Relating instability in synchronous motors to steady-state theory using the Hurwitz-Routh criterion

Conditions under which spontaneous oscillations can occur in synchronous motors are evaluated in terms of normalised parameters. The method involves the development of the characteristic equation of the motor model in which viscous friction to ground or inertial damping is included. Application of the Hurwitz-Routh criterion to this equation reveals that a single dynamic stability boundary equation may be obtained within the region of `statically stable¿ operation. The Hurwitz-Routh criterion is also shown to indicate the region of static instability. The findings are related directly to classical theory. In particular, when there is a complete absence of viscous friction, the dynamic stability boundary on the circle diagram of the motor is also shown to be circular. Experimental evidence is presented in support of the findings. The treatment is self-contained and should be within the scope of final-year undergraduates.