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Due to the advancement in the development of semiconductors used in the power converters, the printed circuit boards (PCBs) require an in-depth study of their electromagnetic behavior. To characterize the behavior of the PCBs, the Darwin model is employed, which can take into account all the coupled effects, namely resistive, inductive, and capacitive effects, at the intermediate frequencies. Nevertheless, the study of particular structures having a geometric dimension smaller than the others can create meshing difficulties. The modeling of thin structures by the finite element method requires the optimization of the mesh. To circumvent this issue, the shell elements for both node and edge elements are applied in this work. Finally, to validate the proposed approaches, two PCBs with different geometries are studied in both time and frequency domains, where the measurements for a single PCB are provided to compare with the numerical results.

The magnetic behavior of a lamination stack made of grain-oriented electrical steel (GOES) is investigated under non-conventional 3D magnetic flux excitations. An experimental demonstrator has been designed to study a normal orientation of the magnetic flux path, with regard to the lamination plane, combined with different in-plane orientations of the easy magnetization axis of the lamination stack. The results in terms of the magnetic flux distribution and the iron losses are presented and discussed.

The Darwin model, which simultaneously incorporates resistive, capacitive, and inductive effects but neglects the radiation one, has recently attracted more and more attention in the research area. For our industrial application needs, the finite-element (FE) system to solve derived from the Darwin model generally has a large size, which is beyond the capabilities of the direct solvers due to the memory limitation. In this work, a specially designed formulation amenable to an iterative solver is proposed for industrial applications. Moreover, a detailed comparison of different cases is carried out on two different examples.

Regularly used in power transformers, grain-oriented (GO) steels are also usually chosen for the manufacturing of the stator cores of hydro and turbo-generators. These steels are renowned for their high magnetic performances in the rolling direction (high permeability and low magnetic losses). Nevertheless, in a turbo-generator where GO steels are employed to reduce the size of the stator core, the magnetic flux flows through several successive directions within the plane of the steel. So, the anisotropic behavior of the GO steel has to be considered in the design step of the related devices in order to improve their energy efficiency as well as their diagnosis based on modeling. In this paper, an anisotropic phenomenological iron loss model, quite recently developed, has been studied and successfully implemented in a finite element method (FEM) simulation environment. The implementation has been validated against experimental data achieved on an industrial conventional GO grade typically used in turbogenerators. The results show a good agreement of the computational results with the experiments for both quasi-static and dynamic regimes.

The purpose of this study is to investigate, through finite element (FE) simulations, the effect of the demagnetizing field in Epstein characterization of grain-oriented electrical steels. A 3D finite element simulation has been realized to represent the parallel and X-stacking configurations in the Epstein frame. The numerical results have been compared with experimental measures. In a parallel configuration, the measured induction is actually the one in the material, whereas the resulting magnetic field differs from the applied one (in magnitude and angle) due to the shape anisotropy (demagnetizing field). In X-stacking configuration, the resulting magnetic field is close to the applied magnetic field (and then the supposed excitation field in the Epstein frame), whereas the magnetic induction has deviated from the axis of the strips.

The modeling of the capacitive phenomena, including the inductive effects becomes critical, especially in the case of a power converter with high switching frequencies, supplying an electrical device. At a low frequency, the electro-quasistatic (EQS) model is widely used to study the coupled resistive-capacitive effects, while the magneto-quasistatic (MQS) model is used to describe the coupled resistive-inductive effects. When the frequency increases, the Darwin model is preferred, which is able to capture the coupled resistive-capacitive-inductive effects by neglecting the radiation effects. In this work, we are interested in specifying the limits of these models, by investigating the influence of the frequency on the electromagnetic field distributions and the impedance of electromagnetic devices. Two different examples are carried out. For the first one, to validate the Darwin model, the measurement results are provided for comparison with the simulation results, which shows a good agreement. For the second one, the simulation results from three different models are compared, for both the local field distributions and the global impedances. It is shown that the EQS model can be used as an indicator to know at which frequency the Darwin model should be applied.

This paper presents a novel method for demagnetization fault detection in permanent magnet synchronous machine (PMSM). Demagnetization fault is a common problem existing in PMSM which deteriorates the machine performance and can lead to serious subsequential machine damages. Unlike the most popular method based on the analysis of the machine currents for detecting this type of fault, the approach proposed in this paper analyzes the voltage signal of a non-invasive search coil by means of Hilbert Huang transform. Simulations are carried out with a two dimensional finite element analysis (FEA) for different demagnetization levels to test the capability of the proposed method to detect PM demagnetization faults.

