Dynamic model of induction motor in the hyper-complex space

In this paper, the stator and rotor voltage differential equations of an induction motor with a squirrel-cage rotor (IM) and electrical torque formula are presented in frame of the quaternion tools. The mathematical representation has been obtained after different coordinates transformations which are invariant with respect to the scalar quantities. The applying of the IM dynamic models based on the hyper-complex space allows the separation of the instantaneous power into real and imaginary components and by this to describe the electromechanical energy conversion in more detail.