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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 quality of a local physical quantity obtained by the numerical method such as the finite element method (FEM) attracts more and more attention in computational electromagnetism. Inspired by the idea of goal-oriented error estimate given for the Laplace problem, this work is devoted to a guaranteed a posteriori error estimate adapted for the quantity of interest (QOI) linked to magnetostatic problems, in particular, to the value of the magnetic flux density. The development is principally based on an equilibrated flux construction, which ensures fully computable estimators without any unknown constant. The main steps of the mathematical development are given in detail with the physical interpretation. An academic example using an analytical solution is considered to illustrate the performance of the approach, and a discussion about different aspects related to the practical point of view is proposed.

This paper studies the electromagnetic noise behaviour of a 5 phase Interior Permanent Magnet Machine with fractional slot concentrated winding designed. A numerical model is used for analysing the torque characteristics and electromagnetic forces. The vibro-acoustics and mechanical resonance of the model are then investigated analytically. The purpose of both analyses is to identify the source of electromagnetic noise within the machine. A sonogram is also carried out on the existing prototype to correlate it with the numerical results. Finally, the choice of the appropriate method to attenuate noise for this case study is elaborated.

In this paper, we analyze the influence of the uncertainties on the behavior constitutive laws of ferromagnetic materials on the behavior of a turboalternator. A simple stochastic model of anhysteretic nonlinear B(H) curve is proposed for the ferromagnetic yokes of the stator and the rotor. The B(H) curve is defined by five random parameters. We quantify the influence of the variability of these five parameters on the flux linkage of one phase of the stator winding depending on the excitation current I. The influence of each parameter is analyzed via the Sobol indices. With this analysis, we can determine the most influential parameters for each state of magnetization (according to the level of I) and investigate where the characterization process of the B(H) curve should focus to improve the accuracy of the computed flux linkage.

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.

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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.

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.

This paper aims to propose an Improved Starting Point (ISP-) Newton method applied to vector potential A formulation for circuit coupled magnetostatic problems. These problems are usually known to vary greatly during the time. This impacts the quality of the initial guess of the Newton method and thus increases significantly the computational cost. The Newton method with vector potential formulation A has been analyzed. Numerical examples show the performance of our proposed ISP-Newton method.

This paper studies the electromagnetic noise behaviour of a 5 phase Interior Permanent Magnet Machine with fractional slot concentrated winding designed. A numerical model is used for analysing the torque characteristics and electromagnetic forces. The vibro-acoustics and mechanical resonance of the model are then investigated analytically. The purpose of both analyses is to identify the source of electromagnetic noise within the machine. A sonogram is also carried out on the existing prototype to correlate it with the numerical results. Finally, the choice of the appropriate method to attenuate noise for this case study is elaborated.

Abstract—The presented paper proposes a topology optimisation methodology based on the density-based method SIMP, and applied to a numerical example to validate the former. The approach and methodology are detailed, and the results for a 3D basic electromagnetic example are presented. The non-linear B(H) curve is also taken into account. Index Terms—gradient-based algorithm, relaxation of variables, SIMP density method, weighted objective sum

This paper presents multiphase permanent magnet machines with concentrated non-overlapped winding as a good candidate for automotive low voltage mild-hybrid applications. These machines often require a trade-off between low speed performances such as high torque density and high speed performances like flux weakening capabilities. This paper describes how to choose a key design parameter to ease this compromise, the slots/poles combination, according to three parameters: winding factor including harmonics factor, rotor losses amount thanks to a comparison factor, and radial forces balancing. The comparison criterions are based on both analytical formula and Finite Element Analysis

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.

This paper investigates the influence of the rotor structure on torque and Flux weakening region of V-shape IPM machine from TOYOTA PRIUS type, more specifically, keeping always the same magnet volume, we study the effect of the open angle between the two magnet segments of each V-shape pole on the machine performance. Moreover, in order to examine the impact of phase number on the machine characteristics, PRIUS structure is transformed into 5-phase machine of the same type and dimensions. As well, an optimization procedure is carried out to determine the optimal open angle according to main characteristics. The previous investigation is done by using a free Finite Elements Methods (FEM) program coupled with another optimization program. Using this obtained methodology the study analyzes for 3-phase and 5-phase machine the average and pulsation of torque, cogging torque, phase back-EMF, constant power operating capability

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.

