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A comprehensive analysis of the dynamic behavior for a rudimentary but representative model of the power system is carried out for the case when control gain and load are varied as parameters. The voltage dynamics model is subject to algebraic constraints in the form of load flow equations and is studied as a differential-algebraic system in state and parameter spaces. Singularities in the state-space (noncausal points) and bifurcations in the parameter space are the principal and interacting structural elements. A rich structure of bifurcations emerges which is analyzed. The mathematical analysis is facilitated by singularly rescaling time, which transforms the differential algebraic system into a smooth dynamic system. In the state space, the characteristics of stability boundaries are observed and a description of the regions of attraction of all equilibria are given. The loosely understood term of voltage collapse is classified into well-defined types on both the dynamic and parameteric sides.>
Venkatasubramanian et al. (Wed,) studied this question.
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