Fast Computation of Multi-Parametric Electromagnetic Fields in Synchronous Machines by Using PGD-Based Fully Separated Representations

Abstract

A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions.

Extending the Multiphysics Modelling of Electric Machines in a Digital Twin Concept

“…Sancarlos et al [30] point out that the employment of the proper generalized decomposition (PGD) techniques in electromagnetism problems is a very active research area at the moment. It applies the PGD method to obtain a magnetostatic solution of a PMSM, which presented an error below 2% when compared to the FEM solution.…”

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

“…In standard finite element simulations, the relative position of the rotor to the stator is considered in the solving process by using interface conditions. In Montier et al (2016), the rotational movement is used as an additional parameter, but the presented approach uses Nonlinear parametric simulation one PGD model for each rotor position as in Sancarlos et al (2021) and interpolating in between. This approach has an advantage, because it is also applicable with other formulations and three-dimensional problems.…”

“…At this point it should be remarked that the IEM inhouse software is yet to be further optimized. In comparison to Sancarlos et al (2021), the limitation to linear material and structured meshes is abolished. The simulations shown in this contribution are computed on a single core and do not exploit parallelization.…”

“…In Montier et al (2016), a rotating electrical machine was linearly modeled with varying material parameters. Another linear parametric problem of an electric machine is presented in Sancarlos et al (2021). However, it is limited by a structured finite element grid.…”

“…A nonlinear transformer is simulated in Henneron and Clénet(2016a) with the PGD and a method to reduce the computational effort related to the evaluation of the nonlinear material by using the discrete empirical interpolation method (DEIM) is shown. Although the parametric PGD (Sancarlos et al , 2021) and the PGD–DEIM (Henneron and Clénet, 2016a) have been used individually to simulate different applications, a combination of both to simulate electrical machines is not yet made. In this paper, a permanent magnet synchronous machine (PMSM) with a parametric excitation is simulated by a parametric PGD in conjunction with the DEIM.…”