The Maxwell Tensor (MT) method is widely used to compute global forces or local surface forces for vibroacoustic design of electrical machines under electromagnetic excitation. In particular, the air-gap MT method is based on a cylindrical shell in the middle of the air gap. This article proposes to quantify the differences between the air-gap MT and the magnetic force wave experienced by the stator. In particular, the air gap to stator transfer and the tooth mechanical modulation effects are studied. A new formula is proposed to extend the tooth modulation effect to tangential forces. A numerical application is performed with a turbo-alternator to illustrate the respective and combined effects of both phenomena. This article highlights that the tooth mechanical modulation is relevant even for electrical machines with a high number of teeth. In addition, the combination of the two phenomena has a clear impact on the calculated surface force. Therefore, it is recommended to take into account the air-gap transfer for any study of the tooth mechanical modulation effect.

An improved starting point Newton method applied to 3-D scalar formulation in magnetostatics is proposed in this paper. Compared with the classical Newton method, the inexact-Newton and quasi-Newton methods are reported by testing on a benchmark problem as well as an industrial example. Remarkable convergence acceleration using the proposed strategy is observed, and thus, it significantly reduces the computational time.

In this paper a guaranteed equilibrated error estimator is developed for the 3D harmonic magnetodynamic problem of Maxwell’s system. This system is recasted in the classical A-phi potential formulation and solved by the Finite Element method. The error estimator is built starting from the A-phi numerical solution by a local flux reconstruction technique. Its equivalence with the error in the energy norm is established. A comparison of this estimator with an equilibrated error estimator already developed through a complementary problem points out the advantages and drawbacks of these two estimators. In particular, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators.

In the domain of field computation with the finite element method, choosing the mesh refinement is an important step to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators are frequently used. In this communication we propose to analyze and to compare residual and equilibrated error estimators for eddy current problems in the case of A-φ and TΩ formulations. The different properties of the estimators will be discussed.

Loss values are key parameters for designing high performance high frequency (HF) magnetic components for power electronics (PE) converters. With the increase of PE switching frequencies, copper losses have to be precisely quantified, ideally until some megahertz. In the literature, many 2-D numerical simulations based on finite element analysis (FEA) are performed for such computations. 3-D FEA studies of planar components are still limited because of modeling problems, computational resources and computing time. In this paper, quantitative comparisons between 2-D and 3-D simulation results for planar inductors are achieved focusing on copper loss computation. Results are compared in terms of simulation performances and accuracy. The aim of the paper is to highlight benefits of 2-D and 3-D FEA simulations in order to choose the appropriate model according to the studied problem.

This paper presents an efficient method to calculate the magnetic forces on bodies in contact. The forces are computed through the local application of the virtual work principle on degenerated air-gap elements. The results from this method are compared with those from other software and validated with measurements on a permanent magnet setup. Not only is this technique very accurate, but it also reduces the computational burden related to the problematic meshing of thin layers. The implementation of this method in an open source finite element software having facilities for higher order elements and parallel computation unlocks a cost effective and effectual platform for an electromechanical computation of electromechanical devices and magnetic materials.

This paper focuses on a topology optimization method for laminated busbars in power converters that minimizes the quantity of copper used while keeping the temperature under the allowed limits. Busbars are widely studied for adding their stray inductance to the commutation loop, which causes surge voltage across the power devices. However, the study of heat dissipation is essential to control hotspots in the busbar and preserve the converter components. Current density and temperature are sensitive to shape modifications; hence, topology optimization based on multiphysics simulations is an aspect to be considered when designing prototypes for a good cost performance ratio. The temperature is calculated by an electrothermal two-dimensional (2-D) finite element method (FEM) superposition approach. Busbar plates are modeled in 2-D since the thickness is constant. Furthermore, the different layers are related by the thermal equations reproducing the heat transfers regarding the overlap in the laminated busbar. Simulation results are validated by experimental tests. Comparison with 3-D FEM proves the 2-D approach to be faster while remaining accurate and a perfect method for topology optimization resolutions, which are very time consuming for three-dimensional (3-D) geometries. The busbar topology optimization is made by maximizing the energy transfer with the environment and by varying the electric and thermal conductivities of the mesh elements. Optimization leads to more than 50% volume reduction.

In this paper a method in 2-D frequency domain is presented to simulate a laminated iron core with a short-circuit between several magnetic sheets. The approach consists in coupling homogenization methods and finite element method. The defect is modeled with A* modified vector potential formulation and the rest of the structure with a homogenization method. The coupled method is applied to a lamination stack containing a short-circuit and compared to the reference, where the A* formulation is applied on the whole domain. Finally, a thermal modeling of lamination stack is presented to study the influence of an insulating defect.

