Improved Mathematical Model and Modeling of Permanent Magnet Synchronous Motors Considering Saturation, Spatial Harmonics, Iron Loss and Deadtime Effect

A machine model of permanent magnet synchronous motors (PMSMs), which combines the improved mathematical model, electrical circuit model and the data-driven method, is proposed to simulate the real nonlinear behavior of PMSMs in this paper. A PMSM used for the electric compressor of electric vehicles (EVs) is analyzed and tested, and the proposed model can be used for PMSMs of various applications. Firstly, the improved mathematical model of PMSMs considering the magnetic saturation, spatial harmonics and iron loss is established. In particular, the torque formulas of PMSMs are analytically derived by using the energy conservation, which predicts the average torque and torque ripple more accurately. Secondly, based on the proposed mathematical model and the data derived from finite-element analysis, the high-fidelity reduced-order model (ROM) with flux linkage as state variable is built, wherein the radial basis function interpolation method is used to interpolate the discrete current points. To consider the deadtime effect, the electrical circuit model of PMSMs is further incorporated into the ROM. Finally, the model-in-the-loop environment is utilized for simulation validation, which along with experiment shows good accuracy of the proposed mathematical model and ROM.