Piecewise Affine Magnetic Modeling of Permanent-Magnet Synchronous Machines for Virtual-Flux Control

Abstract

Accurate flux linkage magnetic models are essential for virtual-flux controllers in PMSMs. Flux linkage exhibits saturation and cross-saturation at high currents, introducing nonlinearities into the machine model. Virtual-flux controllers regulate the flux of a machine by using field-oriented control, such as model predictive control. In this study, a methodology for creating a piecewise affine flux linkage magnetic model is proposed which locally linearizes the inductance and flux offset of the machine. This method keeps the magnetic model and thus the state-space model of the system linear while capturing the saturation effects, enabling robust controls and efficient operation. The model is created using FEA-simulated data points and verified with experimental datapoints. An algorithm to optimize the model in MTPA and derated operation is presented with an average flux error less than 1% and maximum error less than 3% using only 40 points. This represents a ≈ 1–3% and ≈5–8% reduction in the average and maximum flux errors compared with a regularly gridded model, respectively.