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.

L’ajout d’aimants de compensation dans les espaces interpolaires de machines synchrones à pôles saillants permet d’atténuer les flux de fuites inducteur. Un prototype utilisant cette technique, dimensionné et construit, est étudié dans cette communication. L’effet de la compensation est d’abord illustré. Ensuite, le prototype est étudié en utilisant un modèle numérique. Différents points de fonctionnements sont simulés et les résultats sont comparés a des mesures expérimentales tant en grandeurs globales que locales.

This paper investigates the influence of the rotor structure on torque and Flux weakening region of V-shape IPM machine from TOYOTA PRIUS type, more specifically, keeping always the same magnet volume, we study the effect of the open angle between the two magnet segments of each V-shape pole on the machine performance. Moreover, in order to examine the impact of phase number on the machine characteristics, PRIUS structure is transformed into 5-phase machine of the same type and dimensions. As well, an optimization procedure is carried out to determine the optimal open angle according to main characteristics. The previous investigation is done by using a free Finite Elements Methods (FEM) program coupled with another optimization program. Using this obtained methodology the study analyzes for 3-phase and 5-phase machine the average and pulsation of torque, cogging torque, phase back-EMF, constant power operating capability.

C ONTRIBUTION A LA MODELISATION 3D DES SYSTEMES ELECTROMAGNETIQUES BASSE FREQUENCE A L ’ AIDE DE LA METHODE D ’ INTEGRATION FINIE (FIT) Résumé : La méthode des éléments finis (MEF) est la méthode la plus utilisée pour résoudre numériquement des problèmes rencontrés en mécanique, en thermique, en électromagnétisme, etc. Dans le domaine du génie électrique elle permet de réaliser la simulation de dispositifs électromagnétiques avec une grande précision. Cependant, devant les capacités grandissantes des outils de calcul, on est amené à modéliser des systèmes de plus en plus complexes. Paradoxalement, devant les temps de calcul impor- tants que cela engendre, l’intérêt des industriels se porte sur des méthodes alternatives permettant d’obtenir des résultats plus rapidement. Les travaux menés durant cette thèse se sont portés sur l’étude d’une méthode alter- native, la technique d’intégration finie (FIT). Cette méthode permet d’obtenir un bon compromis entre rapidité des temps de calcul et qualité de la solution. À travers des problèmes d’électrocinétique, de magnétostatique et de magnétodynamique, il est mon- tré, avec ces travaux, que les résultats obtenus à l’aide de la FIT sont de bonnes qualités comparés à la méthode des éléments finis. Des outils appliqués à l’imposition des gran- deurs globales électriques et magnétiques sont aussi présentés dans ce travail. Mots clefs : Technique d’intégration finie, modélisation électromagnétique, électrociné- tique, magnétostatique, magnétodynamique, grandeurs globales. CONTRIBUTION TO THE 3D MODELLING OF LOW FREQUENCY ELECTROMAGNETIC SYSTEMS USING FINITE INTEGRATION TECHNIQUE (FIT) Abstract : To solve numerically the mechanics, thermals and magnetodynamics prob- lems, the finite element method is the most used. In electrical engineering, this method allows the simulation of electromagnetic devices with a great accuracy. However, in spite of growing capacity of the computers, the studied models become more and more complicated. From an industrial point of view, these computation times are not accept- able. Therefore, a fast and reliable numerical tool is necessary. The developments realized during this thesis concern an alternative method, the fi- nite integration technique. This method allows finding a compromise between computa- tion times and accuracy. For the cases of electrokinetics, magnetostatics and magneto- dynamics, simulations using FIT proved that results are accurate. Mathematical tools used to impose the electric and magnetic quantities. Keywords : Finite integration technique, electromagnetic modeling, electrokinetic, magnetostatic, magnetodyynamique, global quantities.