Justification of the voltage stability security assessment and diagnostic procedure using a bifurcation subsystem method

The voltage stability security assessment and diagnostic method identifies: (1) coherent bus groups (voltage control areas) that are sufficiently coherent that each has a unique voltage collapse problem; and (2) the reactive reserve basin whose reactive reserves protect the associated coherent bus group from voltage collapse. Each voltage instability agent is defined as being composed of a voltage control area and its associated reactive reserve basin. The VSSAD method of identifying all of the agents is proven to be a modal method. This is true because (a) each agent is determined as the subsystem where reactive stress causes a particular loadflow Jacobian eigenvalue to experience bifurcation; and (b) knowledge of the agent identifies and predicts the discontinuous changes in the eigenvalue that produces voltage instability in that agent. A bifurcation subsystem method is defined that identifies the subsystem (in terms of the voltage control area and its reactive reserve basin) that not only experiences, but produces and causes the voltage collapse observed in the full loadflow model. The bifurcation subsystems or agents are identified for all clogging voltage instability problems. The two conditions for a specific bifurcation subsystem to exist and experience bifurcation are related to two eigenvalue estimates associated with that bifurcation subsystem. These bifurcation subsystem conditions related eigenvalue estimates are used to theoretically justify the diagnostic procedures for determining where, when, why, and what can be done to prevent bifurcation in a specific agent found in VSSAD.