Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires
TL;DR: In this paper, a 2D numerical model based on the finite element method and implementing the H -formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT.
Abstract: © 2018 IOP Publishing Ltd. The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as 'dynamic resistance.' Dynamic resistance is relevant to many potential higherature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H -formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30° and 60° to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire's superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, I c( B ), of the wire. It is shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until J c is exceeded and flux-flow resistance occurs.
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TL;DR: The basics of the finite-element method (FEM) based on theinline-formula, its evolution from 2D to 3D, its application for calculating critical currents and AC losses as well as magnetization of HTS bulks and tape stacks, and its application to study the dynamic resistance of superconductors and flux pumps are reviewed.
Abstract: This paper reviews the modeling of high-temperature superconductors (HTS) using the finiteelement method (FEM) based on the H-formulation of Maxwell's equations. This formulation has become the most popular numerical modeling method for simulating the electromagnetic behavior of HTS, especially thanks to the easiness of implementation in the commercial finite-element program COMSOL Multiphysics. Numerous studies prove that the H-formulation is able to simulate a wide scope of HTS topologies, from simple geometries such as HTS tapes and coils, to more complex HTS devices, up to large superconducting magnets. In this paper, we review the basics of the H-formulation, its evolution from 2D to 3D, its application for calculating critical currents and AC losses as well as magnetization of HTS bulks and tape stacks. We also review the use of the H-formulation for large-scale HTS applications, its use to solve multi-physics problems involving electromagnetic-thermal and electromagnetic-mechanical couplings, and its application to study the dynamic resistance of superconductors and flux pumps.
142 citations
Cites methods from "Numerical modelling of dynamic resi..."
...This model helped explain the origin and characteristics of dynamic resistance including the relationship with the applied field and current, the onset of nonlinear flux-flow resistance and the threshold field [125]....
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TL;DR: In this paper, it was shown that the overcritical currents experienced a non-linear local resistivity which altered the output voltage waveform obtained in the superconducting state, and the full-cycle integral of this altered waveform outputs a nonzero time-averaged DC voltage.
Abstract: Despite their proven ability to output DC currents of >100 A, the physical mechanism which underpins the operation of a high-Tc superconducting (HTS) dynamo is still debated widely. Here, we show that the experimentally observed open-circuit DC output voltage, Vdc, is due to the action of overcritical eddy currents within the stator wire. We demonstrate close agreement between experimental results and numerical calculations, and show that large over-critical currents flow within the high-Tc stator during certain parts of the dynamo cycle. These overcritical currents experience a non-linear local resistivity which alters the output voltage waveform obtained in the superconducting state. As a result, the full-cycle integral of this altered waveform outputs a non-zero time-averaged DC voltage. We further show that the only necessary requirement for a non-zero Vdc output from any dynamo is that the stator must possess a non-linear local resistivity. Here, this is provided by the flux-flow regime of an HTS coated conductor wire, where conduction is described by the E–J power law. We also show that increased values of Vdc can be obtained by employing stator wires which exhibit a strong in-field dependence of the critical current J c ( B , θ ). However, non-linear resistivity is the key requirement to realize a DC output, as linear magneto-resistance is not sufficient. Our results clarify this longstanding conundrum, and have direct implications for the optimization of future HTS dynamo devices.
44 citations
37 citations
TL;DR: In this paper, the authors measured dynamic resistance in a four-tape coated conductor stack when exposed to AC magnetic fields with different magnetic field angles (the angles between the magnetic field and normal vector component of the tape surface, θ ) at 77 K.
Abstract: The dynamic resistance which occurs when a superconductor carrying DC current is exposed to alternating magnetic field plays an important role in HTS applications such as flux pumps and rotating machines. We report experimental results on dynamic resistance in a four-tape coated conductor stack when exposed to AC magnetic fields with different magnetic field angles (the angles between the magnetic field and normal vector component of the tape surface, θ ) at 77 K. The conductors for the stack are 4-mm-wide SuperPower SC4050 wires. The field angle was varied from 0° to 120° at a resolution of 15° to study the field angle dependence of dynamic resistance on field angle as well as wire I c ( B , θ ). We also varied the field frequency, the magnetic field amplitude, and the DC current level to study the dependence of dynamic resistance on these parameters. Finally, we compared the measured dynamic resistance results at perpendicular magnetic field with the analytical models for single wires. Our results show that the dynamic resistance of the stack was mainly, but not solely, determined by the perpendicular magnetic component. I c ( B , θ ) influences dynamic resistance in the stack due to tilting of the crystal lattice of the superconductor layer with regard to buffer layers.
37 citations
Cites background or methods from "Numerical modelling of dynamic resi..."
...Measured Ic (B, θ) values for a single coated conductor at 77 K [19]....
