Efficient Computations of a Security Index for False Data Attacks in Power Networks

Abstract

Abstract-The resilience of Supervisory Control and Data Acquisition (SCADA) systems for electric power networks for certain cyber-attacks is considered. We analyze the vulnerability of the measurement system to false data attack on communicated measurements. The vulnerability analysis problem is shown to be NP-hard, meaning that unless P = NP there is no polynomial time algorithm to analyze the vulnerability of the system. Nevertheless, we identify situations, such as the full measurement case, where it can be solved efficiently. In such cases, we show indeed that the problem can be cast as a generalization of the minimum cut problem involving costly nodes. We further show that it can be reformulated as a standard minimum cut problem (without costly nodes) on a modified graph of proportional size. An important consequence of this result is that our approach provides the first exact efficient algorithm for the vulnerability analysis problem under the full measurement assumption. Furthermore, our approach also provides an efficient heuristic algorithm for the general NP-hard problem. Our results are illustrated by numerical studies on benchmark systems including the IEEE 118-bus system.

Security analysis of control system anomaly detectors

“…The nonlinear covert attack is deemed to be more difficult to implement than the linear one due to the changes in the operating points of the system caused by the attack. Hendrickx et al [6] has again a different approach of handling the threat of an attack. This article tries to identify weaknesses in a static model of a power grid by calculating a security index for each measurement taken.…”

“…This can be used to determine the threat an attack poses. In this context minimum-resource attacks are defined, which are closely related to the security index problem in [6]. Furthermore a minimumresource, maximum-impact attack for dynamic systems is defined, which can also be used in the risk management context to determine the likelihood and impact of an attack.…”

“…with i ∈ {3, 4, 5} and according to Chebyshev's inequality 11.1111%, 6.25% or 4% of the nominal values of ||r k || 2 2 will lie outside this threshold. This should therefore prevent too many false alarms caused by noise and at the same time should not be too high to detect dubious distortions of the system for the stateless detector.…”

“…So all r k ∈ R p are reachable with the attack a k and with (3.19) one can also define a new system with the residual as an input µ k+1 = A e µ k + B e a k = (A e − B e D + e C e )µ k + B e D + e r k + B e a Null and use this equation to maximize the final state as it is done in Section 3. 6. 3.…”

Cyber security analysis of power networks by hypergraph cut algorithms

“…Sandberg et al [12] also formulated a similar optimization problem for finding a sparsest attack including a given measurement point and defined the optimal value as the security index of the point. After Sandberg et al [12] proposed a simple heuristics to find a suboptimal solution for the problem, Sou et al [13], [14] and Hendrickx et al [2] provided efficient solution methods as follows. It was shown in [13] that the problem reduces to a minimum cost node-bipartitioning problem, which is approximately solved by finding a minimum s-t cut in the given network.…”