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This paper provides an of overview of local bifurcation theory and its application to power system voltage stability analysis. The qualitative behavior of power system dynamics as modeled by differential-algebraic equations is discussed, followed by a summary of the concepts and tools for the analysis of local bifurcation from equilibria. Computational methods for locating and classifying bifurcation points as they have been applied in power system analysis are reviewed. Several examples are given.
Kwatny et al. (Sun,) studied this question.