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Article
Publication date: 1 January 2006

P. Dular, J. Gyselinck and L. Krähenbühl

To develop a homogenization technique to directly and efficiently take the eddy current effects in laminated magnetic cores within time domain finite element (FE) analyses.

323

Abstract

Purpose

To develop a homogenization technique to directly and efficiently take the eddy current effects in laminated magnetic cores within time domain finite element (FE) analyses.

Design/methodology/approach

The technique is developed for being used within a 3D magnetodynamic b‐conform FE formulation, e.g. using a magnetic vector potential. To avoid a fine FE discretization of all the laminations of a magnetic core, this one is considered as a source region that carries predefined current and magnetic flux density distributions describing the eddy currents and skin effect along each lamination thickness. Both these distributions are related and are first approximated with sub‐basis functions. Through the homogenization or averaging of the sub‐basis functions contributions in the FE formulation, the stacked laminations are then converted into continua, thus implicitly considering the eddy current loops produced by parallel magnetic fluxes. The continuum is then approximated with classical FE basis functions and can be defined on a coarser discretization.

Findings

The developed method appears attractive for directly and efficiently taking into account within finite element analyses the eddy current effects, i.e. the associated losses and magnetic flux reduction, that are particularly significant for high frequency excitations. The time domain analysis allows the consideration of both non‐linear and transient phenomena.

Originality/value

The averaging of sub‐basis functions contributions, describing fine distributions of fields, in an FE formulation leads to an original way of homogenizing laminated regions. The proposed method is naturally adapted for time domain analyses and in some sense generalizes what can be done more easily in the frequency domain.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 September 2004

P. Dular, J. Gyselinck, T. Zeidan and L. Krähenbühl

Develops a method to take the eddy currents in stacked thin regions, in particular lamination stacks, into account with the finite element method using the 3D magnetic vector…

188

Abstract

Develops a method to take the eddy currents in stacked thin regions, in particular lamination stacks, into account with the finite element method using the 3D magnetic vector potential magnetodynamic formulation. It consists in converting the stacked laminations into continuums with which terms are associated for considering the eddy current loops produced by both parallel and perpendicular fluxes. Non‐zero global currents can be considered in the laminations, in particular for studying the effect of imperfect insulation between their ends. The method is based on an analytical expression of eddy currents and is adapted to a wide frequency range.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 January 2017

Patrick Dular, Patrick Kuo-Peng, Mauricio Valencia Ferreira da Luz and Laurent Krahenbuhl

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

92

Abstract

Purpose

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

Design/methodology/approach

The progressive modeling of transformers is performed via a subproblem (SP) FE method. A complete problem is split into SPs with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, one-dimensional to two-dimensional to three-dimensional models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings and homogenized to fine models of cores and coils, with any coupling of these changes.

Findings

The proposed unified procedure efficiently feeds each SP via interface conditions (ICs), which lightens mesh-to-mesh sources transfers and quantifies the gain given by each refinement on both local fields and global quantities, with a clear view on its significance to justify its usefulness, if any. It can also help in education with a progressive understanding of the various aspects of transformer designs.

Originality/value

Models of different accuracy levels are sequenced with successive additive corrections supported by different adapted meshes. The way the sources act at each correction step, up to the full models with their actual geometries, is given a particular care and generalized, allowing the proposed unified procedure. For all the considered corrections, the sources are always of IC type, thus only needed in layers of FE along boundaries, which lightens the required mesh-to-mesh projections between subproblems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 7 September 2015

Patrick Dular, Mauricio V. Ferreira da Luz, Patrick Kuo-Peng and Laurent Krähenbühl

The purpose of this paper is to develop a subproblem finite element method for progressive modeling of lamination stacks in magnetic cores, from homogenized solutions up to…

77

Abstract

Purpose

The purpose of this paper is to develop a subproblem finite element method for progressive modeling of lamination stacks in magnetic cores, from homogenized solutions up to accurate eddy current distributions and losses.

