Voltage Distribution Modeling Along Stator Windings in Permanent Magnet Synchronous Machines Using Coil-Based Grey Box Models

A coil-based grey box model is developed for high-frequency modeling of permanent magnet synchronous machines (PMSMs) with interior magnets in rotors to predict the voltage distribution along stator winding. Unlike the grey box model in the literature, the developed coil-based model can predict the voltage distribution along stator winding. Compared to the white box model, no complex modeling based on finite element simulation results is required. As the name suggests, the developed model has each winding coil as a basis, and the entire model is created by connecting coils according to the winding schema. Furthermore, the coil-based model considers frequency-dependent inductive and capacitive coupling within electrical machines, including skin and proximity effects. The model is parametrized using an optimization program based on measured impedance spectra at machine terminals. As a result, an average deviation of less than 4 % is observed in the impedance modeling. With the coil-based model's help, the common mode voltage distribution is predicted with almost zero errors between modeled and measured voltage peak values. Regarding the differential mode voltage distribution, the voltage maximum can be predicted with a maximum relative error of less than 10 % in the time domain.