Predetermination of losses and inductance values in the design phase, is necessary for the development of high-performance magnetic components for power electronics. Numerical modeling, based on the Finite Element Method (FEM) can be used to determine the characteristics of a particular component with a complex geometry in high frequency (HF). These models are very accurate but the computation time required is high compared to analytical models. The Model Order Reduction (MOR) methods can be applied to reduce the computation time while maintaining high accuracy. Nowadays, the Proper Orthogonal Decomposition (POD) is the most popular of MOR approaches. This technique has been applied to study problems in many elds of engineering. In this paper, the POD method is developed to solve magneto-harmonic problems in order to study a planar magnetic inductor.

A framework for the finite element implementation of the formulas of local and global electromagnetic forces is presented. The theoretical framework, based on the Lie derivative, is applicable to 2-D and 3-D problems in the presence of arbitrary materials. The numerical properties of the proposed implementation, in terms of accuracy and convergence, are analyzed. An experimental setup is also presented for which accurate measurements have been carried out, and that can serve as a benchmark for the implementation.

In the modeling of eddy current problems, potential formulations are widely used in recent days. In this paper, the results of residual-based a posteriori error estimators, which evaluate the discretization error in the finite-element computation, are extended to the case of several kinds of source terms for both A/φ and T/Ω harmonic formulations. The definitions of the estimators are given and some numerical examples are provided to show the behavior of the estimators.

A strategy of mesh adaptation in eddy current finite element modeling is developed from both residual and hierarchical error estimators. Wished distributions of element sizes of adapted meshes are determined from the element-wise local contributions to the estimators and define constraints for the mesh generator. Uniform distributions of the local error are searched.

In this work, an a posteriori residual error estimator is presented for the 3D eddy current problem modeled by the space-time A-phi potential formulation. It is solved by the finite element method in space and the backward Euler scheme in time. Once the reliability as well as the efficiency of the estimator are established, two numerical tests are proposed: an analytical one in order to validate the theoretical results and a physical one in order to illustrate the performance for a real eddy current problem.

The finite element computation of eddy current problems introduces numerical error. This error can only be estimated. Among all error estimators (EEs) already developed, two estimators, called residual and hierarchical EEs, proven to be reliable and efficient, are theoretically and numerically compared. Both estimators show similar behaviors and locations of the error.

In finite element computations, the choice of the mesh is crucial to obtain accurate solutions. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we develop residual-based error estimators for magnetostatic problems with both classical formulations in term of potentials used, as well as the equilibrated error estimator. We compare their behaviors on some numerical applications, to understand the interest of each of them in the remeshing process.

Purpose: In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation. Design/methodology/approach: The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency). Findings: This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation. Originality/value: In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

For eddy current problems, potential formulations are widely used nowadays. In this paper, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A /φ and T /Ω harmonic formulations. A device with eddy currents is studied in order to show the efficiency of the proposed estimators.

In this paper, we focus on an a posteriori residual-based error estimator for the T/Omega magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/Phi formulation, the weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition for the T/Omega case is derived, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.

This paper is devoted to the derivation of an a posteriori residual-based error estimator for the A-Phi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.

The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.

In this paper, a spectral stochastic finite element method (SSFEM) is described and applied to quantify uncertainties in an industrial eddy current non destructive testing (NDT) problem. A new iterative solver based on the fixed-point method is proposed to solve the large scale linear system. The efficiency of the suggested iterative solver to tackle the SSFEM computational complexity is demonstrated. The SSFEM results and the computation times obtained with 2 and 4 random variables are compared to those given by the anisotropic adaptive sparse grid non intrusive spectral projection (NISP). On this application, the SSFEM dedicated solver is competitive with the adaptive sparse grids strategy.

Stochastic spectral finite-element method can be used to take into account some random aspects in the input data (material characteristic, source terms) involved in static electromagnetism problems. Similarly to the deterministic case, two potential formulations can be used in the stochastic case. The vector potential formulation applied to static problems is developed and compared to the scalar potential one, previously developed.

This paper deals with the study of static and dynamic rotor eccentricities of a synchronous generator using 3D FEM. First, both eccentricity cases are introduced as well as the used approach. Then the models of the structure, based on the magnetic scalar potential formulation and on the magnetic vector potential formulation, are presented. Two eccentricity modeling methods are introduced, the 2D eccentricity and the 3D eccentricity. Results obtained for magnetostatic and magnetodynamic cases related to both defects and their combination are presented and discussed.

The presented work is about the implementation of a vector hysteresis model in a Finite Integration Technique (FIT) calculation code. This is achieved in the magnetostatic case using the vector potential formulation and with the external electric circuit coupling. The used behavior law model is the vectorized Jiles-Atherton model with the magnetic flux density as input variable. The proposed approach is illustrated by modeling a coil made of Soft Magnetic Composite (SMC) magnetic core. Comparison with measured global quantities is also performed.

