A method for estimating the severity of generator unit outage and multi-terminal branch outage contingencies with respect to voltage collapse in large-scale electric power systems which includes the steps of estimating a post-contingency saddle-node bifurcation induced voltage collapse point of an electric power system following a set of generator unit outages and/or a set of branch outages and calculating a distance to collapse of said power system. The post-contingency voltage collapse point is determined by application of a nonlinear contingency screening method.