Transient stability assessment with unstable limit cycle approximation

Unstable equilibrium points (UEPs) have been studied extensively in the transient stability literature previously for understanding the transient stability boundary structure of the system operating point. In contrast with UEP's, unstable limit cycles (ULCs) can represent the critical portion of the transient stability boundary for a detailed power system model under certain operating conditions. Using Hopf bifurcation theory, it is shown that ULCs are likely to be present on the transient stability boundary when the operating condition has poorly damped oscillatory modes which are subcritical (that is, nonlinear unstable). Because it is extremely difficult to compute ULCs in general power system models, a novel technique to approximate unstable limit cycles through reverse-time integration on a center manifold approximation is proposed in the paper. The technique is illustrated by computation of ULCs in 9-bus and 4-bus test systems. Transient stability assessments based on ULCs are tested for computation of critical clearing times and maximum loading scenarios.