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The loading margin to a saddle-node or fold bifurcation measures the proximity to voltage collapse blackouts of electric power transmission systems. Sensitivities of the loading margin can be used to select controls to avoid voltage collapse. We analytically justify the use of static models to compute loading margins and their sensitivities and explain how the results apply to underlying dynamic models. The relation between fold bifurcations of the static models and saddle-node bifurcations of the underlying dynamic models is clarified.

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities