The authors focus on bifurcation of modes associated with both the generator and load dynamics to show the relations between two different critical states. The authors observe that a system encounters both oscillatory-type instability and collapse-type instability using a sample power system model developed by I. Dobson et al. (1988). In addition to the collapse-type instability reported by Dobson et al., oscillatory-type instability is analyzed by using Hopf bifurcation theory. The authors analyze these two types of system instability in a sample power system via bifurcation theory. Collapse-type instability is studied through the center manifold reduction technique, which reduces the entire system dynamic model to a one dimensional manifold.
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