Proper Generalized Decomposition Applied on a Rotating Electrical Machine

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. The Proper Generalized Decomposition (PGD) is a model order reduction method which allows to reduce the computational time of a numerical problem by seeking for a separated representation of the solution. The PGD has been already applied to study an electrical machine but at standstill without accounting the motion of the rotor. In this paper, we propose a method to account for the rotation in the PGD approach in order to build an efficient metamodel of an electrical machine. Then, the machine metamodel will be coupled to its electrical and mechanical environment in order to obtain accurate results with an acceptable computational time on a full simulation.

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

“…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. The authors of [31] use the PGD technique which resulted in an improvement of the solution time by about 900 when compared to the original FEM model, despite the torque estimation being in general agreement with the FEM model it presented some noticeable errors because it is calculated through the virtual work principle. In addition, the work developed in [32] shows the possibility to express deviations within the PGD framework, which is an interesting feature because these deviations can represent external disturbances and even the difference between the predictions and measurements.…”

Error Estimators for Proper Generalized Decomposition in Time-Dependent Electromagnetic Field Problems

“…For linear problems with several excitation sources, like multiple coils, the general approach stated above may not converge or produce adverse results. Due to the linear nature of the field problem in absence of nonlinear materials, the superposition of the fields produced by each of the k sources add up to the total field distribution and therefore, an adapted approach is employed (3) [12].…”

“…A-priori methods such as the Proper Generalized Decomposition (PGD) method construct a reduced order model without any previously obtained solutions [1]. The PGD has been applied to different problems in mechanics [1]- [4] and electromagnetics [5]- [10], [12], [13] and represents a desirable strategy to solve engineering problems. While different error criteria for a-posteriori methods have been formulated [6], a reasonable criterium for a-priori methods has not been stated yet.…”

Constrained Algorithm for the Selection of Uneven Snapshots in Model Order Reduction of a Bearingless Motor

“…These challenges are related to the dependency of the reduced Jacobian matrix and the reduced residual vector on the full-order solution of the system, which will be investi- The overlapping FEM (Tsukerman, 1992) is another alternative to the remeshing process. This method was applied along with POD-DEIM (Montier et al, 2016) and PGD (Montier et al, 2018) to reduce the order of rotating electrical machines.…”