Effective material modeling for laminated iron cores with a T, ϕ - ϕ formulation

Abstract

In the effective medium theory, a material parameter of a heterogeneous structure is replaced by an effective material. Effective materials are based on physical observable values such as eddy current losses and reactive powers and are calculated a priori using a meaningful part of the heterogeneous structure. An effective material is derived from this cell problem using the physical variables, which is then used in a simulation with a homogenised core, i.e. without taking the periodic structure into account. The results of this simulation can then be used to determine the eddy current losses and reactive power of the machine or transformer with a laminated core. Furthermore, the averaged eddy current loss and reactive power density distributions can also be determined. For this work, a nonlinear magnetic material is used for the simulation of a single-phase transformer. Compared to the reference simulations of the numerical example with a laminated core, the novel approach with the homogenised core and the effective material can dramatically reduce the demands on the computer structure, whereby the eddy current losses as well as the reactive power and the corresponding averaged distributions are very well approximated.