Loss of voltage controllability as a cause of voltage collapse

Voltage stability and controllability definitions are proposed that can be applied at any time instant along the transient stability model trajectory or at the equilibrium point. Voltage controllability is defined at PQ buses. Conditions on sensitivity matrices that guarantee voltage controllability are then developed. The conditions for PQ voltage controllability are shown to encompass all of the known tests. Voltage collapse is shown to be a midterm stability problem that can occur due to a bifurcation of the midterm transient stability model. A compatible load flow and transient stability model is developed that allows the determination of voltage collapse conditions based on the load flow model or midterm stability model. The satisfaction of the tests for voltage controllability along the midterm stability trajectory ensures that voltage collapse will not occur at any point in time, given a particular midterm/transient trajectory. The midterm transient stability model and the compatible load flow model are developed. PQ test conditions for PQ controllability are developed for both nondecoupled and decoupled models