Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study

Mehdi Doostinia, Davide Falabretti (), Giacomo Verticale and Sadegh Bolouki
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Mehdi Doostinia: Electrical Engineering, Department of Energy, Polytechnic University of Milan, 20156 Milan, Italy
Davide Falabretti: Electrical Engineering, Department of Energy, Polytechnic University of Milan, 20156 Milan, Italy
Giacomo Verticale: Department of Electronics, Information, and Bioengineering, Polytechnic University of Milan, 20133 Milan, Italy
Sadegh Bolouki: Department of Computer and Software Engineering, Polytechnique Montréal, Montreal, QC H3T 1J4, Canada

Energies, 2025, vol. 18, issue 11, 1-26

Abstract: In today’s world, power distribution systems and information and communication technology (ICT) systems are increasingly interconnected, forming cyber–physical power systems (CPPSs) at the core of smart grids. Ensuring the resilience of these systems is essential for maintaining reliable performance under disasters, failures, or cyber-attacks. Identifying critical nodes within these interdependent networks is key to preserving system robustness. This paper applies complex network (CN) theory—specifically degree centrality (DC), closeness centrality (CC), and betweenness centrality (BC)—to a real-world distribution grid integrated with an ICT layer in northeastern Italy. Simulations are conducted across three scenarios: a directed power network, an undirected power network, and an undirected ICT network. Each centrality metric generates a ranking of nodes which is validated using node removal performance (NRP) analysis. In the directed power network, in-closeness centrality and out-degree centrality are the most effective in identifying critical nodes, with correlations of 84% and 74% with NRP, respectively. DC and BC perform best in the undirected power network, with correlation values of 67% and 53%, respectively. In the ICT network, BC achieves the highest correlation (64%), followed by CC at 55%. These findings demonstrate the potential of centrality-based methods for identifying critical nodes and support strategies for enhancing CPPS resilience and fault recovery by distribution system operators.

Keywords: power distribution grids; ICT systems; resilience; cyber–physical power systems; centrality; complex networks (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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