Effective Material Modeling for Laminated Iron Cores With a <i>T</i>, ϕ - ϕ Formulation

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