Power Grid Vulnerability to Geographically Correlated Failures -   Analysis and Control Implications
  We consider power line outages in the transmission system of the power grid, and specifically those caused by a natural disaster or a large scale physical attack. In the transmission system, an outage of a line may lead to overload on other lines, thereby eventually leading to their outage. While such cascading failures have been studied before, our focus is on cascading failures that follow an outage of several lines in the same geographical area. We provide an analytical model of such failures, investigate the model's properties, and show that it differs from other models used to analyze cascades in the power grid (e.g., epidemic/percolation-based models). We then show how to identify the most vulnerable locations in the grid and perform extensive numerical experiments with real grid data to investigate the various effects of geographically correlated outages and the resulting cascades. These results allow us to gain insights into the relationships between various parameters and performance metrics, such as the size of the original event, the final number of connected components, and the fraction of demand (load) satisfied after the cascade. In particular, we focus on the timing and nature of optimal control actions used to reduce the impact of a cascade, in real time. We also compare results obtained by our model to the results of a real cascade that occurred during a major blackout in the San Diego area on Sept. 2011. The analysis and results presented in this paper will have implications both on the design of new power grids and on identifying the locations for shielding, strengthening, and monitoring efforts in grid upgrades. 
Andrey Bernstein, Daniel Bienstock, David Hay, Meric Uzunoglu, and Gil   Zussman
cs.SY cs.PF math.OC