AC machine dynamics described by space vectors using state‐space notation

Asynchronous machines represent by now the majority of applications in the sector of variable speed drives. The demands on the performance of their control have risen as they by now replace DC machines with sophisticated control. Therefore it is necessary to describe the dynamic behaviour of an AC machine correctly and at the same time as simply and graphically as possible, because efficient control schemes can be designed best based on a complete understanding of the AC machine dynamics. Such a simple and graphical description can be achieved by combining the space‐vector theory introduced by Kovacs and Racz with the state‐space notation. Additionally it is advantageous to introduce a rotating reference frame which can be selected according to the problem at hand. Combining space vectors and state‐space notation leads to single complex eigenvalues instead of the usual pair of an eigenvalue and its conjugate. Changing the velocity of the reference frame naturally changes the eigenfrequencies, as can be seen from the eigenvalues in their analytic form calculated and discussed in this paper. It is shown that the effects caused by introducing a rotating reference frame in general have not necessarily to do with induced voltages and Faraday's law.