Effects of the Magnetic Model of Interior Permanent Magnet Machine on MTPA, Flux Weakening and MTPV Evaluation

Interior permanent-magnet synchronous machines are widely spreading in automotive and vehicle traction applications, because of their high efficiency over a wide speed range. This capability can be achieved by appropriated control strategies: Maximum Torque per Ampere (MTPA), Flux Weakening (FW) and Maximum Torque per Volt (MTPV). However, these control trajectories are often based on an simplified magnetic model of the electrical machine. In order to improve the evaluation of machine output capabilities, nonlinear magnetic behavior must be modeled. This is not only related to the final application with a given drive and control structure, but also during the design process of the electric machine. In the design process, the output torque Vs. speed characteristic must be calculated following MTPA, MTPV and FW in the most accurate way to avoid significant error. This paper proposes a set of algorithms to compute MTPA, FW and MTPV curves for interior permanent-magnet synchronous machines taking into account the machines’ nonlinearities caused by iron saturation and compares differed approaches to highlight the torque–speed capabilities for the same machine following different methods. The algorithms are based on the maps of the equivalent inductances of a reference interior permanent-magnet synchronous machine and inductances maps were obtained via 2-D Finite Element Analysis over the machine’s operating points in id − iq reference plane. The effects of different 2-D finite element methods are also computed by both standard nonlinear magnetostatic simulations and Frozen Permeability simulations. Results show that the nonlinear model computed via frozen permeability is more accurate than the conventional linear and nonlinear models computed via standard magnetostatic simulations; for this reason, during the electrical machine design, it is important to check the expected performance employing a complete inductance map and frozen permeability.