This paper deals with the study of static and dynamic rotor eccentricities of a synchronous generator using 3D FEM. First, both eccentricity cases are introduced as well as the used approach. Then the models of the structure, based on the magnetic scalar potential formulation and on the magnetic vector potential formulation, are presented. Two eccentricity modeling methods are introduced, the 2D eccentricity and the 3D eccentricity. Results obtained for magnetostatic and magnetodynamic cases related to both defects and their combination are presented and discussed.

This work deals with the implementation of a vector hysteresis model in a 2D finite element code with vector potential formulation. The inverse Jiles-Atherton hysteresis model leads to obtain a differential reluctivity tensor which can be directly applied to the field calculation equations.

Efficient numerical models have been already developed in 2D to take into account the movement of electromagnetic devices with rotating parts in the framework of the Finite Element Method (FEM). When the movement becomes complex it leads to large mesh distortions.A remeshing step is then required which increases the computational complexity and can also lead,in some cases,to numerical ripples on forces and torques due to the field projections between old and new meshes.Moreover,remeshing procedures in 3D remain an open topic.Meshless methods seem an appealing choice for alleviating the mesh constraints.The Natural Element Method (NEM)which,has known a growing interest in the domain of mechanics,allows to proceed in the meshless framework,avoiding one of the main drawbacks related to the vast majority of meshless techniques,as is the imposition of essential boundary conditions.In this paper,a variant of the NEM,known as constrained natural element method (C-NEM)is applied for simulating electromagnetic machines involving rotating parts.A new mixed strategy combining the finite element and the constrained natural element methods is proposed and then tested by using an appropriate error estimator.

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Abstract - To solve the Maxwell’s equations in the magnetosatic case the formulations in terms of vector potential or scalar potential can be used. If to solve the equations we use the Finite Element Method on the primal mesh we obtain two complementary solutions. In this paper, both formulations in terms of potential and using the fields H and B are developed and solved with the help of the Finite Integration Technique. The solutions computed in the primal and dual meshes are analysed and discussed.

In this paper the slip surface and the moving band techniques are used to model the rotation of electrical machines in 3D with FEM and the results are compared. For the slip surface technique, several method are explained; such as the locked-step approach and linear and quadratic interpolation. For this study, the proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no-load for the electromotive force and the cogging torque. Furthermore, the torque is also compared for the short-circuit case.

In this paper, the Finite Integration Technique and an approach to solve simultaneously the magnetic and electric circuit equations is presented in magnetostatic case. The developments of the FIT will be compared with those used for the Finite Element Method. As example of application an iron core coil is studied and the results of both approaches are compared

This communication presents a method to discretize electromagnetic source fields in the Whitney element spaces for static electromagnetic potential formulations. This method requires no finite element solution to calculate this source fields. It is based on the use of a facet or an edge tree. We will test it on electrokinetic, electrostatic and magnetostatic examples

In this paper, a claw pole permanent magnet machine is studied using a 3D scalar potential formulation. First, the discretization of Maxwell’s equations using Whitney’s elements is presented. Especially, the method to take the winding current distribution into account by means of source fields is detailed. Then, a numerical model of the studied machine is presented. Simulation results (inductance, EMF, torque) are discussed by comparison with experimental ones.

This paper presents a method of coupling magnetostatic potential formulations with electrical circuits for the 3D FEM. Allowing for the current density distribution in stranded conductors, two vectors N and K are introduced. A systematic method of decomposing both vectors in Whitney’s element spaces is suggested. This method can be used for coils with a complex shape. As an example of application a three-phase transformer is studied.

In this paper we propose, an approach for coupling magnetostatic and electric circuit equations applicable to the case of stranded conductors. The method based on the calculation of global quantities is presented and applied to the magnetic formulation Hs-Ă. The properties and calculation of source field Hs are also discussed. As an example we have studied a permanent magnet synchronous machine. At no load, the magnetomotive force is determined and compared with experimental results. A calculation when the generator has a resistance load is also presented

In this paper we study different approaches to introduce the source terms due to the inductors crossed by a uniform current density J 0 in 3D FEM. Two equivalent methods are developed to decompose the current density J in the facet element space with divergence free close to J0. This decomposition is used in the a-formulation without gauge condition. Moreover, from the flux facet the source field Hs can be calculated in the edge element space and introduced into the ö-formulation. As examples of applications we have studied a coil with a complex geometry and a iron core coil

Cette communication présente une approche permettant d’imposer le courant ou la différence de potentiel dans le cas d’un problème d’électrocinétique. Pour une formulation en potentiel vecteur, l’approche proposée a été implantée dans un code de calcul basé sur la Technique d’Intégration Finie et dans un code éléments finis. Des simulations sont réalisées pour des cas simples et les résultats sont comparés à ceux obtenus à l’aide de la méthode des éléments finis.

