New methods for computing a closest saddle node bifurcation and worst case load power margin for voltage collapse

Voltage collapse and blackout can occur in an electric power system when load powers vary so that the system loses stability in a saddle node bifurcation. The authors propose new iterative and direct methods to compute load powers at which bifurcation occurs and which are locally closest to the current operating load powers. The distance in load power parameter space to this locally closest bifurcation is an index of voltage collapse. The pattern of load power increase need not be predicted; instead the index is a worst case load power margin. The computations are illustrated in the six-dimensional load power parameter space of a five bus power system. The normal vector and curvature of a hypersurface of critical load powers at which bifurcation occurs are also computed. The sensitivity of the index to parameters and controls is easily obtained from the normal vector