Individual Branch and Path Necessary Conditions for Saddle-Node Bifurcation Voltage Collapse

This paper explores the relation between saddle-node bifurcation voltage collapse and complex flow limits of individual transmission elements. Two necessary conditions for power system voltage collapse are presented. First, when a transfer of power takes place in a power system, at least one line must reach its static transfer stability limit (STSL) at or before the point of voltage collapse. Second, for a point-to-point transfer, a path from the source to the sink, formed by lines all of which have reached their STSL limits, must be formed in the network before the point of collapse is reached. We present numerical examples confirming these two necessary conditions.