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

Abstract

The high-T c superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. Finally, a critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom, tolerance settings and the approximate time taken per cycle for each model. This benchmark and the results contained herein provide researchers with a suitable framework to validate, compare and optimise their own methods for modelling the HTS dynamo.

Essential Material Knowledge and Recent Model Developments for REBCO-Coated Conductors in Electric Power Systems

“…In the MVP domain ( ), the source is the current density which is divided into three parts: (1) the external current density ( ), (2) the induced current density ( ) that are computed in the MVP domain, and (3) the superconductor current density ( ) that is calculated in the CVP domain ( ). Using the MVP, the magnetic field is computed in the whole domain knowing the B - H relation for the material through , whereas the CVP is used to calculate the current density only in the superconducting regions [ 55 , 63 , 64 , 65 ]. Equations ( 16 ) and ( 17 ) present the T - A formulation.…”

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

“…The constrains on the transport current are implemented by imposing the appropriate sets of boundary conditions with variable T T T on the ends or edges of the superconductors. With great potentials in multi-physics coupling and 3D modeling, models of HTS dynamo [31], quench [32], and cables with 3D structure [23] were developed. In our study, we used the original T-A formulation in 2D and 3D, as in [27] and [28], which considers a uniform distribution of current density across the thickness.…”

“…It is worth noting that the coupled A-H formulation [44], proposed for the modeling of superconducting electrical machines, is also among similar methods. Although not included in this paper, such discussions could be found in [31] and [45].…”

“…With the T-A formulation, it was reported in [29] and [31] that with first or second order Lagrange elements for both T and A, spurious oscillations could appear in the current density J profile at certain study steps. However, because such oscillations mostly occur within the subcritical region, where the current density is lower than the critical current density J c , the influence on the resulting AC losses is insignificant.…”

The Application of a CMR-B-Scalar Sensor for the Investigation of the Electromagnetic Acceleration of Type II Superconductors

“…In the past decade, due to developments in software and computing power, the modelling of the electrodynamic behavior of type II superconductors has become less restrictive, and good agreements between experiments and simulations have been achieved when investigating superconductor magnetization [ 20 , 21 ] and magnetic levitation [ 22 , 23 , 24 ]. Various eddy current problem formulations have been proposed, suited to handle different superconductor application scenarios or to improve computation times [ 25 , 26 , 27 , 28 , 29 ].…”