Robust Design Optimization of Electric Machines with Isogeometric Analysis

Theodor Komann (), Michael Wiesheu, Stefan Ulbrich and Sebastian Schöps
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Theodor Komann: Department of Mathematics, Technical University of Darmstadt, Dolivostraße 15, 64297 Darmstadt, Germany
Michael Wiesheu: Computational Electromagnetics Group, Technical University of Darmstadt, Schloßgartenstraße 8, 64289 Darmstadt, Germany
Stefan Ulbrich: Department of Mathematics, Technical University of Darmstadt, Dolivostraße 15, 64297 Darmstadt, Germany
Sebastian Schöps: Computational Electromagnetics Group, Technical University of Darmstadt, Schloßgartenstraße 8, 64289 Darmstadt, Germany

Mathematics, 2024, vol. 12, issue 9, 1-18

Abstract: In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB ® , employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.

Keywords: robust PDE constrained design optimization; isogeometric analysis; electrical machines; bilevel optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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