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Article
Publication date: 11 May 2020

Fabian Müller, Lucas Crampen, Thomas Henneron, Stephane Clénet and Kay Hameyer

The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate…

Abstract

Purpose

The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated.

Design/methodology/approach

The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort.

Findings

Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown.

Originality/value

In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 2 May 2017

Guillaume Caron, Thomas Henneron, Francis Piriou and Jean-Claude Mipo

The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient…

Abstract

Purpose

The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.

Design/methodology/approach

In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.

Findings

The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.

Research limitations/implications

The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.

Practical/implications

In the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.

Social/implications

The proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.

Originality/value

The novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 8 May 2009

Jean‐Yves Roger, Emmanuel Vrignaud, Thomas Henneron, Abdelkader Benabou and Jean‐Pierre Ducreux

Coreplates in large generators may suffer from local short circuits. An accurate analysis is required to avoid these failures and detect them when occurring. The purpose…

Abstract

Purpose

Coreplates in large generators may suffer from local short circuits. An accurate analysis is required to avoid these failures and detect them when occurring. The purpose of this paper is to develop a lamination stack model compliant with interlamination default analysis.

Design/methodology/approach

An electromagnetic model should account for the eddy‐current in the lamination stack. To avoid the modelling of the insulation between the steel sheets, the authors propose to introduce a condition on the fields applied between each sheet. In the case of electric fault between several sheets, the conducting domain, i.e. the sheets, is not simply connected. Then, T‐Ω formulation must be adapted to solve such problem.

Findings

The model allows to account for thin plates, insulating layers and electrical faults in electromagnetic modeling of core plates. This study leads to a first evaluation of eddy current losses in steel laminations with defaults.

Research limitations/implications

The present study does not take into account thermal effects. The next step will consist in a magneto‐thermal computation. Thus, an electromagnetic finite element software must be coupled with a thermal one. An other improvement will rely on the study of actual situation in order to evaluate the accuracy of industrial sensors and to compare with measurements.

Originality/value

The paper develops a lamination stack model compliant with interlamination default analysis. As far as the authors know, this is the first study on 3D electromagnetic modeling.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 24 June 2022

Fabian Müller, Paul Baumanns, Martin Marco Nell and Kay Hameyer

The accurate simulation of electrical machines involves a large number of degrees of freedom. Particularly, if additional parameters such as remanence variations or…

Abstract

Purpose

The accurate simulation of electrical machines involves a large number of degrees of freedom. Particularly, if additional parameters such as remanence variations or different operating points have to be analyzed, the computational effort increases fast, known as the “curse of dimensionality.” The purpose of this study is to cope with this effort with the parametric proper generalized decomposition (PGD) as a model order reduction (MOR) technique. It is combined with the discrete empirical interpolation method (DEIM) and adapted to study characteristic electrical machine parameters.

Design/methodology/approach

The PGD is an a priori MOR technique. The technique is adapted to incorporate several additional parameters, such as the current excitation or permanent magnet remanence, to overcome the increasing computational effort of parametric studies. Further, it is combined with the DEIM to approximate the nonlinearity of the flux guiding material.

Findings

The parametric version of the PGD in combination with the DEIM is a suitable numerical approach to reduce computational effort of parametric studies, while considering nonlinear materials. The computational reduction is related to the influence of the different parameter variations on the field and on the number of parameters.

Originality/value

The extension of the PGD by several parameters associated with parametric studies of electrical machines enables to cope with the “curse of dimensionality.” The parametric PGD and the standard PGD–DEIM have been individually used to study different problems. The combination of both techniques, the parametric PGD and the DEIM, for nonlinear parametric studies of electrical machines represents the scientific contribution of this research.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 September 2012

Juliana Luísa Müller, Raphaël Romary, Abdelkader Benabou, Thomas Henneron, Francis Piriou, João Pedro Assumpção Bastos and Jean‐Yves Roger

Interlaminar short circuits in turbo generator stators can lead to local damage of the iron core. The purpose of this paper is to model an interlaminar short circuit…

Abstract

Purpose

Interlaminar short circuits in turbo generator stators can lead to local damage of the iron core. The purpose of this paper is to model an interlaminar short circuit diagnosis test on an existing structure.

Design/methodology/approach

This work presents the modeling of short‐circuited laminations in a stator yoke of a turbo‐generator. A 3D finite element model, associated to a homogenization technique, is used to calculate the short‐circuit current. The diagnosis test known as El Cid has been modelled as well.

