Model‐order nonlinear subspace reduction of electric machines by means of POD and DEI methods for copper losses calculation

Abstract

The simulation of electric machines in order to calculate the copper losses is about a time‐dependent electromagnetic problem. When the finite element method associated with a time stepping scheme is used to solve the problem, the solution is strongly linked to initial conditions, among which the most important is the solution at the initial time. Because it is practically chosen as an arbitrary solution, several time‐consuming electrical excitation periods must be simulated therefore to reach finally the steady‐state conditions. The copper losses can be calculated now without any transient components that can affect the credibility of the copper losses amount. This article suggests a model‐order reduction method that benefits from the complete model finite element solution of the first transient electrical period, to calculate the reduced model solution in the subsequent periods using the proper orthogonal decomposition approach combined with the discrete empirical interpolation method. Nevertheless, in case of relatively high frequency excitation, the full reduction of the problem leads to significant imprecision in the amount of copper losses. To improve the accuracy, therefore, a nonlinear subspace model‐order reduction is adopted. It ensures concurrently higher precision and a reduced computational time.

Model order reduction using hyperreduction methods (DEIM, ECSW) for magnetodynamic FEM problems

“…In Figs. 20,21,22, the reduced model results are plotted for the 3 sets of reduction parameters. The plots for the power loss and the magnetic field energy are not shown here, as they do not differ in any method in a visible way.…”

“…Its application to structural dynamics problems was investigated in [20,21]. It was applied in combination with a POD to magnetostatic problems in [4,6,22,23]. To preserve the generality of the method's description, the vector 𝒈(𝒖) will continue to be called internal force as a generic denomination independent of the underlying physics.…”

Special issue: The 10th International Symposium on Electric and Magnetic Fields (EMF 2016)

“…The third major topic concerns fast solvers for electromagnetic applications with contributions on ultra weak variational formulations and the behavior of natural and finite element interpolation functions, domain decomposition methods for finite volume, finite element and boundary element schemes,() explicit time integration of eddy current problems, and the GPU acceleration of Maxwell solvers for differents applications. () The fourth major topic concerns the application of electromagnetic modelling, uncertainty quantification and model order reduction techniques to novel or challenging applications, with contributions to electrothermal field problems, electric machine modelling,() lightning‐produced electromagnetic fields, electronic circuits, and electrical capacitance tomography sensors …”