Efficient Synchronization Stability Metrics for Fault Clearing
  Direct methods can provide rapid screening of the dynamical security of large numbers fault and contingency scenarios by avoiding extensive time simulation. We introduce a computationally-efficient direct method based on optimization that leverages efficient cutting plane techniques. The method considers both unstable equilibrium points and the effects of additional relay tripping on dynamical security\cite{01SH}. Similar to other direct methods, our approach yields conservative results for dynamical security, however, the optimization formulation potentially lends itself to the inclusion of additional constraints to reduce this conservatism. 
Scott Backhaus, Russell Bent, Daniel Bienstock, Michael Chertkov, and   Dvijotham Krishnamurthy
cs.SY math.OC