Identification of a nonlinear PMSM model using symbolic regression and its application to current optimization scenarios

This article presents the nonlinear modeling of the torque of brushless PMSMs by using symbolic regression. It is still popular to characterize the operational behavior of electrical machines by employing linear models. However, nowadays most PMSMs are highly utilized and thus a linear motor model does not give an adequate accuracy for subsequently derived analyses, e.g., for the calculation of the maximum torque per ampere (MTPA) trajectory. This article focuses on modeling PMSMs by nonlinear white-box models derived by symbolic regression methods. An optimized algebraic equation for modeling the machine behavior is derived using genetic programming. By using a Fourier series representation of the motor torque a simple to handle model with high accuracy can be derived. A case study is provided for a given motor design and the motor model obtained is used for deriving the MTPA-trajectory for sinusoidal phase currents. The model is further applied for determining optimized phase current waveforms ensuring zero torque ripple.