Computational Analysis of Cascading Failures in Power Networks

We focus on cascading line failures in the transmission sys-tem of the power grid. Recent large-scale power outages demonstrated the limitations of epidemic- and percolation-based tools in modeling the cascade evolution. Hence, based on a linearized power flow model, we obtain results regarding the various properties of a cascade. Specifically, we consider performance metrics such as the distance between failures, the length of the cascade, and the fraction of demand (load) satisfied after the cascade. We show, for example, that due to the unique properties of the model: (i) a set of initial line failures may have a smaller effect than a failure of one of the lines in the set, (ii) the distance between subsequent failures can be arbitrarily large and the cascade may be arbitrar-ily long, and (iii) minor changes to the network parameters may have a significant impact. Moreover, we show that find-ing the set of lines whose removal has the most significant impact (under different metrics) is NP-hard. Finally, for specific graphs, we develop a fast algorithm to determine if a set of line failures initiates a cascade. The results can pro-vide insight into the design of smart grid measurement and control algorithms that can mitigate a cascade