In this research, we propose an ad hoc method for identifying adequate full permeability tensors for finite element method (FEM) simulation of grain oriented electrical steels (GOES). The tensors are obtained from dedicated measurements requiring only unidirectional excitation field. This method relies on the one hand, on the Enokizono approach which was originally established based on measurements under rotating field and on the other hand on the Fiorillo model of magnetization processes in GOES.

In this research, the magnetic behavior of a lamination stack made of grain-oriented electrical steel (GOES) is investigated under non-conventional 3D magnetic flux excitations. An experimental prototype has been designed to study different orientations of the magnetic flux path, with regard to the lamination plane, combined with different in-plane orientations of the GOES easy magnetization axis.

The modeling of the capacitive phenomena including the inductive effects becomes critical, especially in the case of a power converter with high switching frequencies supplying an electrical device. To capture the coupled capacitive-inductive effects, the Darwin model is invoked in the frequency domain, which only neglects the radiation effects of the full Maxwell system. In this work, we are interested in the comparison of the different solvers, both iterative and direct, for ungauged and gauged finite-element (FE) systems for Darwin model. In addition, to handle the huge FE resulting matrix due to the industrial application, a novel formulation is proposed.

Grain-oriented (GO) materials are widely known for their strong anisotropic behavior. Their magnetic characteristics depend on the angle between the applied magnetic field and rolling direction (RD). However, these characteristics can be further modified according to their stacking configuration and to the influence of the demagnetizing field. In this paper, a 3-D finite element analysis is performed in order to study the effect of the parallel and x-stacking configuration on the magnetic properties of the lamination stack. The results are interpreted in terms of the demagnetizing field which vectorially combined with the applied field affects the magnetization.

Grain-oriented (GO) materials are widely known for their strong anisotropic behavior. Their magnetic characteristics depend on the angle between the applied magnetic field and rolling direction (RD). However, these characteristics can be further modified according to their stacking configuration and to the influence of the demagnetizing field. In this paper, a 3-D finite element analysis is performed in order to study the effect of the parallel and x-stacking configuration on the magnetic properties of the lamination stack. The results are interpreted in terms of the demagnetizing field which vectorially combined with the applied field affects the magnetization.

The Maxwell Tensor (MT) method is widely used to compute global forces or local surface forces for vibroacoustic design of electrical machines under electromagnetic excitation. In particular the airgap Maxwell Tensor method is based on a cylindrical shell in the middle of the airgap. This communication proposes to quantify the differences between the airgap MT and the magnetic force wave experienced by the stator. In particular the airgap to stator transfer and the tooth mechanical modulation effect are studied. A numerical application is performed with a turbo-alternator to illustrate the respective and combined effects of both phenomena. The communication highlights that the tooth mechanical modulation alone is not necessary relevant for electrical machines with a high number of tooth. However the combination of both phenomena has a clear impact on the computed magnetic surface force.

This paper presents a novel method for demagnetization fault detection of per-manent magnet synchronous machine (PMSM). Demagnetization fault is a common problem existing in PMSM which deteriorates the machine performance and can lead to serious secondary machine damages. Unlike the most popular method for detecting this fault which is based on the analysis of the machine current, the approach proposed in this paper analyses the voltage signal of a non-invasive search coil by means of Hilbert Huang transform. Simulations are carried out with a two dimensional finite element anal-ysis (FEA) for different demagnetization levels to verify the proposed method.

In an electrical machine, the Maxwell Tensor is widely used to compute global forces or local pressure along a surface in the air. This communication proposes to highlight the limits of the method with an academic case of slotless stator and rotor. In particular an analytic demonstration shows the existence of coefficients depending on the geometry and the wavenumber between the application of the Maxwell Tensor in the air-gap and the stator magnetic pressure.

Shaft voltage is present in all electrical machines and can be useful as a diagnosis variable but first, it is important to quantify the effect of some defects. 2D numerical models have already been used to tackle this point. However, 3D effects due to end windings can have a significant influence on this voltage. This paper deals with the study of a turbo-generator using a 3D finite element model in order to investigate this task.

Integrated Drives are a target in terms of simplicity in complex systems such as transportation. Anyway the integration of the power component inside the electrical machine induces challenges if the compactness is required. The CE2I project, for “Smart Integrated Drives”, searches to deal simultaneously with the constraints such as better thermal control and modelling, more efficient numerical virtual modelling for co-simulation, exploration of new materials and use of low losses, high frequency wide-band-gap (WBG) components.

Harmonic Balance Finite Element method combined with homogenization method is used to model lamination stacks. The Harmonic Balance gives directly the steady-state solution and the homogenization method reduces the number of unknowns. The numerical model takes into account the nonlinear magnetic behavior and the electric conductivity. The results of the proposed method are compared with those obtained from a classic approach.

