Saliency Model Extension for Sensorless Initial Position and Polarity Detection of Permanent Magnet Synchronous Motors

In this paper, we propose an extended permanent magnet synchronous motor model that incorporates a quadratic flux-current function to determine the polarity-dependent saliency and develop a sensorless initial position detection method that is capable of polarity detection. The quadratic model extension is based on the second-order Taylor polynomial of the flux-current function. We present the model equations in both the stator- and the rotor-oriented reference frames as well as the Park and inverse Park transforms of the quadratic terms and Hessian matrices. The transient behavior and the dependency of the extended model on the rotor position have been validated. The proposed initial position detection method injects non-modulated even square wave voltage signals and relies only on phase-current measurements. We analyzed the effect of the pulse length on the errors of the position estimation and polarity detection. We provide machine parameter-based approximations of the current components dependent on the rotor position and, based on them, present a quantitative pulse-length design method.