Purpose The accurate simulation of electrical machines involves a large number of degrees of freedom. Particularly, if additional parameters such as remanence variations or different operating points have to be analyzed, the computational effort increases fast, known as the “curse of dimensionality.” The purpose of this study is to cope with this effort with the parametric proper generalized decomposition (PGD) as a model order reduction (MOR) technique. It is combined with the discrete empirical interpolation method (DEIM) and adapted to study characteristic electrical machine parameters. Design/methodology/approach The PGD is an a priori MOR technique. The technique is adapted to incorporate several additional parameters, such as the current excitation or permanent magnet remanence, to overcome the increasing computational effort of parametric studies. Further, it is combined with the DEIM to approximate the nonlinearity of the flux guiding material. Findings The parametric version of the PGD in combination with the DEIM is a suitable numerical approach to reduce computational effort of parametric studies, while considering nonlinear materials. The computational reduction is related to the influence of the different parameter variations on the field and on the number of parameters. Originality/value The extension of the PGD by several parameters associated with parametric studies of electrical machines enables to cope with the “curse of dimensionality.” The parametric PGD and the standard PGD–DEIM have been individually used to study different problems. The combination of both techniques, the parametric PGD and the DEIM, for nonlinear parametric studies of electrical machines represents the scientific contribution of this research.
Purpose The calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations. Design/methodology/approach The POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process. Findings The hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems. Originality/value The PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.
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