Herbert De Gersem

Finite-Element Modeling of Magnetic Material Degradation Due to Punching

Aiming to better understand and model the different loss mechanisms occurring within electric machines during operation, we present a method to consider the degradation of steel during manufacturing due to punching in finite-element modeling of electric machines. The approach introduces a certain number of boundary layers along the punched edges, with the relative permeability decreasing toward the edge. The method, its implementation, and two example applications are presented and supported with experimental results.

A Cosimulation Framework for Multirate Time Integration of Field/Circuit Coupled Problems

This paper proposes a framework of waveform relaxation methods to simulate electromagnetic fields coupled to electric networks. Within this framework, a guarantee for convergence and stability of Gauß-Seidel-type methods is found by partial differential algebraic equation (PDAE) analysis. It is shown that different time step sizes in different parts of the model can be automatically chosen according to the problems dynamics. A finite-element model of a transformer coupled to a circuit illustrates the efficiency of multirate methods.

Simulation of wave propagation effects in machine windings

Purpose – The purpose of this paper is to offer a simulation method for predicting the impedance of machine windings at higher frequencies.Design/methodology/approach – A transmission‐line model (TLM) is developed based on parameters calculated on the basis of electroquasistatic and magnetoquasistatic finite‐element (FE) model of the winding cross‐section.Findings – The FE formulations for the low‐ and high‐frequency limits give acceptable results for the respective frequency ranges. An eddy‐current formulation is only accurate on a broader region when the FE mesh is sufficiently fine to resolve the skin depth.Research limitations/implications – The paper is restricted to frequency‐domain simulations.Practical implications – The results of the paper improve the understanding of higher‐frequency parasitic effects in electrical drives with long windings.Originality/value – The paper shows the limitations of the FE methods used for determining the parameters of the TLMs and remedies to avoid these.

Strong coupled multi‐harmonic finite element simulation package

The harmonic balanced finite element method offers a valuable alternative to the transient finite element method for the quasi‐static simulation of electromagnetic devices operating at steady‐state. The specially designed iterative solver, the adaptive relaxation of the non‐linear loop and the embedding of the harmonic balanced finite element method within a state‐of‐the‐art finite element package, leads to a solver in the frequency domain that is competitive to time stepping. The benefits of this approach are illustrated by its application to an inductor with a ferromagnetic core.

Comparison of sliding‐surface and moving‐band techniques in frequency‐domain finite‐element models of rotating machines

The sliding‐surface and moving‐band techniques are introduced in frequency‐domain finite element formulations to model the solid‐body motion of the rotors in an cylindrical machine. Both techniques are compared concerning their feasibility and computational efficiency. A frequency‐domain model of a capacitor motor is equipped with a sliding surface and compared to a transient model with moving band. This example illustrates the advantages of frequency‐domain simulation over transient simulation for the simulation of steady‐state working conditions of electrical machines.

Winding functions in transient magnetoquasistatic field-circuit coupled simulations

Purpose – The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation. Design/methodology/approach – The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis. Findings – This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation. Originality/value – The presentat...

Efficient calculation of current densities in the human body induced by arbitrarily shaped, low-frequency magnetic field sources

In this paper, we extend the scalar-potential finite-difference (SPFD) approach in order to consider arbitrarily shaped time-harmonic field sources. The SPFD approach is commonly used to compute the currents induced by an externally applied magnetic field in regions with weak, heterogeneous conductivities such as, e.g., the human body. We present the extended scalar-potential finite-difference (Ex-SPFD) approach as a two step algorithm. In the first step, the excitation is computed by solving the magnetoquasistatic curl-curl equation on a coarse grid that is well adapted for the field sources. In the second step, the magnetic vector potential is prolongated onto a finer grid and a divergence correction inside the conductor is applied. Using the Maxwell-grid-equations (MGEs) of the finite integration technique, a geometric discretization scheme for Maxwells equations, this new approach has been implemented in a parallel environment in order to account for the memory-demanding high-resolution anatomy models used for the calculation of induced currents inside the human body. We demonstrate the validity and the improved numerical performance of the new approach for a test case. Finally, an application example of a human exposed to a realistic electromagnetic field source is presented.

Decomposition and regularization of nonlinear anisotropic curl‐curl DAEs

Purpose – The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically time discretized by an implicit method. This requires the solution of large linear systems in the Newton iterations. The authors seek to speed up this procedure. In most relevant applications, several materials are non‐conducting and behave linearly, e.g. air and insulation materials. The corresponding matrix system parts remain constant but are repeatedly solved during Newton iterations and time‐stepping routines. The paper aims to exploit invariant matrix parts to accelerate the system solution.Design/methodology/approach – Following the principle “reduce, reuse, recycle”, the paper proposes a Schur complement method to precompute a factorization of the linear parts. In 3D models this decomposition requires a regularization in non‐conductive regions. Therefore, the grad‐div regularization is revisited and tailored such that it ...

Quantification of Uncertainty in the Field Quality of Magnets Originating from Material Measurements

A challenge in accelerator magnet design is the strong nonlinear behavior due to magnetic saturation. In practice, the underlying nonlinear saturation curve is modeled according to measurement data that typically contain uncertainties. The electromagnetic fields and in particular the multipole coefficients that heavily affect the particle beam dynamics inherit this uncertainty. In this paper, we propose a stochastic model to describe the uncertainties and we demonstrate the use of generalized polynomial chaos for the uncertainty quantification of the multipole coefficients. In contrast to previous works we propose to start the stochastic analysis from uncertain measurement data instead of uncertain material properties and we propose to determine the sensitivities by a Sobol decomposition.

Determination of Original Nondegraded and Fully Degraded Magnetic Properties of Material Subjected to Mechanical Cutting

The cutting process has a substantial influence on the ferromagnetic material properties of electrical steel sheets. In this paper, the properties of the degraded and nondegraded zones result from data obtained by two Epstein frame measurements using sample strips of two different widths. The magnetic characteristics of the degraded and nondegraded material are inserted into a finite-element model, which accounts for arbitrary geometries. The simulation results for the influence of degradation on a stator lamination stack are verified by measurements at three different frequencies and two different materials.