Model Order Reduction: Proper Generalized Decomposition in the Context of Non-linearity and Motion in Electrical Machines

In the design stage of electrical machines, the Finite Element Analysis is one of the most widely used numerical simulation tools to analyse electromagnetic fields and the machines' behaviour. It is able to compute complicated geometries in two- and three-dimensions with a good accuracy. However, this numerical approach may involve a huge number of unknowns, which have to be determined. To give general answers to physical and technical relevant questions, several problem classes can be distinguished. Basically, there are transient processes resulting in eddy currents, which have to be resolved in space and time. The non-linearity of the flux-guiding ferromagnetic material
has to be considered and the relative motion between static and moving
parts of the machine is crucial. Here, parameters vary depending on time or space. The degrees of freedom associated with the simulations, particularly if many operating points or machine design parameter combinations have to be studied, increases significantly.
To reduce the degrees of freedom of the set model, model order reduction techniques can be applied. A promising model order reduction technique to enable the computation of electromagnetic fields is the Proper Generalized Decomposition. It can be adapted and extended with dedicated numerical techniques to be employable in the simulation of electrical machines, reducing the computational effort while ensuring a technical relevant accuracy of the solution.