Findings

Calculation results are compared with the experiment. The same tendency has been observed both in experimental and numerical results.

Research limitations/implications

Additional calculations may be performed (parametric studies) in order to investigate El Cid measuring under different conditions (different material properties, fault position, size), which may lead to a better interpretation of the results.

Practical implications

Modelling of short circuit diagnosis tests under different conditions may help with the interpretation of measuring results, predicting the fault size/seriousness and location. So, only the concerned parts of the stator have to be disassembled and repaired/rebuilt.

Originality/value

It is not easy to model numerically a structure with a short circuit inside, since different dimensions are involved: the fault and the varnish between laminations are much smaller than the stator itself. Thus, homogenization techniques have been used to model the lamination stack region. The combination of this technique with the modelling of the El Cid test constitutes a tool to study this kind of fault and calculate its severity and location in a stator.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 2004

T. Henneron, S. Clénet and F. Piriou

Methods to impose a voltage or a current in massive conductors in dual magnetodynamic potential formulations (Aφ and TKI‐Ω) are presented. In the Aφ formulation, a…

Abstract

Methods to impose a voltage or a current in massive conductors in dual magnetodynamic potential formulations (Aφ and TKI‐Ω) are presented. In the Aφ formulation, a supply voltage can be naturally imposed at the terminals of a conductor, but not a supply current. An equation must be added. This is the opposite for the TKI‐Ω formulation. In the paper all methods are described and compared on the basis of an example.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 17 January 2020

David Pánek, Pavel Karban, Tamás Orosz and Ivo Doležel

The purpose of this paper is to compare different reduced-order models for models of control of induction brazing process. In the presented application, the problem is to…

Abstract

Purpose

The purpose of this paper is to compare different reduced-order models for models of control of induction brazing process. In the presented application, the problem is to reconstruct temperature at the points of interests (hot spots) from information measured at accessible places.

Design/methodology/approach

The paper describes the process of induction brazing. It presents the full field model and evaluates the possibilities for obtaining reduced models for temperature estimation. The primary attention is paid to the model based on proper orthogonal decomposition (POD).

Findings

The paper shows that for the given application, it is possible to find low-order estimator. In the examined linear case, the best estimator was created using POD reduced model together with the linear Kalman filter.

Research limitations/implications

The authors are aware of two main limitations of the presented study: material properties are considered linear, which is not a completely realistic assumption. However, if strong coupling and nonlinear material parameters are considered, the model becomes unsolvable. The process and measurement uncertainties are not considered.

Originality/value

The paper deals with POD of multi-physics 3 D application of induction brazing. The paper compares 11 different methods for temperature estimator design.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 July 2020

Abdoulaye Ba, Huu Kien Bui, Gérard Berthiau, Didier Trichet and Guillaume Wasselynck

This paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing…

Abstract

Purpose

This paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing (NDT) technique to reduce the computation time.

Design/methodology/approach

The time harmonic electromagnetic problem is expressed in Aϕ formulation and lightened by using the surface impedance boundary condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved by using surface electromagnetic power density as thermal source.

Findings

The accuracy and the usefulness of the method for the design of the induction thermography NDT technique have been shown with acceptable deviation compared with a full FEM model. It is also observed that at high frequency, when the ratio between the local radius of the conductor and the skin depth is high, a very good accuracy can be obtained with the SIBC methods. At lower frequency, the effect of the curvature of the surface becomes significant. In this case, the use of the Mitzner’s impedance can help to correct the error.

Originality/value

The SIBC can be used for both massive coil and workpieces with open cracks to alleviate 3D FEMs of the coupled electrothermal model. The implementation in matrix form of the coupled electrothermal formulation is given in details. The comparisons with reference analytical solution and full 3D FEM show the accuracy and performance of the method. In the test case presented, the computation time is 6.6 times lower than the classical model.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 6 March 2017

Lorenzo Codecasa, Federico Moro and Piergiorgio Alotto

This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.

Abstract

Purpose

This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.

Design/methodology/approach

A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.

Findings

The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.

Research limitations/implications

Only linear magnetic materials are considered in the present formulation.

Practical implications

The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.

Originality/value

The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 September 2021

Miwa Tobita, Hamed Eskandari and Tetsuji Matsuo

The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN…

Abstract

Purpose

The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation.

Design/methodology/approach

This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state.

Findings

Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used.

Practical implications

The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large.

Originality/value

The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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