Variable-Temperature PMSM Dynamic Model Based on Spline Interpolation of Coenergy Map

In this paper, a model for the dynamic simulation of permanent magnet synchronous motors (PMSM) is presented. The model takes into account the effects of magnetic saturation, harmonics and permanent magnet (PM) temperature variation. The proposed solution is designed with the objective of providing smooth transitions of the physical quantities as a function of the state variables, and to comply with the concept of energy conservation. This is achieved starting from the map of the magnetic coenergy of the motor, obtained with Finite Element (FE) analysis as a function of four variables: d-axis current, q-axis current, rotor angle, and PM temperature. The coenergy map is then interpolated via four-dimensional cubic spline interpolation, which is used to retrieve all quantities required for the model, namely flux linkage, incremental inductances and cogging torque. In particular, these quantities are described as functions obtained by differentiating the polynomials defining the coenergy map interpolation. In conclusion, examples of the results obtainable with the proposed model are shown, highlighting both the different terms that compose the voltage components and the importance of taking into account the effect of PM temperature.