Bifurcation subsystem method and its application to diagnosis of power system bifurcations produced by discontinuities

Recurrent problems in diagnosing the cause and location of a stability problem in a power system are that of (a) the size and complexity of the model, (b) the various kinds and classes of bifurcations, and (c) the effects of discontinuous hard limit or equipment outage-induced transitions. Problem diagnosis in power systems is in need of stability assessment methods that (i) take into account both the existence of discontinuities and their effect, and (ii) identifies which physical elements or subsystems are associated with a specific bifurcation observed on the full model.;Second, an Epoch-Based Trajectory Stability Assessment Methodology that is aimed at assessing asymptotic stability within time intervals free of hard limits discontinuities is presented. In this method, the stability assessment requires testing of quasi equilibria, limit cycles and trajectories within each epoch, rather than attempting to study stability of the entire trajectory.;The third major step is to identify the smallest subsystem, a subset of the equations of the full system model that experiences the same bifurcation in the full system model. The bifurcation subsystem must satisfy both the linear and the transversality conditions for the bifurcation that is being experienced in the full system model. The portion of the full system external to this bifurcation subsystem has no effect on the linear conditions for bifurcation to be satisfied in the full system model, and yet the equilibrium point is dependent on the variations in the full system equations which results in bifurcation in both the full system and the bifurcation subsystem. The bifurcation subsystem method utilizes the geometry associated with the various submatrices of the differential-algebraic Jacobian J and with the eigenvectors associated with the bifurcating eigenvalue to establish conditions for existence of such subsystems. Two examples for validating and using the bifurcation subsystem method to identify bifurcation subsystems in a model are presented, and the results are compared with right eigenvector and participation information. The bifurcation subsystem method can be in disagreement with both eigenvector and participation information.;The bifurcation subsystem and the model dependency of test matrices T, K;First, diagnosis is initiated by performing a classification of the modeling complexity and of the various bifurcations, based on their kinds and classes. The dynamic behavior of a simulated stability problem depends on the modeling complexity used.