Electromagnetic modelling of superconductors with a smooth current-voltage relation: variational principle and coils from a few turns to large magnets

Abstract

Many large-scale applications require electromagnetic modelling with extensive numerical computations, such as magnets or 3-dimensional (3D) objects like transposed conductors or motors and generators. Therefore, it is necessary to develop computationally time-efficient but still accurate numerical methods. This article develops a general variational formalism for any $\mathbf{E}(\mathbf{J})$ relation and applies it to model coated-conductor coils containing up to thousands of turns, taking magnetization currents fully into account. The variational principle, valid for any 3D situation, restricts the computations to the sample volume, reducing the computation time. However, no additional magnetic materials interacting with the superconductor are taken directly into account. Regarding the coil modelling, we use a power law $E(J)$ relation with magnetic field-dependent critical current density, $J_c$, and power law exponent, $n$. We test the numerical model by comparing the results to analytical formulas for thin strips and experiments for stacks of pancake coils, finding a very good agreement. Afterwards, we model a magnet-size coil of 4000 turns (stack of 20 pancake coils of 200 turns each). We found that the AC loss is mainly due to magnetization currents. We also found that for an $n$ exponent of 20, the magnetization currents are greatly suppressed after 1 hour relaxation. In addition, in coated conductor coils magnetization currents have an important impact on the generated magnetic field; which should be taken into account for magnet design. In conclusion, the presented numerical method fulfills the requirements for electromagnetic design of coated conductor windings.

arXiv comment44 pages, 17 figures (footnote with reference information added, margins reduced)

References in corpus (10)

• The Flux-Line Lattice in Superconductors
• Calculation of AC losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications
• Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents
• AC loss in ReBCO pancake coils and stacks of them: modelling and measurement
• Computing AC losses in stacks of high-temperature superconducting tapes
• General critical states in type-II superconductors
• Current distribution and ac loss for a superconducting rectangular strip with in phase alternating current and applied field
• Vector magnetic hysteresis of hard superconductors
• AC loss calculation in coated conductor coils with a large number of turns
• Theory of flux cutting and flux transport at the critical current of a type-II superconducting cylindrical wire

Cited by in corpus (22)

• T-A Formulation to Model Electrical Machines with HTS Coated Conductor Coils
• A new benchmark problem for electromagnetic modelling of superconductors: the high-Tc superconducting dynamo
• 3D computation of non-linear eddy currents: variational method and superconducting cubic bulk
• AC loss modelling in superconducting coils and motors with parallel tapes as conductor
• Modeling of screening currents in coated conductor magnets containing up to 40000 turns
• Electromagnetic Modeling of Superconductors with Commercial Software: Possibilities with Two Vector Potential-Based Formulations
• Influence of Coil Position on AC Losses of Stator Superconducting Windings of a Synchronous Machine for a 10 MW Wind Turbine
• Modeling the charging process of a coil by an HTS dynamo-type flux pump
• Demagnetization of cubic Gd-Ba-Cu-O bulk superconductor by cross-fields: measurements and 3D modelling
• Fast and accurate electromagnetic modeling of non-insulated and metal-insulated REBCO magnets
• Cross-field demagnetization of stacks of tapes: 3D modelling and measurements
• 3D magnetization currents, magnetization loop, and saturation field in superconducting rectangular prisms
• Modeling cross-field demagnetization of superconducting stacks and bulks for up to 100 tapes and 2 million cycles
• Real-time simulation of large-scale HTS systems: multi-scale and homogeneous models using T-A formulation
• Modelling the mechanics of 32 T REBCO superconductor magnet using numerical simulation
• A novel and fast electromagnetic and electrothermal software for quench analysis of high field magnets
• Electro-Thermal Modelling by Novel Variational Methods: Racetrack Coil in Short-Circuit
• Foil Conductor Model for Efficient Simulation of HTS Coils in Large Scale Applications
• 3D Homogenized T-A Formulation for Modeling HTS Coils
• Electromagnetic modeling of large-scale high-temperature superconductor systems
• Three-dimensional electromagnetic modeling of practical superconductors for power applications
• T-A homogenized and multi-scale models with real-time simulation capabilities for large-scale HTS systems