Characterization of Permanent Magnet Synchronous Machines based on semi-analytic model reduction for drive cycle analysis

TL;DR

The paper addresses the computational burden of characterizing interior permanent magnet synchronous machines (IPMSMs) for drive-cycle analysis. It introduces a semi-analytic workflow that precomputes nonlinear magnetic behavior in flux-linkage LUTs from a minimal set of 2D FE simulations, and then analytically post-processes results for varied load torques and speeds, while enforcing DC-bus and current limits; losses are modeled via analytic expressions. To accelerate design exploration, the authors reduce model complexity through 2D symmetry, current-sweep and angle-range reductions, and a spline-based geometry description that eliminates repeated meshing, enabling CAD-driven adaptations and automatic mesh deformation. The approach is further boosted by parallelizing computations across operating points, yielding substantial speedups. The resulting framework provides comprehensive performance maps and KPIs for drive-cycle analysis, supporting fast, large-scale design space exploration and optimization of IPMSMs in EV applications.

Abstract

The characterization of an interior permanent magnet synchronous machine (IPMSM) requires numerical analysis of the nonlinear magnetic motor model in different load conditions. To obtain the case-specific best machine behavior, a strategy for the determination of stator input current amplitude and angle is employed for all possible load torques given a limited terminal current amplitude and DC bus voltage. Various losses are calculated using state of the art loss models. The electromagnetic performance of the electric machine is stored in lookup tables. These can then be used for the drive cycle analysis of the electric drive train in the design and optimization stages. To avoid the use of a dedicated mesh generator in the numerical analysis, volumetric spline-based models are suggested.With this approach, the mesh can be generated directly from the Computer Aided Design (CAD) geometry. This enables an automatic adaption of the grid following a geometry perturbation. With this the approximated solution is kept consistent over the different iterations of an overlying optimization, improving its convergence behavior.

Figures (6)

• Figure 1: Single pole model of the presented electric machine. The rotating part comprise the shaft , laminated rotor yoke and the magnets in their air pockets. Between rotor and stator is the air gap . The stator is comprised of the windings in the slots, seperated by the teeth , which are part of the laminated stator yoke . The air surrounding the stator back side is .
• Figure 2: $\hat{\Psi}_\mathrm{d}$ and $\hat{\Psi}_\mathrm{q}$ depending on the stator currents. The MTPA trajectory as explained in the following paragraph is shown in red. The current limit is depicted as a circle.
• Figure 3: Efficiency plot of an 8-pole IPMSM.
• Figure 4: Symmetries in the full machine model (left) allow the reduction of the calculation domain to a single pole. For integer-slot windings, shown here with two slots per pole and phase ($q = 2$), the magnetic field repeats anti-periodically for each subsequent pole.
• Figure 5: Reconstruction of $\Psi$ over one electrical period from the simulated first sixth of a period by inversion and phase shifting. The solid lines show the simulated phase values , while the dashed lines indicate their continuation over the full period.