Dynamic voltage instability

Several researchers have dealt with the problem of voltage collapse as a loss of equilibria or by noting the singularity of the Jacobian at the onset of the phenomenon. In these cases the problem is characterized as a quasi-static bifurcation occuring in response to a slowly varying increase or decrease in load. However, dynamic load characteristics have long been known to have an effect on system stability and in fact, assumptions about the load model will significantly affect any predictions. In this paper, we discuss voltage stabilities as a function of loads. We investigate the stability characteristics of a basic configuration consisting of a generator, an induction motor load, and a static load. Using an aggregated steady-state equivalent circuit representation for the induction motor, we derive a motor torque-slip differential equation. We show that when induction motor charactestics are incorporated the voltage stability region is smaller than that defined by Venikov's steady-state stability limits 1. We also present an example of a voltage collapse using the induction motor torque-slip differential equation that is different from those described before.