[31]  Nenad Mijatovic,et al.  Calculation of alternating current losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications , 2013, 1308.2568.

[32]  W. T. Norris,et al.  Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets , 1970 .

[33]  Wilfried Goldacker,et al.  Roebel cables from REBCO coated conductors: a one-century-old concept for the superconductivity of the future , 2014 .

[34]  Min Zhang,et al.  A finite element model for simulating second generation high temperature superconducting coils/stacks with large number of turns , 2017 .

[35]  Antti Stenvall,et al.  Development of a three-dimensional finite-element model for high-temperature superconductors based on the H-formulation , 2013 .

[36]  Min Zhang,et al.  Fully superconducting machine for electric aircraft propulsion: study of AC loss for HTS stator , 2019, Superconductor Science and Technology.

[37]  Y. Mawatari,et al.  Electromagnetic coupling of twisted multi-filament superconducting tapes in a ramped magnetic field , 2018, Superconductor Science and Technology.

[39]  Antonio Morandi,et al.  Comparison of Constitutive Laws for Modeling High-Temperature Superconductors , 2019, IEEE Transactions on Applied Superconductivity.

[40]  S. Russenschuck,et al.  Powering of an HTS dipole insert-magnet operated standalone in helium gas between 5 and 85 K , 2018 .

[41]  Francesco Grilli,et al.  Real-time simulation of large-scale HTS systems: multi-scale and homogeneous models using the T–A formulation , 2018, Superconductor Science and Technology.

[42]  Min Zhang,et al.  An efficient 3D finite element method model based on the T–A formulation for superconducting coated conductors , 2017 .

[43]  F. Sirois,et al.  Analytical Methods and Formulas for Modeling High Temperature Superconductors , 2013, IEEE Transactions on Applied Superconductivity.

[44]  Luciano Martini,et al.  A Finite-Element Method Framework for Modeling Rotating Machines With Superconducting Windings , 2017, IEEE Transactions on Applied Superconductivity.

[45]  Christopher J. Lammi,et al.  VIPER: an industrially scalable high-current high-temperature superconductor cable , 2020, Superconductor Science and Technology.

[46]  M. Durante,et al.  The EuCARD2 Future Magnets Program for Particle Accelerator High-Field Dipoles: Review of Results and Next Steps , 2018, IEEE Transactions on Applied Superconductivity.

[47]  Joseph V. Minervini,et al.  HTS twisted stacked-tape cable conductor , 2011 .

[48]  Francesco Grilli,et al.  A full 3D time-dependent electromagnetic model for Roebel cables , 2013 .

[49]  Francesco Grilli,et al.  Numerical models for ac loss calculation in large-scale applications of HTS coated conductors , 2015, 1509.05560.

[50]  W. Luo,et al.  Next-generation highly flexible round REBCO STAR wires with over 580 A mm−2 at 4.2 K, 20 T for future compact magnets , 2019, Superconductor Science and Technology.

[51]  Jakob Rhyner,et al.  Magnetic properties and AC-losses of superconductors with power law current-voltage characteristics , 1993 .

[52]  M. Zhang,et al.  Study of the magnetization loss of CORC® cables using a 3D T-A formulation , 2019, Superconductor Science and Technology.

[53]  M. Maciejewski,et al.  A Coupled A–H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets , 2019, IEEE Transactions on Applied Superconductivity.