Attack Vulnerability of Power Systems Under an Equal Load Redistribution Model

This paper studies the vulnerability of flow networks against adversarial attacks. In particular, consider a power system (or, any system carrying a physical flow) consisting of N transmission lines with initial loads L
₁
, . . . , L
_N
and capacities C
₁
, . . . , C
_N
, respectively; the capacity C defines the maximum flow allowed on line i. Under an equal load redistribution model, where load of failed lines is redistributed equally among all remaining lines, we study the optimization problem of finding the best k lines to attack so as to minimize the number of alive lines at the steady-state (i.e., when cascades stop). This is done to reveal the worst-case attack vulnerability of the system as well as to reveal its most vulnerable lines. We derive optimal attack strategies in several special cases of load-capacity distributions that are practically relevant. We then consider a modified optimization problem where the adversary is also constrained by the total load (in addition to the number) of the initial attack set, and prove that this problem is NP-hard. Finally, we develop heuristic algorithms for selecting the attack set for both the original and modified problems. Through extensive simulations, we show that these heuristics outperform benchmark algorithms under a wide range of settings.