Spatial and Topological Interdiction for Transmission Systems

This paper presents novel formulations and algorithms for the $N$-$k$ interdiction problem in transmission networks. In particular, it models two new classes of $N$-$k$ attacks: (i) Spatial $N$-$k$ attacks where the attack is constrained to be within a specified distance of a bus chosen by an attacker and (ii) Topological $N$-$k$ attacks where the attack is constrained to connected components. These two specific types of $N$-$k$ attacks compute interdiction plans designed to better model localized attacks, such as those induced by natural disasters or physical attacks. We formulate each of these problems as bilevel, max-min optimization problems and present an algorithm to solve these formulations. Detailed case studies analyzing the behavior of these interdiction problems and comparing them to the traditional worst-case $N$-$k$ interdiction problem are also presented.