In large turbo-generators, the analysis of the shaft voltage can be useful to diagnose some defects such as eccentricities or rotor short circuit. To do that, the first step is to quantify the inherent effect of each defect on that voltage. This paper deals with the study of a simplified synchronous generator with a smooth slotless stator using a numerical model in order to well understand the effect of each defect.

The Harmonic Balance combined with the finite element method enables to obtain the steady-state solution of electromagnetic problems. In this communication, we propose to apply this approach to study a laminated iron core submitted to a magnetic flux arising from a Pulse Width Modulation (PWM) voltage. The proposed numerical model takes into account the nonlinear magnetic behaviour, the electric conductivity and a short circuit between steel sheets.

This paper presents an efficient method to calculate the magnetic forces on bodies in contact. The forces are computed through local application of the Virtual Work principle on degenerated airgap elements. The results from this method are compared with those from another software and validated with measurements on a permanent magnet setup. Not only is this technique very accurate, but also reduces the computational burden related to the problematic meshing of thin layers. The implementation of this method in an open source finite element software having facilities for higher order elements and parallel computation unlocks a cost effective and effectual platform for electromechanical computation of electromechanical devices and magnetic materials.

In the case of high power synchronous machines, shaft voltage can induce high currents yielding to bearing damages but it can also constitutes a variable to be used to diagnosis some machine defects. Therefore, it is important to well model the phenomenon in order to use it in further diagnosis tool.

In this paper, the Harmonic Balance Method is used to obtain the steady-state solution of a laminated iron core with an imposed magnetic flux. The numerical model takes into account the nonlinear magnetic behaviour, the electric conductivity and a short circuit between steel sheets. The results of the Harmonic Balance Method are compared with those obtained from a classic approach.

The goal of this paper is to identify rotor inter-turn short-circuits of an alternator. The detection method is based on the analysis of a ux probe signal located in the air gap of the machine. Previous works have shown that pattern recognition can be applied to detect such a fault by using the experimental data as prototypes. A new method is developed here by considering a learning step based on simulation. Therefore the machine is modeled and validated. A feature selection is made by considering feature correlation and disparity. Finally, k nearest neighbors is used to classied experimental test data.

Predetermination of inductances and losses are needed to effectively design magnetic components used in power electronic converters. Their behaviours change with frequency and have to be determined accurately over a wide frequency range, commonly up to 30MHz to account for EMI aspects. In many papers, 2D finite element simulations are widely performed for the calculations of inductances and losses of planar components. These 2D numerical models are generally taken as references to develop analytical models, including the specific case of High Frequency copper losses. 3D studies of such planar components are still limited because they leads to problems related to modeling, computing resources and computing time. In this paper comparisons in terms of performance and precision for 2D and 3D models of planar inductors is presented. The obtained results are compared with impedance measurements on prototypes.

The finite element computation of eddy current problems gives numerical error. This error cannot be calculated, but can only be estimated. Among all error estimators already developed, it is proposed to compare two proven estimators called residual and hierarchical error estimators.

The goal of this paper consists in applying pattern recognition methods to turbo-generators. Previous works have shown that a monitor, thanks to pattern recognition, is practical on asynchronous machines. This procedure has rarely taken advantage of these methods for turbogenerator. The statistical model has been obtained from harmonics extracted from flux probes and from stator current and voltage. For this purpose, the main way is to build a learning matrix to predict the functional state of a new measurement. Finally, three classifiers have been compared: k Nearest Neighbors, Linear Discriminant Analysis and Support Vector Machines. The best classification result is obtained by Linear Discriminant Analysis combined with Factorial Discriminant Analysis achieving a score of 84.6%.

For the eddy current problem, the potential formulations are widely used today. In this communication, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A-Phi and T-Omega harmonic formulations. An example is carried out to show the behavior of our estimators.

The parallelization of numerical simulation algorithms, i.e., their adaptation to parallel processing architectures, is an aim to reach in order to hinder exorbitant execution times. The parallelism has been imposed at the level of processor architectures and graphics cards are now used for general-purpose calculation, also known as “General-Purpose computation on Graphics Processing Unit (GPGPU)”. The clear benefit is the excellent performance over price ratio. Besides hiding the low level programming, software engineering leads to a faster and more secure application development. This paper presents the real interest of using GPU processors to increase performance of larger problems which concern electrical machines simulation. Indeed, we show that our auto-generated code applied to several models allows achieving speedups of the order of 10x.

In this paper a residual-based error estimator is proposed to evaluate the numerical error induced by the computation of the electromagnetic systems using a Finite Element Method in the case of the harmonic A-Phi formulation. This estimator is based on the evaluation of quantities weakly verified by the formulation. Furthermore as this estimator verifies the notions of reliability and efficiency it allows to estimate the qualities of local and global solutions. Two examples of electromagnetic systems with current density induced are used to show the efficiency of the proposed estimator.

