[Paper Review] Spatial and Topological Interdiction for Transmission Systems

Kaarthik Sundar, Sidhant Misra+2 more|arXiv (Cornell University)|Apr 17, 2019

Infrastructure Resilience and Vulnerability Analysis19 references4 citations

TL;DR

This paper introduces spatial and topological $N$-$k$ interdiction models for transmission systems, formulating them as bilevel max-min optimization problems to better simulate localized attacks like natural disasters or physical strikes. The proposed algorithms effectively identify critical vulnerabilities under realistic attack constraints, outperforming traditional worst-case $N$-$k$ approaches in modeling spatial and topological limitations.

ABSTRACT

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.

Motivation & Objective

• To address the limitations of traditional $N$-$k$ interdiction by modeling attacks that are spatially or topologically constrained, reflecting real-world scenarios like natural disasters or physical attacks.
• To develop novel bilevel max-min optimization formulations that capture the strategic behavior of attackers targeting transmission networks under spatial and topological constraints.
• To design efficient algorithms for solving these new interdiction problems and evaluate their performance against standard $N$-$k$ worst-case interdiction.

Proposed method

• Formulate spatial $N$-$k$ interdiction as a bilevel optimization where the attacker selects a bus and disrupts lines within a specified distance, constrained by spatial proximity.
• Model topological $N$-$k$ interdiction as a bilevel problem where the attacker targets a connected component of the network, ensuring attack feasibility within a single network segment.
• Use a bilevel max-min framework to represent the attacker's goal of maximizing system disruption, while the defender aims to minimize the worst-case impact.
• Develop a solution algorithm tailored to the structure of the bilevel problems, leveraging decomposition and optimization techniques to improve computational efficiency.
• Implement and test the models on case studies to compare performance and robustness against traditional $N$-$k$ interdiction.

Experimental results

Research questions

• RQ1 How do spatially constrained $N$-$k$ attacks affect the vulnerability assessment of transmission networks compared to traditional worst-case $N$-$k$ attacks?
• RQ2 To what extent do topological constraints on interdiction improve the realism of attack modeling in power systems?
• RQ3 Can the proposed bilevel optimization formulations and algorithms effectively identify critical network components under localized attack scenarios?
• RQ4 How do the new attack models compare in terms of system impact and computational complexity to standard $N$-$k$ interdiction?

Key findings

• The spatial $N$-$k$ model identifies attack patterns that are more geographically concentrated, reflecting realistic scenarios such as earthquakes or storms.
• The topological $N$-$k$ model reveals vulnerabilities within specific network components, highlighting the importance of connectivity in attack planning.
• Both models produce interdiction plans that are more strategically plausible than traditional $N$-$k$ attacks, which often assume arbitrary component removal.
• Case studies show that the new models can identify critical lines and buses that are overlooked by standard $N$-$k$ approaches, improving system resilience assessment.