Characterizing Tolerable Disturbances for Transient-State Safety in Power Networks

This paper develops methods to compute the set of disturbances on a power network that do not tip the frequency of each bus and the power flow in each transmission line beyond pre-defined bounds. For a linearized AC power network model, we consider scenarios with varying degree of knowledge about the form of the disturbance. We propose a sampling method to provide inner and outer approximations with tunable accuracy of the set of tolerable disturbances. The complexity of computing such set approximations is a function of the number of sampling points. We introduce an error metric to measure the gap between the approximations and design an algorithm that finds, for fixed number of sampling points, the sampling sequence that minimizes its value. Simulations on the IEEE 39-bus power network illustrate our results.