Conference Agenda

Milliken conductors are a widely used design for the inner conductors of AC high-voltage power cables. Determining their AC resistance numerically is a challenge due to the inherent multiscale nature of the problem, involving the strand diameter, the pitch length of strand layers, and the pitch length of the segments. To address this, we propose a finite element model that takes advantage of homogenization techniques based on helicoidally symmetric boundary value problems.

The magnetoquasistatic simulation of laminated ferromagnetic structures at elevated frequencies is a challenging task, which quickly becomes impossible for three-dimensional models, especially if a nonlinear magnetization curve must be considered. In this contribution, we show how existing homogenization techniques for the linear case can be combined with the harmonic balance finite element method to also account for the nonlinearity of the magnetization curve. This leads to a method which does not necessitate resolving the individual laminations with the finite element mesh and avoids time-stepping, thus allowing us to conduct nonlinear eddy current simulations of large three-dimensional models at frequencies in the kilohertz range efficiently. In particular, we demonstrate the usefulness of this new approach for simulating fast orbit corrector magnets in particle accelerators.

The traditional multi-scale finite element method (FEM) used to solve the lamination eddy current problem does not define the gauge condition of magnetic vector potential, which leads to numercial instability problems such as excessive residuals in the corresponding equations during the solution process. In this paper, a Coulomb gauged multi-scale FEM is proposed for the eddy current problem in lamination iron cores, which ensures the solution uniqueness of magnetic vector potential by weakly defining the global divergence of the potential function, thereby improving the numerical stability of the FEM solutions. The benchmark model TEAM 21d is solved by using the proposed method, and the comparison of calculated results and measured ones show that the method can effcetively and accurately solve the eddy current problem in the laminated cores.

Foil windings have, due to their special layered structure, different properties than wire windings, with advantages for high frequency applications. Both electromagnetic and thermal analyses are relevant for foil windings. Both physical phenomena are coupled through Joule losses and temperature dependent material properties. For an efficient simulation of foil windings, homogenization techniques are used to avoid resolving the single turns. This paper comprises a weakly coupled magneto-thermal simulation that uses a homogenization method in the electromagnetic and thermal part. The method is validated with a commercial solver.

The electric and magnetic response of type-II irreversible superconductors to external field and transport current is hysteretic due to magnetic flux pinning in the material. This hysteretic behavior can be accurately reproduced in finite element models with a nonlinear electrical resistivity, but it leads to computationally expensive simulations. Consequently, this approach is unrealistic for large-scale systems such as superconducting accelerator magnets which are multi-scale structures with a cross section containing hundreds or thousands of superconducting strands. In this contribution, we present reduced order methods based on an energy-based vector hysteresis model to describe the macroscopic response of composite superconductors without a need to compute the detailed current density distribution. The model also reproduces rate-dependent effects due to eddy currents and coupling currents in normal conducting parts of the composite.

Ferrites cores are used in power electronics at increasingly higher frequencies, hence it is crucial to have predictive models to evaluate magnetic losses. In this article an original easy numerical homogeneization method which allow to compute losses in ferrite cores excited by sinusoidal currents. The model requires only 5 parameters, which can be easily obtained. The model has been extensively validated by numerical simulations and with experiments on three different ferrites.

Based on the finite difference time domain (FDTD) method and the three-stage split-step precise integration time domain method (SS2-PITD), a hybrid subgridding method is proposed for solving multi-scale problems. In this proposed method, SS2-PITD is applied to analyze the small-scale fine structure with fine cells, while the FDTD method is employed for the extensive background region with coarse cells. Since SS2-PITD breaks the Courant–Friedrichs–Lewy (CFL) condition, the time step sizes in the fine and coarse cell regions can be synchronized, thus reducing the number of updating steps in the fine cell region and improving the computational speed. Numerical experiments are simulated to show the effectiveness of the proposed method.

This paper proposes the multiscale homogenization method for the analysis of Litz wire. By sequentially homogenizing Litz wire at the strand, bundle and winding levels, the coil region can be approximated as a uniform material with the complex relative permeability. The accuracy of the method is validated by comparing the computed relative permeability, stored energy, and Joule loss with finite element model. This algorithm serves as a solid basis for the shape optimization of a coil composed of Litz wire.

To simulate the high frequency (HF) response of an inductor at the MHz range by the full-wave electromagnetic field finite element analysis (FEA), the wire of winding should be modeled directly to take account of the stray capacitance and the wire length of the winding. However, it causes high computation cost. In this paper, a homogenization technique for winding taking account of the stray capacitance and the wire length is proposed. The winding wounding around the iron core is modeled to be the solid coil used in the ordinary FEA by using the equivalent conductivity and permittivity. It is shown that the HF response of the ring core inductor obtained from the proposed homogenized-winding model is in good agreement with those obtained from the real-winding model and measurement with significantly reducing the computation cost.

Simulations of eddy currents in laminated ferromagnetic cores typically require a homogenization method.

This paper introduces a numerical homogenization method based on computationally inexpensive simulations on well-constructed two-dimensional problems in the preprocessing phase.

As a novelty, this method yields a complex-valued effective material that accounts for the nonlinearity of material properties and the edge effects of eddy currents, all without introducing additional degrees of freedom.

The advantages of this approach are demonstrated through a comparison with an analytical homogenization procedure based on a one-dimensional approximation of eddy currents.

Effective materials are an efficient way to solve the eddy current problem for devices consisting of many thin steel sheets. They allow to replace the fine-structured geometry by a bulk medium that is cheap to resolve in the finite element mesh. The parameters of this effective material are obtained using a suitable cell problem. By utilizing a complex permeability, the effective formulation becomes a static one, requiring only a magnetic scalar potential, which further reduces both the required memory and the computation time. However, conventional effective material theory requires the magnetic flux to be aligned with the sheets, i.e. stray fields cannot be accounted for. This paper presents a way to include stray fields in an effective material in an efficient way. Numerical experiments show very satisfying results at the cost of only a single additional scalar potential restricted to the bulk medium.

The numerical modeling of 3D electrical devices that contain composite materials, such as electrical machines, transformers, and new devices made from soft magnetic and 3D-printed magnetic materials, has yet to be fully realized. Current modeling approaches mainly rely on homogenization methods applied to 2D sections of device components, such as 2D slices of a transformer core or portions of 3D magnetic composites. However, some effects can only be accurately captured using 3D multiscale models of the entire device. The challenges of applying these methods to 3D nonlinear eddy current problems in composites arise from the high computational cost due to the multiscale nature of the materials. The method must also be capable of handling nonlinear material laws. Furthermore, the presence of strong eddy currents may require advanced upscaling techniques that ignore the macroscale contribution of eddy currents confined within the cell. This paper combines the multiscale method with massive parallelization to produce initial modeling results for a 3D three-phase transformer