Comparative Analysis of the Steady-State Model Including Non-Linear Flux Linkage Surfaces and the Simplified Linearized Model when Applied to a Highly-Saturated Permanent Magnet Synchronous Machine—Evaluation Based on the Example of the BMW i3 Traction Motor

Abstract

This paper presents a finite element method (FEM)-based model, which describes the magnetic circuit of the BMW i3 traction machine. The model has been reconstructed based on data available in the public domain. The reader is provided with numerical data regarding flux linkage surfaces in d- and q-axes, as well as with all the information needed to develop a space-vector model of the machine in steady-state, taking into consideration the non-linearity of the magnetic circuit. Hence, the data of a highly-saturated machine from a renowned product are provided, which can serve as a reference design for research. After that, torque curve and partial load operation points are calculated. Finally, the machine model is linearized and the calculations are repeated with the simplified linearized model. The results from both models are then compared with each other. This comparison is intended to assess the magnitude of the expected inaccuracies, when simplified analytical tools are applied to highly-saturated machines (which are the backbone of automotive electrical drivetrains). It is especially important with regard to preliminary design of electrical drivetrains, as at this stage detailed machine geometry and materials are not known.

Keywords

• field-weakening
• permanent magnet synchronous machine (PMSM)
• finite element method (FEM)