Using FE calculations and data-based system identification techniques to model the nonlinear behavior of PMSMs

This paper investigates the modeling of brushless permanent-magnet synchronous machines (PMSMs). The focus is on deriving an automatable process for obtaining dynamic motor models that take nonlinear effects, such as saturation, into account. The modeling is based on finite element (FE) simulations for different current vectors in the $dq$ plane over a full electrical period. The parameters obtained are the stator flux in terms of the direct and quadrature components and the air-gap torque, both modeled as functions of the rotor angle and the current vector. The data are preprocessed according to theoretical results on potential harmonics in the targets as functions of the rotor angle. A variety of modeling strategies were explored: linear regression, support vector machines, symbolic regression using genetic programming, random forests, and artificial neural networks. The motor models were optimized for each training technique, and their accuracy was then compared based on the initially available FE data and further FE simulations for additional current vectors. Artificial neural networks and symbolic regression using genetic programming achieved the highest accuracy, particularly with additional test data.