High-Frequency d– q Model of Synchronous Machines for Sensorless Control

This paper describes a d-q-axis model of synchronous permanent-magnet machines at high frequency. Both the inductive and resistive saliencies are taken into account, and the model is suitable for investigating the self-sensing capability of the machines. It is proved that the high-frequency machine response can be described by means of three complex parameters, which form a symmetrical matrix. It is also shown that the high-frequency resistances between the d- and q-axes exist, and they may assume a negative value. Experimental results are included in this paper to prove the developed theory.