Electromagnetic computations with Preisach hysteresis model

Bermdez, Alfredo; Dupr, Luc; Gmez, Dolores; Venegas, Pablo

doi:10.1016/j.finel.2016.11.005

Cited by 17 publications

(9 citation statements)

References 23 publications

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“…We observe a linear order of convergence in norm L 2 (0, T ; H 1 (Ω)) and a quadratic order in L 2 (0, T ; L 2 (Ω)). A similar behavior is also observed when the rate-independent Preisach model is considered (see [3]).…”

Section: Convergence Analysissupporting

confidence: 77%

“…The term was initially coined in the area of magnetism [17] given that many ferromagnetic materials present hysteresis behavior that is reflected in the magnetization curves describing the magnetic response of the material to an applied magnetic field. From the electrical engineering point of view, having a good hysteresis model is fundamental to, for instance, correctly estimate the energy losses in electrical machines, a very important characteristic to take into account when designing an electrical device; in particular, the so-called hysteresis and excess losses [3]. Consequently, building a mathematical model of this relation is a very important (and difficult) task and numerical simulation of devices involving ferromagnetic materials is still quite a challenge.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Bermúdez

Gómez

Venegas

2020

Journal of Computational and Applied Mathematics

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Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of classical or rate-independent hysteresis models are known, this is not the case for dynamic models where current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we show the well posedness of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model.

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Section: Convergence Analysissupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Bermúdez

Gómez

Venegas

2020

Journal of Computational and Applied Mathematics

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“…As shown in [24], in this situation, it is possible to reduce the computational domain to the meridian section of one single sheet for which it is necessary to derive appropriate boundary conditions. More precisely, the axisymmetric transient eddy current problem to be solved reads:…”

Section: Hysteresis Power Losses Computationmentioning

confidence: 99%

“…We have employed the usual notation: H is the magnetic field, B the magnetic induction and σ the electrical conductivity. Moreover, it can be shown that (see [24] for details):…”

Section: Toroidal Laminated Media (Left) and Its Meridian Section (Ce...mentioning

confidence: 99%

“…During the last few years, the authors of this chapter have been working on the mathematical modeling, numerical analysis and computation of PDE hysteresisrelated problems motivated by real applications, with special emphasis on the hysteresis of ferromagnetic materials. This work is a survey of previous co-authored studies [17, [23][24][25], where we have intended to provide original steps into the mathematical and numerical treatment of parabolic problems with hysteresis. In all of them, the Preisach model was considered as hysteresis operator.…”

Section: Introductionmentioning

confidence: 99%

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Preisach Hysteresis Model – Some Applications in Electrical Engineering

Bermúdez¹,

Gómez²,

Venegas³

2024

Modern Permanent Magnets - Fundamentals and Applications

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In this chapter we recall the well-known hysteresis Preisach model, widely employed in the area of magnetism. Some applications of this model in electrical engineering are also described, with a specific focus on the estimation of electromagnetic losses in electrical machines, the simulation of magnetization-demagnetization processes arising in magnetic particle inspection, and the mathematical modeling of batteries for electric vehicles.

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Some Case Studies in Environmental and Industrial Mathematics

Bermúdez

2022

SEMA SIMAI Springer Series

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This presentation deals with four case studies in environmental and industrial mathematics developed by the mathematical engineering research group (mat+i) from the University of Santiago de Compostela and the Technological Institute for Industrial Mathematics (ITMATI). The first case involves environmental fluid mechanics: optimizing the location of submarine outfalls on the coast. This work, related to shallow water equations with variable depth, led us to develop a theory for numerical treatment of source terms in nonlinear first order hyperbolic balance laws. More recently, these techniques have been applied to solve Euler equations with source terms arising from numerical simulation of gas transportation networks when topography via gravity force is considered in the model. The last two problems concerns electromagnetism. One of them is related to nondestructive testing of car parts by using magnetic nanoparticles (the so-called magnetic particle inspection, MPI): mathematical modelling of magnetic hysteresis to simulate demagnetization. Finally, we present a mathematical procedure to reduce the computing time needed to achieve the stationary state of an induction electric machine when using transient numerical simulation.

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Electromagnetic computations with Preisach hysteresis model

Cited by 17 publications

References 23 publications

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Preisach Hysteresis Model – Some Applications in Electrical Engineering

Some Case Studies in Environmental and Industrial Mathematics

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