The Voltage Stability Security Assessment and Diagnostic Method [1] 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 protects 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 [2] 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 (voltage control area and reactive reserve basin) 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 condition 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.Index Terms-Agent, bifurcation, clogging voltage instability, eigenvalue, loss of control voltage instability, reactive reserve basin, voltage control area, voltage stability.
This paper presents a method for determining reduced-order subsystems called bifurcation subsystems, that experience bifurcation, and produce the bifurcation in the full power system dynamic model. The bifurcation subsystem is generally a subset of the center manifold subsystem. The bifurcation subsystem is in fact the singular perturbation determined slow subsystem within the center manifold dynamics that actually experiences and produces the bifurcation in the center manifold dynamics. The test procedure used to determine a bifurcation subsystem is described in this paper and does not require performing a nonlinear transformation required to determine the center manifold. The theory provides two singular perturbation based test conditions for existence of bifurcation subsystems. Examples that demonstrate the systematic use of this test procedure are presented for saddle-node and Hopf bifurcations in a single-machine-infinite-bus-model. Results when the test procedure for finding a bifurcation subsystem is applied to the large dominant elements of the tight eigenvector and the participation factor of a bifurcating eigenvalue are compared.
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