Scientific Research in the Field of Mesh Method Based Modeling of AC Losses in Superconductors: A Review

Lahtinen, Valtteri; Stenvall, Antti

doi:10.1007/s10948-013-2443-6

Cited by 5 publications

(6 citation statements)

References 70 publications

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“…Once these variables are obtained, the AC loss can be calculated according to the methods presented in Section II-C in [21]. The primary modelling of HTS CCs is based on Maxwell's equations and finite element methods (FEM), which is typically achieved by four kinds of formulations, including T-φ formulation [66][67][68], A-V formulation [69][70][71][72][73][74][75][76], E-formulation [77], and H-formulation [78][79][80][81][82].…”

Section: Modelling Methodsmentioning

confidence: 99%

Alternating Current Loss of Superconductors Applied to Superconducting Electrical Machines

Zhang¹,

Wen²,

Grilli

et al. 2021

Energies

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Superconductor technology has recently attracted increasing attention in power-generation- and electrical-propulsion-related domains, as it provides a solution to the limited power density seen by the core component, electrical machines. Superconducting machines, characterized by both high power density and high efficiency, can effectively reduce the size and mass compared to conventional machine designs. This opens the way to large-scale purely electrical applications, e.g., all-electrical aircrafts. The alternating current (AC) loss of superconductors caused by time-varying transport currents or magnetic fields (or both) has impaired the efficiency and reliability of superconducting machines, bringing severe challenges to the cryogenic systems, too. Although much research has been conducted in terms of the qualitative and quantitative analysis of AC loss and its reduction methods, AC loss remains a crucial problem for the design of highly efficient superconducting machines, especially for those operating at high speeds for future aviation. Given that a critical review on the research advancement regarding the AC loss of superconductors has not been reported during the last dozen years, especially combined with electrical machines, this paper aims to clarify its research status and provide a useful reference for researchers working on superconducting machines. The adopted superconducting materials, analytical formulae, modelling methods, measurement approaches, as well as reduction techniques for AC loss of low-temperature superconductors (LTSs) and high-temperature superconductors (HTSs) in both low- and high-frequency fields have been systematically analyzed and summarized. Based on the authors’ previous research on the AC loss characteristics of HTS coated conductors (CCs), stacks, and coils at high frequencies, the challenges for the existing AC loss quantification methods have been elucidated, and multiple suggestions with respect to the AC loss reduction in superconducting machines have been put forward. This article systematically reviews the qualitative and quantitative analysis methods of AC loss as well as its reduction techniques in superconductors applied to electrical machines for the first time. It is believed to help deepen the understanding of AC loss and deliver a helpful guideline for the future development of superconducting machines and applied superconductivity.

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Section: Modelling Methodsmentioning

confidence: 99%

Alternating Current Loss of Superconductors Applied to Superconducting Electrical Machines

Zhang¹,

Wen²,

Grilli

et al. 2021

Energies

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“…2 External magnetic field is set by fixing H on the boundary of the modelling domain and net currents are forced using constraints based on integrals of current density over conducting surfaces. 3 This is, of course, also true for meshes consisting of, e.g., hexahedra, pyramids or prisms. 4 Superconducting composite wires are typically made of superconducting and normal conducting materials.…”

Section: Introductionmentioning

confidence: 95%

“…However, it is well known that expressing H with a scalar potential provides a substantial advantage in terms of degrees of freedom (DOFs) as there are much less nodes than edges in a simplicial finite element mesh. 3 Hence, there is a legitimate desire for getting rid of the conducting air regions in hysteresis loss modelling, and superconductor AC loss modelling in general. 4 In such classical H -oriented formulations, which express H using the current vector potential T and magnetic scalar potential ϕ, this is especially easy when only applied fields are considered and no net current flows in the conducting parts of the domain [11].…”

Section: Introductionmentioning

confidence: 99%

A Finite Element Simulation Tool for Predicting Hysteresis Losses in Superconductors Using an H-Oriented Formulation with Cohomology Basis Functions

Lahtinen

Stenvall

Sirois

et al. 2015

J Supercond Nov Magn

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Currently, modelling hysteresis losses in superconductors is most often based on the H -formulation of the eddy current model (ECM) solved using the finite element method (FEM). In the H -formulation, the problem is expressed using the magnetic field intensity H and discretized using edge elements in the whole domain. Even though this approach is well established, it uses unnecessary degrees of freedom (DOFs) and introduces modelling error such as currents flowing in air regions due to finite air resistivity. In this paper, we present a modelling tool utilizing another H -oriented formulation of the ECM, making use of cohomology of the air regions. We constrain the net currents through the conductors by fixing the DOFs related to the so-called cohomology basis functions. As air regions will be truly non-conducting, DOFs and running times of these nonlinear simulations are reduced significantly as compared to the classical H -formulation. This fact is demonstrated through numerical simulations.

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“…In this paper we focus on the hysteresis losses, which have negligible frequencydependence [3], [4]. Hysteresis losses are computationally studied primarily with two different approaches [5]- [7]. In the other, superconductor is treated like a normal conductor but with highly non-linear resistivity.…”

Section: Introductionmentioning

confidence: 99%

Utilizing Triangular Mesh With MMEV to Study Hysteresis Losses of Round Superconductors Obeying Critical State Model

Ruuskanen

Stenvall

Lahtinen

2015

IEEE Trans. Appl. Supercond.

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Nature's minimum energy principle formulated in minimum magnetic energy variation (MMEV) and coupled with the Bean's critical state model (CSM) has resulted in feasible tools to model hysteresis losses in superconductors. These tools have been applied for single wires as well as for multi-turn coils in two-dimensional modelling domains. However, so far the discretization of the modelling domain has always relied on regular rectangular meshes. Therefore, the mesh representation of round filaments suffers from large discretization error if the mesh is not refined considerably more than triangular meshing would need. In this paper, we study the utilisation of triangular mesh in such a hysteresis loss modelling tool. We present the required extension to the already available knowledge that is needed to implement such a modelling tool. With our home-brewed tool, we study the convergence of the simulated transport current losses in the cross-section of a round wire represented with triangular and rectangular meshes of different types and of different densities. According to the results, triangular meshing is considerably more efficient than rectangular meshing for simulating transport current losses in the investigated situation.Index Terms-Critical state model, hysteresis losses, minimum magnetic energy variation, numerical modelling.

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Scientific Research in the Field of Mesh Method Based Modeling of AC Losses in Superconductors: A Review

Cited by 5 publications

References 70 publications

Alternating Current Loss of Superconductors Applied to Superconducting Electrical Machines

Alternating Current Loss of Superconductors Applied to Superconducting Electrical Machines

A Finite Element Simulation Tool for Predicting Hysteresis Losses in Superconductors Using an H-Oriented Formulation with Cohomology Basis Functions

Utilizing Triangular Mesh With MMEV to Study Hysteresis Losses of Round Superconductors Obeying Critical State Model

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