This paper deals with the study of the effects of the eddy current induced in the damper bars of a synchronous machine at steady state. A non-salient pole synchronous machine, with damper bars, is modelled in magnetostatic and magnetodynamic cases taking into account the end rings. The time variation of the no load back emf is calculated in both cases and the results are compared to measurements to highlight the effects of the induced currents.

In time-domain electromagnetic fields computation, numerical methods (such as Finite Element Method (FEM), Finite Integration Technique (FIT) [1-3] and etc.) have been applied. For the time- domain integration solution, explicit and implicit schemas have been widely used. In comparison with implicit methods, the explicit methods are easier to realize in terms of computation complexity, however, they are constrained by the stability condition. This condition may require a small time step and therefore a prohibitive computing time. Another possibility is to use an implicit schema which ensures the numerical stability. Unfortunately the implicit methods require equation solved at each time step [4]. As a consequence, despite of a free choice on time step, the computation time using the full implicit methods increases. In this paper, fixed-point explicit calculation is introduced to an implicit schema. This method combines the two advantages of implicit and explicit methods: no stability condition and no equation solving. The solver is then applied to a time-domain eddy current problem. Using orthogonal mesh cells and FIT, the mass-matrices in discrete formulations are diagonal. The fixed- point explicit method allows direct calculations without matrix inversion or decomposition.

In finite element computations, the choice of the mesh is crucial to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we analyze and compare the residual and equilibrated error estimators for magnetostatic problems.

This paper deals with the study of rotor turbogenerator eccentricities using an analytical approach and FEM. First, we present the cases of eccentricities and the method, based on the measure of the flux density in the air-gap, used to detect the faults. Both models, the analytical approach and the numerical one are then introduced. Using these models, static, dynamic and combined eccentricities are studied at no load. The results obtained by both approaches are compared and the limits of the analytical model are underlined relatively to the effect of the non linearity of the magnetic material characteristic and the induced eddy currents.

This paper deals with the study of interturn short circuits in rotor windings of a synchronous generator using FEM. Results obtained for magnetostatic and magnetodynamic cases are presented and discussed.

Stochastic Spectral Finite Element Method (SSFEM) can be used to take into account some random aspects in the input data (material characteristic, source terms) involved in static electromagnetism problems. Similarly to the deterministic case, two potential formulations can be used in the stochastic case. The vector potential formulation applied to static problems is developed and compared to the scalar potential one, previously developed.

The modeling and simulation of electrical systems use a very large computational algorithms to solve their problems. The Conjugate Gradient (CG) solver is an effective technique for symmetric positive definite systems. It is suitable for systems of the form Ax=b, where A is a known, square, symmetric, positive-definite sparse matrix, x is a unknown solution vector and b is a known vector. A and b are obtained from the discretization of the Finite-Element Method (FEM).

The paper deals with the study of static and dynamic rotor eccentricities of a synchronous generator using 3D FEM. First, both eccentricity cases are introduced as well as the used approach. Then, the model of the structure, based on the vector potential formulation is presented. Results obtained for magnetostatic case related to both defects and their combination are presented and discussed. The saturation effect is highlighted.

The Finite Integration Technique is used in the different engineering domains as well as to computing the electromagnetic phenomena. This technique is efficient if the mesh is generated by hexahedron elements. Moreover the matrix system, obtains from a regular mesh, can be exploit to use the parallel direct solver. In fact, in reordering the unknowns by the nested dissection method, it is possible to construct directly the lower triangular matrix of the Cholesky factorization with many processors without assembling the matrix system. In this paper, the parallel direct solver is described and the efficiency is shown as function to the number of processors.

In this paper we present a formulation to solve 3D magnetostatic field called “source-field” method. In this method the influence of the imposed coil current is replaced by the magnetic fields created by the coil on the edges of the finite element mesh. This technique is very robust and presents accurate and fast results, but the edge tree construction can be a delicate task. We present, firstly, the source-field method and then we propose a way intended to create the edges tree as well as the conductor facets tree, also necessary.

This paper presents a method allowing to impose global electrics quantities, in a time step magnetodynamic case, simulated with the Finite Integration Technique. The A- and T-Ω formulations are developed and two vectors fields are associated in order to impose and compute global quantities, such as currents and voltages. Several simulations, applied to a system with two conductors, were carried out and the results were compared to those obtained with the finite element method.

Application of different iterative methods (CG,MRTR, SQMR, MINRES) are proposed to solve linear systems from Finite Element Method (FEM) in 3-D electromagnetic field analysis, and their convergences are compared.

In this paper, the overlapping method is applied to connect non-conforming tetrahedral meshes. At first the FEM formulation is described. The overlapping method is presented as well as its implementation in a FEM calculation code. At last, applications will be studied and discussed.

