Methods for determining proximity to voltage collapse

Theoretical results have shown that PQ controllability is sufficient to insure that every known test for prevention of voltage collapse is satisfied. This result unifies the theoretical basis for voltage collapse, since these tests were developed based on radically different power system models, tested very different matrices and conditions, and were based on different theoretical approaches. This theoretical foundation is used to develop methods of determining the proximity to voltage collapse. An algorithm for computing voltage control areas, which are groups of interconnected buses, is developed. It is shown that proper system and operation planning must be undertaken in each voltage control area if voltage collapse is to be prevented. A measure of the proximity to voltage collapse is shown to be the reactive reserves in a voltage control area boundary.>