Transient stability assessment with unstable limit cycle approximation

Unstable equilibrium points (UEP's) have been studied extensively in the tr ansient stability literature previously for understanding the transient sta bility boundary structure of the system operating point. In contrast with U EP's, unstable limit cycles (ULC's) can represent the critical portion of t he transient stability boundary for a detailed power system model under cer tain operating conditions. Using Hopf bifurcation theory, it is shown that ULC's are likely to be present on the transient stability boundary when the operating condition has poorly damped oscillatory modes which are subcriti cal (that is, nonlinear unstable). Because it is extremely difficult to com pute ULC's in general power system models, a novel technique to approximate unstable limit cycles through reverse-time integration on a center manifol d approximation is proposed in the paper. The technique is illustrated by c omputation of ULC's in 9-bus and 4-bus test systems. Transient stability as sessments based on ULC's are tested for computation of critical clearing ti mes and maximum loading scenarios.