Design/methodology/approach

The homogenization of lamination stacks, subject to both longitudinal and transversal magnetic fluxes, is first performed and is followed by local correction subproblems in certain laminations separately, surrounded by their insulating layers and the remaining laminations kept homogenized. The sources for the local corrections are originally defined via interface conditions to allow the coupling between homogenized and non-homogenized portions.

Findings

The errors proper to the homogenization model, which neglects fringing effects, can be locally corrected in some selected portions via local eddy current subproblems considering the actual geometries and properties of the related laminations. The fineness of the mesh can thus be concentrated in these portions, while keeping a coupling with the rest of the laminations kept homogenized.

Research limitations/implications

The method has been tested on a 2D case having linear material properties. It is however directly applicable in 3D. Its extension to the time domain with non-linear properties will be done.

Originality/value

The resulting subproblem method allows accurate and efficient calculations of eddy current losses in lamination stacks, which is generally unfeasible for real applications with a single problem approach. The accuracy and efficiency are obtained thanks to a proper refined mesh for each subproblem and the reuse of previous solutions to be locally corrected only acting in interface conditions. Corrections are progressively obtained up to accurate eddy current distributions in the laminations, allowing to improve the resulting global quantities: the Joule losses in the laminations, and the resistances and inductances of the surrounding windings.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 11 September 2009

P. Di Barba and M.E. Mognaschi

The purpose of the paper is to show that the a posteriori analysis of the Pareto front associated with a given design problem facilitates the task of the decision maker and…

642

Abstract

Purpose

The purpose of the paper is to show that the a posteriori analysis of the Pareto front associated with a given design problem facilitates the task of the decision maker and possibly helps to identify innovative solutions. The idea is to investigate the similarities existing among non‐dominated solutions.

Design/methodology/approach

A permanent‐magnet alternator for automotive applications is considered as case study. The design problem exhibits six design variables and two energy‐related objective functions. A suitable sampling of the objective space is made and non‐dominated solutions, located along an L‐shaped front, are approximated. Results are assessed by means of a successive optimization using NSGA‐II algorithm.

Findings

From the approximated Pareto front, three optimal devices have been selected and remapped in the design space in order to compare their performance. This is done in terms of iron and copper losses, material costs, rated voltage, and air‐gap induction. Moreover, making the NSGA‐II start from the knee‐point of the front, it is shown that a direct approximation of the two sub‐fronts is possible.

Originality/value

In this paper, a method to sort out the optimal solutions located along the Pareto front is proposed as a possible criterion of decision making; so doing, previously unpredicted solutions might be identified.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 11 May 2010

Bo Zhang, Jinliang He, Rong Zeng and Xidong Liang

The purpose of this paper is to introduce an efficient model for analysis of the voltage distribution along the long ceramic insulator strings in a high‐voltage tower window…

530

Abstract

Purpose

The purpose of this paper is to introduce an efficient model for analysis of the voltage distribution along the long ceramic insulator strings in a high‐voltage tower window, especially when the structure and parameters of the ceramic insulator are unknown. The effect of the grading ring on the voltage distribution is also investigated.

Design/methodology/approach

A circuit model composed of capacitors is used to analyze the voltage distribution along the ceramic insulator strings in a transmission tower window. The capacitances of the disk insulators, line conductors, and tower are obtained by using the finite element method, charge simulation method, boundary element method, and measurement according to their characteristics.

Findings

The model is very efficient. The voltage distribution along insulator strings can be optimized by adjusting the parameters of the grading ring. The maximum amount of voltage applied to a single insulator disk can be reduced effectively by increasing either the diameter of the grading ring or the distance from the upper surface of the grading ring to the high‐voltage end of the insulator string.

Originality/value

The model is very efficient for analysis of the voltage distribution along the long ceramic insulator strings, especially when the structure and parameters of the ceramic insulator are unknown.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 16 November 2010

Ruth V. Sabariego, Peter Sergeant, Johan Gyselinck, Patrick Dular, Luc Dupré and Christophe Geuzaine

The aim of this paper is the experimental validation of an original time‐domain thin‐shell formulation. The numerical results of a three‐dimensional thin‐shell model are compared…

176

Abstract

Purpose

The aim of this paper is the experimental validation of an original time‐domain thin‐shell formulation. The numerical results of a three‐dimensional thin‐shell model are compared with the measurements performed on a heating device at different working frequencies.

