Nonlinear parametric simulation by proper generalized decomposition on the example of a synchronous machine

Abstract

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.

Citation

Müller, F., Baumanns, P., Nell, M.M. and Hameyer, K. (2022), "Nonlinear parametric simulation by proper generalized decomposition on the example of a synchronous machine", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 41 No. 4, pp. 1171-1180. https://doi.org/10.1108/COMPEL-11-2021-0431