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

One of the main challenges in superconductivity modeling stems from the strong nonlinearity of the E-J power law relationship. To overcome this difficulty, various numerical models have been developed by the superconductivity community, such as the H formulation and the T-A formulation. These models are implemented based on different state variables in Maxwell’s equations and have the advantage of efficiency and versatility. In this study, a finite element model based on the J-A formulation is further developed to enhance its accuracy and versatility. The discontinuous Lagrange shape function is employed in the J formulation to stabilize the numerical results. Meanwhile, the Lagrange multiplier method is applied to impose the transport current on the superconductors. In terms of applications, the J-A formulation can efficiently simulate the electromagnetic responses not only of superconducting films but also of superconducting bulks. Moreover, homogeneous and multi-scale strategies are introduced to simplify the model and reduce the computation cost, allowing efficient simulation of large-scale HTS systems. Finally, the three-dimensional (3D) J-A formulation is proposed to incorporate the 3D structure of HTS systems, examples including the CORC cables as well as the racetrack coils. These results reveal that the J-A formulation is an efficient and versatile numerical method for calculating the electromagnetic behavior of high temperature superconductors.

Section: Discussionmentioning

confidence: 99%

Numerical calculations of high temperature superconductors with the J-A formulation

Wang,

Yong,

Zhou

2023

“…An improved T-A formulation is developed to calculate the distribution of the screening current and magnetic field in both the superconducting and normal states. The governing equations of the T-A formulation are [44,[47][48][49]]…”

Section: Numerical Modelmentioning

confidence: 99%

Non-uniform current distribution in parallel-wound no-insulation high-temperature superconductor coil during ramping and fast discharging operations

Fu,

Wang,

Peng

et al. 2023

A parallel-wound no-insulation (PWNI) high-temperature superconductor (HTS) coil is a kind of pancake-shaped no-insulation (NI) coil wound with parallel-stacked HTS tapes, which combines the characteristics of a NI coil and non-twisted stacked-tape cable. It shows a significant advantage in accelerating the ramping response compared with traditional NI HTS coils wound by a single tape, and is a promising alternative for large-scale high-field magnets. The stacked cable approach can lead to current redistribution between parallel tapes during ramping operations. It couples with the turn-to-turn current redistribution and leads to a much more complicated current redistribution inside the PWNI coil, the mechanism of which remains unclear so far. The aim of this work is to investigate electromagnetic behavior of a PWNI HTS coil in ramping and fast discharging process. A simulation model was developed by integrating an equivalent circuit network model and an improved T–A model. A three-tape PWNI coil and its insulated counterpart were wound and tested, and this model was validated by charging and discharging tests. Results show that there is a significant non-uniform current distribution on parallel tapes in the same turn during ramping operations and the maximum azimuthal current (transport current) can be 2.26 times the minimum one in the three-tape PWNI coil in this study. Meanwhile, the radial current shows a considerable accumulation in the tape near turn-to-turn contacts and the radial current through the turn-to-turn contacts can be 4.16 times of that the flow through tape-to-tape contacts (parallel tapes) in the same turn. During the fast discharging process, a significant coupling current is generated in the PWNI coil, leading to a large opposite transport current in local areas; the amplitude of variation of this can be 4.66 times the initial operating current. The radial current shows a similar distribution but opposite direction to that during ramping, and its amplitude is two orders of magnitude higher. These results provide practical guidelines for the design of large-scale high-field HTS magnets.

“…Such possibility is given by coupling the commercial software COMSOL Multiphysics with Simulink of MATLAB. Some previous efforts have been carried out in that direction, see [23][24][25][26]. Nevertheless, the co-simulation technique presents some challenges for modeling HTS devices.…”

Section: Introductionmentioning

confidence: 99%

FEM-Circuit co-simulation of superconducting synchronous wind generators connected to a DC network using the homogenized J–A formulation of the Maxwell equations

Durante-Gómez,

Trillaud,

dos Santos

et al. 2024

Self Cite

High-temperature superconductors (HTS) are greatly appealing for the development of high efficient, and high energy density power devices. They are particularly relevant for applications requiring light and compact machines such as wind power generation. In this context, to ensure the proper design of the superconducting machines and their reliable operation in power systems, it is then important to develop models that can accurately include their physics but also can describe properly their interaction with the system. Thus, one approach is the co-simulation. The goal of the present work is to put to use this numerical technique when superconducting components are involved. Here, the case study is a 15 MW hybrid superconducting synchronous generator (HTS rotor and conventional stator) coupled to a direct current (DC) network via a rectifier and its associated filter. The case study related to wind power application allows grasping the technical issues when employing co-simulation dealing with HTS machines. The FEM of the generator is done in COMSOL Multiphysics, which interacts with the circuit simulator Simulink through the built-in Functional Mock-up Unit (FMU). For the present study, a new version of the latest J-A formulation combined with homogenization technique is introduced allowing an even faster computation time compared to the T-A formulation. Distributed variables and global variables such as current density, magnetic flux density, and local losses for the former and voltage, current, electromagnetic torque, and power quality for the latter are estimated and compared for both formulations. The idea is to find the best-suited combination FEM-circuit under criteria of computational speed, accuracy, and numerical stability. It is then shown that all formulations generate an error of less than 5% on the machine parameters; and the J-A formulation with first order elements stands out with a significant 4-fold reduction in computational costs.