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...9 shows the measured Ic values of a coated conductor, which is cut from the same source material as the conductors used in the stack in this work, at different field angles at 77 K [19]....
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...magnetic field with various field angles [18], [19]....
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34 citations
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TL;DR: Analytical results are at variance with the critical-state model for longitudinal geometry and explain numerous experiments in a natural way without the assumption of a surface barrier.
Abstract: Current density, magnetic field, penetrated magnetic flux, and magnetic moment are calculated analytically for a thin strip of a type-II superconductor carrying a transport current [ital I] in a perpendicular magnetic field [ital H][sub [ital a]] Constant critical current density [ital j][sub [ital c]] is assumed The exact solutions reveal interesting features of this often realized [ital perpendicular] geometry that qualitatively differs from the widely used Bean critical state model: At the penetrating flux front the field and current profiles have vertical slopes; the initial penetration depth and penetrated flux are [ital quadratic] in [ital H][sub [ital a]] and [ital I]; the initial deviation from a linear magnetic moment is [ital cubic] in [ital H][sub [ital a]]; the hysteresis losses are proportional to the [ital fourth] power of a small ac amplitude; the current density [ital j] is [ital finite] over the entire width of the strip even when flux has only partly penetrated; in thin films, as soon as the direction of the temporal change of [ital H][sub [ital a]] or [ital I] is reversed, [ital j] falls below [ital j][sub [ital c]] [ital everywhere], thus stopping flux creep effectively; the Lorentz force can drive the vortices uphill'' againstmore » the flux-density gradient These analytical results are at variance with the critical-state model for longitudinal geometry and explain numerous experiments in a natural way without the assumption of a surface barrier« less
984 citations
TL;DR: In this paper, a numerical method is proposed to analyse the electromagnetic behavior of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current.
Abstract: A numerical method is proposed to analyse the electromagnetic behaviour of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current. The E–J constitutive law together with an H-formulation is used to calculate the current distribution and electromagnetic fields in HTSCs, and the magnetization of HTSCs; then the forces in the interaction between the electromagnet and the superconductor and the AC loss of the superconducting cable can be obtained. This numerical method is based on solving the partial differential equations time dependently and is adapted to the commercial finite element software Comsol Multiphysics 3.2. The advantage of this method is to make the modelling of the superconductivity simple, flexible and extendable.
428 citations
TL;DR: In this article, a new numerical model for computing the current density, field distributions and AC losses in superconductors is presented, based on the direct magnetic field H formulation without the use of vector and scalar potentials.
Abstract: This paper presents a new numerical model for computing the current density, field distributions and AC losses in superconductors. The model, based on the direct magnetic field H formulation without the use of vector and scalar potentials (which are used in conventional formulations), relies on first-order edge finite elements. These elements are by construction curl conforming and therefore suitable to satisfy the continuity of the tangential component of magnetic field across adjacent elements, with no need for explicitly imposing the condition . This allows the overcoming of one of the major problems of standard nodal elements with potential formulation: in the case of strong discontinuities or nonlinearities of the physical properties of the materials and/or in presence of sharp corners in the conductors' geometry, the discontinuities of the potentials' derivatives are unnatural and without smoothing artifices the convergence of the algorithm is put at risk. In this work we present in detail the model for two-dimensional geometries and we test it by comparing the numerical results with the predictions of analytical solutions for simple geometries. We use it successively for investigating cases of practical interest involving more complex configurations, where the interaction between adjacent tapes is important. In particular we discuss the results of AC losses in superconducting windings.
421 citations
TL;DR: In this paper, a theory of magnetic properties and AC-losses in superconductors with smooth current-voltage characteristics is proposed, which is applied to supercondors with a power law characteristic, E ≈ jα.
Abstract: In many high-Tc superconductors the critical current density jc is an ill-defined quantity due to the smooth current—voltage characteristic. Since jc is the basic parameter entering the critical state model, its application to such materials becomes problematic. In this paper, a theory of magnetic properties and AC-losses in superconductors with smooth current—voltage characteristics is proposed. It is applied to superconductors with a power law characteristic, E ≈ jα. The AC-losses are calculated analytically; simple scaling rules are obtained for their dependence on the frequency and the field amplitude. Moreover, it is shown that the normal ohmic conductor and the “perfect” type-II superconductor (critical state) emerge as limiting cases, α = 1 and α = ∞, from the theory.
376 citations
TL;DR: This paper presents a literature review of the methods for computing ac losses in HTS tapes, wires, and devices and provides an estimation of the losses occurring in a variety of power applications.
Abstract: Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms, and predicting the performance of high-temperature-superconductor (HTS) tapes, wires, and devices. This is particularly true for ac loss calculation since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, which are based on different techniques and implementations, has been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This paper presents a literature review of the methods for computing ac losses in HTS tapes, wires, and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy-current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications.
290 citations