Quantification of uncertainty in the magnetic characteristic of steel and permanent magnets and their effect on the performance of permanent magnet synchronous machine

The numerical calculation of the electromagnetic fields within electric machines is sensitive to the magnetic characteristic of steel. However, the magnetic characteristic of steel is uncertain due to fluctuations in alloy composition, possible contamination, and other manufacturing process variations including punching. Previous attempts to quantify magnetic uncertainty due to punching are based on parametric analytical models of B-H curves, where the uncertainty is reflected by model parameters. In this work, we set forth a data-driven approach for quantifying the uncertainty due to punching in B-H curves. In addition to the magnetic characteristics of steel lamination, the remanent flux density (B_r) exhibited by the permanent magnets in a permanent magnet synchronous machine (PMSM) is also uncertain due to unpredictable variations in the manufacturing process. Previous studies consider the impact of uncertainties in B-H curves and B_r of the permanent magnets on the average torque, cogging torque, torque ripple and losses of a PMSM. However, studies pertaining to the impact of these uncertainties on the combined machine/drive system of a PMSM is scarce in the literature. Hence, the objective of this work is to study the effect of B-H and B_r uncertainties on the performance of a PMSM machine/drive system using a validated finite element simulator.

Our approach is as follows. First, we use principal component analysis to build a reduced-order stochastic model of B-H curves from a synthetic dataset containing B-H curves affected by punching. Second, we model the the uncertainty in B_r and other uncertainties in B-H characteristics e.g., due to unknown state of the material composition and unavailability of accurate data in deep saturation region. Third, to overcome the computational limitations of the finite element simulator, we replace it with surrogate models based on Gaussian process regression. Fourth, we perform propagation studies to assess the effect of B-H and B_r uncertainties on the average torque, torque ripple and the PMSM machine/drive system using the constructed surrogate models.