Recently, magnetic gearboxes know a real interest and have been the subject of many studies due to their high performances. However, their principle is often issue from the mechanical gearbox one and then they do not offer any degree of freedom. In this paper, we propose a magnetic gearbox constituted of two electromagnetic structures. This introduces two degrees of freedom and then the system can also insure clutch operating. First, the operating of the system is described. Then, its behavior is studied using a numerical model based on 3DFEM. Different results given by 3D analysis are presented.

In this paper, the overlapping method is applied to connect non-conforming tetrahedral meshes. At first the FEM formulation is described. The overlapping method is presented as well as its implementation in a FEM calculation code. At last, applications will be studied and discussed.

In this paper, a hybrid method is proposed for the simulation of rotating electrical machines taking into account the end winding effect. The method is based on the sliding surface that is decomposed on two parts. In the air gap we use the interpolation method at the second order and in the area of the end winding the Surface Interpolation Method (first order). As application a turbo-generator is studied.

Usually the Finite Element Method (F.E.M) is used to model the electromagnetic devices for low frequency. But other methods can be used as the Cell-Method and the Finite Integration Technique (F.I.T.). The presented work is a comparative study about these methods. Their theories are reminded to show that the same source field can be used for all methods. The properties of the mass matrices generated though the three different methods are also discussed. Finally, as an example of application an iron core coil supplied by a voltage source is modelled.

In this paper three techniques ( the locked-step approach, the overlapping method and the nodal interpolation method) are compared to model the rotation of electrical machines in 3D using FEM. These methods are associated with a formulation expressed in terms of scalar potential. To extend the possibilities of the interpolation method we propose the Surface Interpolation Method, which allows us to use non-conform meshes in the air gap of the studied machine. These different techniques are used to model a permanent magnet machine and a turbo-generator. The results obtained are compared by calculating the electromotive force and the torque.

In this paper we compare three techniques to model the movement in 3D FEM using both classical formulations to solve the magnetic equations. To compare the methods a permanent magnet synchronous machine is modelled. The comparison is done at no load on the electromotive force and the cogging torque.

Nous proposons une approche de couplage entre une formulation éléments finis spectrale et une approche d’homogénéisation afin de modéliser un empilement de tôles. L’approche spectrale permet d’obtenir directement le régime permanent, l’homogénéisation permet de réduire le nombre d’inconnues et la formulation classique nous permet de prendre en compte les effets de bord des tôles. Notre approche prend en compte une loi de comportement magnétique non linéaire et une conductivité électrique dans les tôles. Les résultats de notre approche de couplage sont comparés aux résultats d’une approche classique de type éléments finis pas à pas dans le temps.

La prédétermination, dans la phase de dimensionnement, des pertes et des valeurs d’inductances est nécessaire à l’élaboration de composants magnétiques performants pour l’électronique de puissance. La modélisation numérique peut être utilisée pour déterminer les caractéristiques propres d’un composant notamment lorsque sa géométrie est "complexe" ou que la fréquence d’utilisation est élevée. Ces modèles sont très précis mais le temps de simulation nécessaire est important par rapport à des modèles analytiques plus simplistes. Les méthodes de réduction de modèles, type POD ou autres, permettent de diminuer le nombre de ces simulations numériques tout en conservant une grande précision.

Dans le monde de l’électronique de puissance il est impératif d’avoir une méthode de conception adaptée aux exigences et aux limitations du produit avec une optimisation sur les coûts et les prestations. Dans ce travail, on présente la simulation électromagnétique des busbars dans le but de calculer avec précision l’inductance et la densité de courant et ainsi de prévoir, par un couplage faible, la température de l’ensemble (conducteurs et isolants).

La pré-détermination des valeurs de pertes et d’inductances est nécessaire à l’élaboration de composants magnétiques performants pour l’électronique de puissance. Leurs caractéristiques propres, variant en fonction de la fréquence, doivent être déterminées de manière précise sur une large gamme de fréquences, idéalement jusqu’à 30MHz pour tenir compte des aspects CEM. Dans la littérature, des simulations éléments finis 2D sont largement utilisées pour ce type de calcul. Ces modélisations servent généralement de référence pour le développement de modèles analytiques, notamment pour le cas spécifique des pertes cuivre. L’étude en 3D de ce type de composant est encore très peu développée car elle engendre des problèmes de modélisation, de ressources informatiques et de temps de calcul. Dans cet article la comparaison en termes de performances et de précisions pour des modèles d’inductances planar en 2D et en 3D est présentée. Les résultats obtenus sont comparés à des mesures d’impédances sur des prototypes.

Cette communication présente une méthode pour discrétiser la densité de courant, en imposant une divergence nulle et en minimisant l’erreur par rapport à la densité de courant exacte et uniforme.