Design/methodology/approach

A time‐domain extension of the classical frequency‐domain thin‐shell approach is used for the finite‐element analysis of a shielded pulse‐current induction heater. The time‐domain interface conditions at the shell surface are expressed in terms of the average flux density vector in the shell, as well as in terms of a limited number of higher‐order components.

Findings

A very good agreement between measurements and simulations is observed. A clear advantage of the proposed thin‐shell approach is that the mesh of the computation domain does not depend on the working frequency anymore. It provides a good compromise between computational cost and accuracy. Indeed, adding a sufficient number of induction components, a very high accuracy can be achieved.

Originality/value

The method is based on the coupling of a time‐domain 1D thin‐shell model with a magnetic vector potential formulation via the surface integral term. A limited number of additional unknowns for the magnetic flux density are incorporated on the shell boundary.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 5 March 2018

Carlo de Falco, Luca Di Rienzo, Nathan Ida and Sergey Yuferev

The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.

128

Abstract

Purpose

The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.

Design/methodology/approach

An approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields.

Findings

The results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost.

Research limitations/implications

Limitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor.

Originality/value

The efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 5 May 2015

Patrick Dular, Laurent Krähenbühl, Mauricio V. Ferreira da Luz, Patrick Kuo-Peng and Christophe Geuzaine

– The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores.

80

Abstract

Purpose

The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores.

Design/methodology/approach

The modeling of inductors is split into a sequence of progressive finite element (FE) SPs. The source fields (SFs) generated by the source conductors alone are calculated at first via either the Biot-Savart (BS) law or FEs. With a novel general way to define the SFs via interface conditions (ICs), to lighten their evaluation process, the associated reaction fields for each added or modified region, mainly the magnetic cores, and in return for the source conductor regions themselves when massive, are then calculated with FE models. Changes of magnetic regions go from perfect magnetic properties up to volume linear and nonlinear properties, and from statics to dynamics.

Findings

For any added or modified region, the novel proposed ICs to define the SFs appear of general usefulness, which opens the method to a wide range of model improvements.

Originality/value

The resulting SPM allows efficient solving of parameterized analyses thanks to a proper mesh for each SP and the reuse of previous solutions to be locally corrected, in association with novel SF ICs that strongly lighten the quantity of BS evaluations. Significant corrections are progressively obtained for the fields, up to nonlinear magnetic core properties and skin and proximity effects in conductors, and for the related inductances and resistances.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 4 January 2008

Patrick Dular, Ruth V. Sabariego and Laurent Krähenbühl

To develop a subdomain perturbation technique to calculate skin and proximity effects in inductors within frequency and time domain finite element (FE) analyses.

235

Abstract

Purpose

To develop a subdomain perturbation technique to calculate skin and proximity effects in inductors within frequency and time domain finite element (FE) analyses.

Design/methodology/approach

A reference limit eddy current FE problem is first solved by considering perfect conductors via appropriate boundary conditions. Its solution gives the source for eddy current FE perturbation subproblems in each conductor with its actual conductivity. Each of these problems requires an appropriate mesh of the associated conductor and its surrounding region.

Findings

The skin and proximity effects in inductors can be accurately determined in a wide frequency range, allowing for a precise consideration of inductive phenomena as well as Joule losses calculations in thermal coupling.

Originality/value

The developed subdomain method allows to accurately determine the current density distributions and ensuing Joule losses in conductors of any shape, not only in the frequency domain but also in the time domain. It extends the domain of validity and applicability of impedance boundary condition techniques. It also allows the solution process to be lightened, as well as efficient parameterized analyses on signal forms and conductor characteristics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 1
Type: Research Article
ISSN: 0332-1649

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