Individual information

This paper describes a methodology for modelling a six-phase claw-pole alternator with its electrical environment. Magnetic nonlinearities, eddy currents and rectifiers are taken into account. To solve magnetodynamic problems, we use the modified magnetic vector potential formulation. The complex structure of the machine requires a 3D finite element analysis. To limit the mesh size, we introduced a refinement strategy based on the calculation of the time derivative of magnetic vector potential, solution of the magnetostatic case. In addition, we propose to reduce the transient state by improving the initial solution from the solution of a magnetostatic problem. These different numerical techniques reduce drastically the computational time and memory resources. To validate the proposed approach, some results are compared with experimental ones.

To determine the steady state of an electromagnetic structure with the finite element method without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important. 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 to Newton method to accelerate the convergence. The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient is very low it is preferable to use the classical approach namely the time stepping finite element method. 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. In the context of the use of the time stepping finite element method, 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 gives directly the steady state. The novelty is the proposal of the waveform relaxation Newton method to obtain directly the steady state in the case of the study of the three phases transformer

In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetic devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared to the time step used to discretize the time domain. In this paper, a method based on Waveform Relaxation Method is developed in order to impose the steady state of the solution in the case of a nonlinear magnetostatic problem coupled with electric circuit equations.

This paper presents a 3-D finite element method to determine the steady state operation for magnetostatic problems coupled with electrical circuit equations. For this purpose, the waveform relaxation method combined with the Newton method (WR-NM) is developed. This method is especially suitable to long transient problems. To show the efficiency of this approach a three-phase transformer is studied. The results show that the WR-NM becomes very efficiency when the transient state is more important than about 10 periods.

In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetism devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared with the time step used to discretize the time domain. In this communication, the Waveform Relaxation Method is developed to impose the steady state of the solution in the case of magnetostatic problem coupled with electric cricuit equation.

Dans le domaine du Génie Électrique, la méthode des éléments finis (MEF) associée à une approche pas à pas dans le temps est la plus simple, la plus précise et la plus robuste des méthodes pour modéliser les champs magnétiques dans des dispositifs électromagnétiques en basse fréquence. Néanmoins, cette méthode peut conduire à des temps de calcul extrêmement importants lorsque la constante de temps du système étudié est relativement petite en comparaison de la durée du régime transitoire. C'est dans ce contexte que s'inscrit ces travaux de thèse intitulés « Modélisation numérique par la méthode des éléments finis des systèmes électrotechniques: recherche du régime permanent ». Dans ce manuscrit, une méthode numérique nommée Waveform Relaxation-Newton Method (WR-NM) a été développée. Celle-ci est basée sur la Waveform Relaxation Method (WRM) à laquelle des conditions de périodicité sont appliquées afin d'imposer le régime permanent directement pour des problèmes électromagnétiques couplés à des équations de circuit. La convergence de cette méthode étant similaire à celle d'une méthode point-fixe, elle a été combinée à la méthode de Newton-Raphson dont la convergence est quadratique. Afin de valider et de tester la robustesse de la WR-NM, plusieurs applications sont présentées dans le manuscrit. Des gains importants en temps de calcul sont signifiés en comparaison à l'approche classique et ce pour une précision de la solution identique. Un dernier exemple concernant la modélisation d'une machine à griffes couplés à un pont redresseur montre que la WR-NM peut également être employé dans un cadre industriel. Recherche du régime permanent, Conditions de périodicité, Couplage circuit, Éléments finis, Méthode des Maxwell, Équations de -- Solutions numériques, Électromagnétisme, Alternateurs, Modélisation tridimensionnelle Numerical modeling by finite element method for electrotechnical systems : steady state investigation In electrical engineering, the Finite Element Method (FEM) associated to the time stepping numerical scheme is the most used approach today. This method is simple, accurate and efficient to modeling magnetic fields in low frequency electromagnetic devices. Nevertheless according to the studied cases, the time constant of the device can lead to prohibitive computation time to obtain the steady state. It is in this context that this PhD thesis is written "Numerical modeling by finite element method for electrotechnical systems: steady state investigation". The Waveform Relaxation-Newton Method (WR-NM) was developed, this method is based on the waveform relaxation method (WRM) in which periodicity conditions are applied to impose the steady state for electromagnetic problems coupled to circuit equations. The convergence of this method is similar to a fixed-point method, thus the method is combined to the method of Newton-Raphson whose convergence is quadratic. In order to validate and test the robustness of WR-NM, several applications are presented in the manuscript. Significant gains in computation time are shown in comparison with the conventional approach and for the same precision of the solution. A final example on the modeling of a claw-pole machine coupled to a bridge rectifier shows that the WR-NM can also be employed in an industrial setting.