Thomas Henneron

Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods

In the domain of numerical computation, model order reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the proper orthogonal decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear (NL) case. In this paper, the discrete empirical interpolation method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of NL magnetostatic problems coupled with an external electrical circuit.

Dual finite element formulations for lumped reluctances coupling

A method for coupling magnetostatic and magnetodynamic finite element formulations with lumped reluctances is developed. Two dual h and b-conform formulations are extended to define the necessary magnetic relations between the magnetic fluxes and the magnetomotive forces. Adequate surface scalar potentials are defined and adequate boundary terms in the weak formulations are used. The magnetic relations can then be included in a reluctance network, in which the coupling of finite element regions and lumped regions aims at higher computational efficiency. The methods are developed in three dimensions, using a coupling of nodal and edge finite element approximations for the unknowns, and can easily be particularized in two dimensions.

Source Field Computation in NDT Applications

Numerical modeling of nondestructive testing (NDT) by eddy currents has been applied for qualification of two monitoring devices. Experimental data have enabled us to validate reliable and relevant finite-element method models. The encountered difficulties due to geometry (size and topology), the nature of the control signal (weak flux differences), and the movement accounting have been successfully overcome by evaluating the A-phi and T-Omega dual formulations with appropriate source fields and applying classical method to suppress the mesh numerical error and choosing the well-known lock-step technique

Evaluation of 3-D finite element method to study and design a soft magnetic composite machine

In this paper, we test a three-dimensional (3-D) magnetostatics model using Whitneys elements to study a permanent magnet machine made up of soft magnetic composite (SMC) material. Models based on both magnetostatic potential formulations are briefly presented. To evaluate the accuracy of these formulations, theoretical fluxes are compared with fluxes measured on permanent magnet machine. Computation resources of both formulations are also compared.

Calculation of extra copper losses with imposed current magnetodynamic formulations

To solve a magnetodynamics problem, two potential formulations can be used. In the case of the A-psi formulation, the voltage at the terminals of a conductor is naturally imposed, which is not the case for the current flowing through the conductor. On the contrary, for the T-Omega formulation, the current can be naturally prescribed, but not the voltage. In order to impose the complementary electric quantity in both formulations, a physics-based approach using a power balance is proposed. Both magnetodynamic formulations are presented by considering a domain made up of multiple conductors. These formulations are used to study the copper losses induced by the franging of the magnetic flux around a small air gap of an iron core coil. Theoretical results are compared with experimental results

Model-Order Reduction of Multiple-Input Non-Linear Systems Based on POD and DEI Methods

The proper orthogonal decomposition combined with the discrete empirical interpolation method is investigated in order to reduce a finite-element model of a multiple-input non-linear device. The non-linear reduced problem is solved using the Newton-Raphson method. The transient state of a three-phase transformer with a variable load is studied with the proposed reduction method for different supply voltage conditions.

Electromagnetic Field Projection on Finite Element Overlapping Domains

Coupled problems are made up of subproblems of which the physical nature differs. Using indirect coupling models, the subproblems are calculated separately on their own meshes to ensure precision. To obtain a precise solution for the total problem, it is important to ensure the transmission of information between the subproblems. In this paper, we present field projection methods on overlapping domains. In comparison to earlier works, the classical L2 or L2 projection theory is extended to H(grad), H(curl) and H(div) to obtain increased projection accuracy for the distributional derivatives. A Petrov-Galerkin method is then presented to fill the test space using a biorthogonal basis, without losing the optimality of the result in comparison to the L2 or L2 Ritz-Galerkin method. Using the Petrov-Galerkin method and biorthogonal test functions, the projection is presented using a diagonal matrix. However, in the standard Ritz-Galerkin projections, a linear system must be solved.

Overlapping Finite Elements Used to Connect Non-Conforming Meshes in 3-D With a Vector Potential Formulation

Overlapping elements can be used to connect non-conforming meshes in the finite-element method. This approach has been developed with the scalar potential formulation and used to solve magnetostatic problems but not in the case of the vector potential formulation. In this paper, we propose to introduce the overlapping element method in this second formulation.

3-D approaches to determine the end winding inductances of a permanent-magnet linear synchronous motor

This paper deals with the determination of the end winding inductance of a permanent-magnet linear synchronous motor (PMLSM). The methods to determine the inductances in three dimensions are given for both classical complementary formulations. In a first step, an elementary cell of the structure is modeled using both methods and the results are analyzed and discussed. In the second step, the complete structure is studied in two and three dimensions using only the scalar potential formulation to limit the computation time. The numerical results are compared with experimental ones.

Electromagnetic modelling of short circuited coreplates

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...