J-A formulation: A finite element methodology for simulating superconducting devices

Santos, Gabriel dos; Santos, Bárbara Maria Oliveira; Sass, Felipe; Martins, Flávio Goulart dos Reis; Sotelo, Guilherme Gonçalves; Andrade, R. de

doi:10.1016/j.supcon.2023.100049

Cited by 12 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the state variable is the current density J sc instead of current vector potential T. Thus far, the J-A formulation has been used to model superconducting tapes using a thin strip approximation [19] with zero element order in the J formulation and second order in A formulation simulating all the tapes (full model) [42]. In the present work, a new version of the J-A formulation is introduced that makes use of the homogenization technique to gain computation speed.…”

Section: J-a Formulationmentioning

confidence: 99%

“…Moreover, for gaining on computation speed, various mixed formulations of the Maxwell equations have been tested thus far [15,16]. The idea here is to use the two latest formulations, namely the T-A [8,17,18] and J-A formulations [19]. It is assumed that the former provides a valid reference for fast computation time and accuracy to the newest J-A formulation since it was successfully cross-checked against the well-established H formulation [20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Supercond. Sci. Technol.

View full text Add to dashboard 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.

show abstract

Section: J-a Formulationmentioning

confidence: 99%

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

Supercond. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…The coupling processes are shown in figure 1. Maxwell's equations are calculated in the A equation, which has the following expressions [47,50]…”

Section: Theory Of the J-a Formulationmentioning

confidence: 99%

“…However, the A-V-J formulation requires denser meshes than the H formulation and the T -φ formulation for reliable results [49]. Notably, since the electric scalar potential V is a 0-form variable [49] and does not appear directly when the global constraint condition is applied, the A-V-J formulation can be reduced to the J-A formulation [50]. Compared to the H formulation and the T-A formulation, the J-A formulation has received less attention.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Wang,

Yong,

Zhou

2023

Supercond. Sci. Technol.

View full text Add to dashboard Cite

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.

show abstract

A coupled electromagnetic-mechanical model and contact behavior of the superconducting coils

Wang,

Tang,

Yong

et al. 2024

Applied Mathematical Modelling

View full text Add to dashboard Cite

J-A formulation: A finite element methodology for simulating superconducting devices

Cited by 12 publications

References 33 publications

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

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

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

A coupled electromagnetic-mechanical model and contact behavior of the superconducting coils

Contact Info

Product

Resources

About