Yvonnick Le Menach

Residual-based a posteriori estimators for the A/phi magnetodynamic harmonic formulation of the Maxwell system

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.

Comparison of slip surface and moving band techniques for modelling movement in 3D with FEM

Purpose – To compare slip surface and moving band techniques for modelling movement in 3D with FEM.Design/methodology/approach – The slip surface and moving band techniques are used to model the rotation of electrical machines in 3D with FEM. The proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no‐load for the electromotive force (EMF) and the cogging torque. The torque is also compared for the short circuit case.Findings – For both the locked‐step and moving band approaches there is no difficulty in establishing the scalar potential and potential vector formulations. However, if step displacement is not equal to the mesh step, the results can show numerical irregularities. Some improvements have been proposed in order to limit this problem.Originality/value – The results of the EMF and the cogging torque are improved.

Residual and equilibrated error estimators for magnetostatic problems solved by finite element method

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.

Comparison of supervised classification algorithms combined with feature extraction and selection: Application to a turbo-generator rotor fault detection

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%.

Hysteresis Phenomenon Implementation in FIT: Validation With Measurements

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.

Thermal Topology Optimization of a Three-Layer Laminated Busbar for Power Converters

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.

Finite Element Implementation and Experimental Validation of 2-D/3-D Magnetic Force Formulas

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.

A posteriori error estimator for harmonic A‐φ formulation

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.

Finite Element Mesh Adaptation Strategy From Residual and Hierarchical Error Estimators in Eddy Current Problems

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.

3D compatible magnetostatic potential formulations coupled with electrical circuits

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.