Homogenization Method Based on Cauer Circuit via Unit Cell Approach

This article proposes a novel homogenization method based on the unit cell approach which provides the continued fraction and, equivalently, the Cauer circuit representation of the complex permeability of fine structure materials. The proposed method makes it possible to perform the homogenization analysis in time domain. It is shown that the proposed method provides a more accurate resistance factor in comparison to the Dowell method and other classical methods

Model Order Reduction for Linear Time-Invariant System With Symmetric Positive-Definite Matrices: Synthesis of Cauer-Equivalent Circuit

This article introduces a new model order reduction method for a linear time-invariant system with symmetric positive-definite matrices. The proposed method allows the construction of a reduced model, represented by a Cauer-equivalent circuit, from the original system. The method is developed by extending the Cauer ladder network method for the quasi-static Maxwell's equations, which is shown to be regarded as the Lanczos algorithm with respect to a self-adjoint matrix. As a numerical example, a Cauer-equivalent circuit is generated from a simple mathematical model as well as the finite-element (FE) model of a magnetic reactor that is driven by a pulsewidth modulation voltage wave. The instantaneous power obtained from the circuit analysis is shown to be in good agreement with that obtained from the original FE model

Fast 3-D Analysis of Eddy Current in Litz Wire Using Integral Equation

Eddy current loss in a litz wire which has 3-D structure is analyzed using the integral equation method considering the proximity effect. In the present method, each wire is modeled as a polygonal line. 1-D integral equation is solved for the dipole magnetization generated by the anti-parallel eddy currents in the wire. The discretized integral equation can effectively be solved using an iterative method solver to compute the eddy current distribution in the wire due to the proximity effect

Fast computation of copper and iron losses using model order reduction

This paper introduces a new method for fast computing of the iron and copper losses in electromagnetic systems. In the method, the finite element equation is reduced to the equivalent Cauer circuit via model order reduction. The nonlinear property due to core saturation is pre-computed and included in the Cauer circuit. While the copper loss is computed as the Jule loss in the circuit, the iron loss is computed in the post process by restoring the field distribution from the solution to the circuit equation with aid of the proper orthogonal decomposition

Time-Domain Analysis of Homogenized Finite-Element Method for Eddy Current Analysis With Reduced Unknown Variables

This article presents a new method for time-domain analysis based on the homogenized finite-element method (FEM). The permeability in the homogenized domain is expressed by the Cauer-equivalent circuit. The auxiliary unknowns relevant to the Cauer circuit are then eliminated using the finite-difference method. The homogenized finite-element (FE) equation without the auxiliary unknowns can be effectively solved

Eddy Current Analysis of Litz Wire Using Homogenization-Based FEM in Conjunction With Integral Equation

A new method is introduced to evaluate the macroscopic permeability of a litz wire which is composed of stranded conductors. In this method, an integral equation is solved for the complex magnetization in the litz wire generated due to the proximity effect. The macroscopic permeability computed from the magnetization is used in the homogenization-based finite-element analysis of eddy currents in a litz-wire coil. It is shown that the wire twist has a little effect on the complex permeability