Kin Cheong Sou

Julien M. Hendrickx, Karl Henrik Johansson, Raphael M. Jungers et al.

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.

Kin Cheong Sou, Henrik Sandberg, Karl Henrik Johansson

This paper considers a smart grid cyber-security problem analyzing the vulnerabilities of electric power networks to false data attacks. The analysis problem is related to a constrained cardinality minimization problem. The main result shows that an $l_1$ relaxation technique provides an exact optimal solution to this cardinality minimization problem. The proposed result is based on a polyhedral combinatorics argument. It is different from well-known results based on mutual coherence and restricted isometry property. The results are illustrated on benchmarks including the IEEE 118-bus and 300-bus systems.

Kin Cheong Sou, Gabriel Malmer, Lovisa Thorin et al.

Network reconfiguration can significantly increase the hosting capacity (HC) for distributed generation (DG) in radially operated systems, thereby reducing the need for costly infrastructure upgrades. However, when the objective is DG maximization, jointly optimizing topology and power dispatch remains computationally challenging. Existing approaches often rely on relaxations or approximations, yet we provide counterexamples showing that interior point methods, linearized DistFlow and second-order cone relaxations all yield erroneous results. To overcome this, we propose a solution framework based on the exact DistFlow equations, formulated as a bilinear program and solved using spatial branch-and-bound (SBB). Numerical studies on standard benchmarks and a 533-bus real-world system demonstrate that our proposed method reliably performs reconfiguration and dispatch within time frames compatible with real-time operation.