Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems

Saddle node bifurcation is a generic instability of parameterized differential equation models. The bifurcation geometry and some implications for the study of voltage collapse in electric power systems is described. The initial direction in state space of dynamic voltage collapse can be calculated from a right eigenvector of a static power system model. The normal vector to the bifurcation set in parameter space is a simple function of a left eigenvector and is expected to be useful in emergency control near bifurcation and in computing the minimum distance to bifurcation in parameter space