Electromagnetic Modeling of Superconductors With Commercial Software: Possibilities With Two Vector Potential-Based Formulations

Grilli, Francesco; Pardo, Enric; Morandi, Antonio; Gömöry, Fedor; Solovyov, Mykola; Zermeño, V.; Brambilla, Roberto; Benkel, Tara; Riva, Nicolò

doi:10.1109/tasc.2020.3013028

Cited by 21 publications

(11 citation statements)

References 36 publications

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“…In order to compare the three coupling scenarios, we chose the coil configuration presented in [9]. Analyzed is the 2D cross section of the straight part of a racetrack coil, composed of four cable turns, each made of 16 stacked tapes.…”

Section: Resultsmentioning

confidence: 99%

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

Santos

Santos²,

Sirois

et al. 2022

IEEE Trans. Appl. Supercond.

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Numerical models based on the finite-element method (FEM) are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the T -A formulation for modeling HTS coils in 2D with different coupling scenarios between the turns. First we consider a racetrack coil wound from one piece of superconducting tape. Then we consider a coil obtained by winding a cable composed of different HTS tapes. In the latter case, the tape turns are either electrically connected along their entire length or just at the two ends of the coil: in the model, these two different types of electrical connection are implemented with the help of the electrical circuit module. The current density distributions and the AC losses of the coils in the different coupling scenarios are compared and discussed. The limits of applicability of the presented approach are pointed out. The model is developed for the straight section of racetrack coils, but can be easily adapted to axisymmetric geometries.

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Section: Resultsmentioning

confidence: 99%

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

Santos

Santos²,

Sirois

et al. 2022

IEEE Trans. Appl. Supercond.

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“…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.…”

Section: Modeling Based On Finite Element Methodsmentioning

confidence: 99%

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

2021

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The manufacturing of commercial REBCO tapes, REBCO referring to Rare-earth barium copper oxide, has matured enough to lead to a variety of applications ranging from scientific instruments to electric power systems. In particular, its large current density with a high n index and low hysteresis losses make it a strong candidate for specific applications relying on the dependence of its resistance on current. Despite its advantages, there are still issues that remain to be addressed, such as the scarcity of experimental data for the basic characteristics of the superconductor over a wide range of temperature and applied magnetic field, the homogeneity of these characteristics along the conductor length, as well as the anisotropy of the critical current and n index with respect to the direction of the applied magnetic field. To better utilize the technology, it is therefore sensible to understand the relevancy of these issues so that one could simulate as accurately as possible the physics of the superconductor, at least the dynamics that may impact the correct operation of the superconducting device. There are different levels of modelling to achieve such a goal that can either focus on the performance of the superconductor itself, or on the whole device. The present work addresses some of the latest developments in the modelling of commercial REBCO tapes in power systems with a particular focus on the thermoelectric behavior of superconducting devices connected to external circuits. Two very different approaches corresponding to two different scales in the modelling of superconducting devices are presented: (1) analysis using equivalent models and lumped parameters to study the thermoelectric response of superconducting devices as a whole, (2) Finite Element Analysis (FEA) to compute distributed fields such as current density, magnetic flux density and local losses in tapes. In this context, this paper reviews both approaches and gives a broad variety of examples to show their practical applications in electric power systems. Firstly, they show the relevance of the technology in power systems engineering. Secondly, they allow inferring the necessary level of model details to optimize the operation of superconducting power devices in power grids. This level of details relies completely on the knowledge of some basic measurable properties of superconducting tapes (critical current and n index) and their cooling conditions.

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“…T of the current vector potential T [56]. This implies that the J-A formulation requires fewer degrees of freedom compared to the T-A formulation.…”

Section: Model Validationmentioning

confidence: 99%

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

Wang,

Yong,

Zhou

2023

Supercond. Sci. Technol.

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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.

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Electromagnetic Modeling of Superconductors With Commercial Software: Possibilities With Two Vector Potential-Based Formulations

Cited by 21 publications

References 36 publications

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

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

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

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

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