Stephane Clenet

The Finite Element method is widely used to study and design electromagnetic devices. This method is very accurate but often requires huge computational time even during the post processing step where quantities of interest are calculated. In this article, we propose to apply and to compare clustering methods, i.e. the K-Means and Gaussian Mixture methods, in order to reduce the computational time of the iron loss distribution in a postprocessing stage. Indeed, the iron loss distribution calculation relies only on the calculation on only a few elements of mesh and not on all elements like in the case of the standard method. The proposed methods are tested on a nonlinear magnetic example based on an axial flux machine showing a good agreement between the iron losses distribution obtained by the standard and the proposed methods.

This article proposes a forward method to determine the optimal direction of the magnetization of permanent magnets, as well as their optimal shape, in order to maximize the magnetic flux in a coil. The method can be advantageously used, for example, during the design stage of an electrical machine in order to maximize the flux in the stator windings generated by the permanent magnets located on the rotor. The method is first developed in the continuous domain. It appears that the optimal permanent magnet configuration can be determined from the magnetic flux density distribution generated by the coil when it is supplied by a current of 1 A. No need to solve any inverse problem to find the optimal configuration since the procedure is explicit. It is shown that this method remains valid in the discrete domain when the finite element method is applied, and can take advantage of this method for topology optimization. Two configurations of permanent magnet magnetization are considered: either having a continuously variable direction or made with blocks in which the direction is constant as in a Halbach array. In the same way, for topology optimization, two cases are considered when the magnetization is fixed or considered as a variable to be optimized. A 3-D example is treated in order to illustrate the effectiveness of the method.

This paper proposes a novel methodology of the topology optimization method considering eddy current effects. The method is applied on chip inductors modelled by the Finite Element Method (FEM). Aiming to meet a specified inductance value while minimizing eddy current losses, we employ a density-based approach to construct a continuous material distribution. The derivative of the objective function with respect to the material distribution is obtained using the adjoint variable method, then the material layout is iteratively updated via the L-BFGS-B algorithm. The proposed framework is validated on both single-turn and multi-turn inductor structures, achieving designs that satisfy the target performance within a limited number of iterations. A key innovation of this work lies in the integration of field-circuit coupling into the topology optimization framework, enabling the analysis of inductors under complex coil configurations involving both series and parallel connections. Additionally, we present an original derivation of the sensitivity formulation associated with the inductance value ensuring that the optimized inductance meets the design specification.

In order to design efficient power converter operating at high switching frequencies, the electromagnetic behavior of the printed circuit board (PCB) must be well known. Then, numerical approaches can be used to study the voltage and current waveforms as well as the current density distribution associated with a PCB. Considering a half-bridge converter connected to a passive electrical load, we propose a co-simulation based on the Cauer ladder network approach providing an equivalent circuit of the PCB combined with models of GaN transistors. The results from the co-simulation are compared with measurements at 1 MHz with an output power of 200 W.

The Cauer ladder network (CLN) method can accelerate eddy current field analysis of electromagnetic devices in the time domain by reducing the order of the finite element (FE) model. To control its accuracy, the reduction error should be estimated without conducting the FE analysis. In this study, we extend the estimation method in the frequency domain developed in a previous study to time-domain analysis. The proposed method is also extended to a multiport system. Numerical examples illustrate that the proposed error estimation method is effective.