A Nonlinear Systems Theory Approach to Assessment of Fault Vulnerability in Power Systems

Engineered systems, such as power systems, naturally experience disruptions to normal operation. Whether a system is able to recover from a particular nonlinear disturbance depends on the values of system parameters, which are typically uncertain and time-varying. Fix a particular disturbance, such as particular fault on a particular transmission line. The goal is to numerically determine the boundary in parameter space, called the recovery boundary, between parameter values which lead to recovery and those which lead to a failure to recover to an initial stable equilibrium point. A class of theoretically motivated algorithms is developed to compute parameter values on the recovery boundary. These rely on the intuition that, on the boundary of the region of attraction of a stable equilibrium point, the system trajectory becomes infinitely sensitive to small perturbations.