  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.
