The Relationship Between Root Locus and Transient Field Components of AC Machines

The dynamic analysis of induction motors is supported by well-known theories: the two-axes transformation, and the space vector theory. Yet some inconsistencies with the theory of dynamic systems exist. The machine eigenvalues suggest the existence of two damped oscillators, physically not understandable. The respective eigenfrequencies change with the angular velocity of the reference frame. This contradicts the understanding that eigenfrequencies are inherent system properties. Physically, the dynamics depend on the continuous distribution of magnetic energy and its spatial displacement during transient processes. Information on the system dynamics is lost when dividing the continuum of magnetic energy into discrete portions. Complex state variables associate the dynamics to the propagation in space of distributed magnetic fields. The dynamic analysis reveals the existence single-complex eigenvalues. These define a novel class of system identifiers. They are characterized by having only one imaginary part instead of a conjugate complex pair. The use of complex state variables conveys insight and physical understanding of the dynamic processes within the machine. The approach constitutes an extension to the theory of dynamic systems.