Robust Optimization of a Permanent-Magnet Synchronous Machine Considering Uncertain Driving Cycles

Abstract

This work focuses on the robust optimization of a permanent magnet (PM) synchronous machine while considering a driving cycle. The robustification is obtained by considering uncertainties of different origins. Firstly, there are geometrical uncertainties caused by manufacturing inaccuracies. Secondly, there are uncertainties linked to different driving styles. The final set of uncertainties is linked to ambient parameters such as traffic and weather conditions. The optimization goal is to minimize the PM's volume while maintaining a desired machine performance measured by the energy efficiency over the driving cycle and the machine's maximal torque. The magnetic behavior of the machine is described by a partial differential equation (PDE) and is simulated by the finite-element method employing an affine decomposition to avoid reassembling of the system of equations due to the changing PM geometry. The Sequential Quadratic Programming algorithm is used for the optimization. Stochastic collocation is applied to compute moments of stochastic quantities. The robustness of the optimized configurations is validated by a Monte Carlo sampling. It is found that the uncertainties in driving style and road conditions have significant influence on the optimal PM configuration.

Robust Design Optimization and Emerging Technologies for Electrical Machines: Challenges and Open Problems

“…Usually, design optimization is quite often based on the application of an electric drive system; for example, Reference [228,229] considered the driving cycles of an EV as a reference. The paper by M. Degano et al [228] dealt with a high-speed PM assisted synchronous reluctance motor design and its optimization according to U.S. standard driving cycles (city: Urban Dynamometer Driving Schedule (UDDS); highway: Highway Fuel Economy Driving Schedule (HWFET)) to evaluate the most representative operating points of the studied application.…”

“…In order to define optimization inputs, a geometrical parameter analysis of the permanent magnet synchronous machine was performed. L. D'Angelo et al [229] considered geometrical defects that are caused by electrical machine manufacturing errors, ambient conditions (including traffic and weather), and possible differences in driving styles to obtain robustification. The object of the study was a permanent magnet synchronous machine, where the rotor's and permanent magnets' geometries varied.…”

Improved Approaches Toward Analysis of Electromagnetic Processes in Electrodynamical Devices Based on the Theory of Electromagnetic Field

“…Because the development of field mathematical models is theoretically and algorithmically complicated, the practical statement of the task can be simplified using a simultaneous application of the principles of both the theories of electromagnetic circuits and electromagnetic field in models for the calculation of electromagnetic processes in electrodynamical devices. This approach allows for a description of electromagnetic phenomena in bulky electrical pathways and in magnetic cores using the theory of electromagnetic field and in electric windings using the theory of electromagnetic circuits [11][12][13][14][15] . One of the most prospective trends of creating mathematical models is the sole use of the theory of electromagnetic field for the analysis of electromagnetic phenomena in movable and immovable media of electrodynamical devices [16][17][18][19][20] .…”