Hans Vande Sande

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.

Solving nonlinear magnetic problems using Newton trust region methods

In this paper, a Newton trust region method is presented as an alternative to the Newton-Raphson method for solving nonlinear magnetic problems. Instead of underrelaxing the Newton step in a line search algorithm, the step is determined by minimizing a local quadratic model of the functional within a trust region. If the Newton step lies outside the trust region, a step with a smaller norm and different direction is computed. The size of the trust region plays a similar role as the relaxation factor in the line search approach. To ensure that the method converges, the trust region size is automatically adjusted from one iteration to the next one, depending on the local accuracy of the quadratic model. The trust region approach is applied to the simulation of an 8/6 switched reluctance motor.

An effective reluctivity model for nonlinear and anisotropic materials in time-harmonic finite element computations

In time-harmonic finite element analysis, the nonlinear behavior of soft-magnetic materials is often modeled by effective reluctivity curves, to account for the time-dependence of the reluctivity during one cycle of the applied sinusoidal signal. In this paper, the effective reluctivity concept is generalized in such a way, that nonlinear and anisotropic materials can be modeled as well. The model is used to simulate the flux line distribution and the loss distribution in a three-phase transformer under no-load operation.

A hybrid method for determining the reluctivity tensor components of Goss textured ferromagnetic materials

For anisotropic materials, the magnetic field vector H→ and the flux density vector B→ are parallel with each other only along a few distinct directions. When performing unidirectional measurements, only the component of B→ along the direction under consideration is measured. It is not possible to deduce the angle between B→ and H→ from unidirectional measurements alone. For ferromagnetic materials having a Goss‐texture, as most transformer steels have, this paper demonstrates a way to compute this angle a posteriori, by the combination of measurements with a physical anisotropy model.

Reducing the computation time of nonlinear problems by an adaptive linear system tolerance

Within the finite-element framework, nonlinear magnetic problems are often solved by an iterative line search strategy. The efforts to achieve convergence concentrate on the selection of an adequate relaxation factor. The line search is performed along a direction obtained by solving a system of linear equations. However, it is not required to compute this intermediate solution with a high accuracy, to ensure convergence. This paper shows how the accuracy of the solver can be modified at each nonlinear iteration, in order to reduce the overall computation time.

3D h-phi finite element formulation for the computation of a linear transverse flux actuator

A finite element analysis of a permanent magnet transverse flux linear actuator is presented. In this application where we need a small model (for optimisation purposes) as well as a high accuracy on the computed force, we propose to combine several models with different levels of size and complexity, in order to progressively elaborate an accurate, but nevertheless tractable, model of the system.