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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mehdi Doostinia & Davide Falabretti & Giacomo Verticale & Sadegh Bolouki, 2025. "Critical Node Identification for Cyber–Physical Power Distribution Systems Based on Complex Network Theory: A Real Case Study," Energies, MDPI, vol. 18(11), pages 1-26, June.
    • Handle: RePEc:gam:jeners:v:18:y:2025:i:11:p:2937-:d:1671082
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    References listed on IDEAS

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    1. Wang, Shuliang & Gu, Xifeng & Chen, Jiawei & Chen, Chen & Huang, Xiaodi, 2023. "Robustness improvement strategy of cyber-physical systems with weak interdependency," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Mahmoud Saleh & Yusef Esa & Ahmed Mohamed, 2018. "Applications of Complex Network Analysis in Electric Power Systems," Energies, MDPI, vol. 11(6), pages 1-16, May.
    3. Lucas Cuadra & Sancho Salcedo-Sanz & Javier Del Ser & Silvia Jiménez-Fernández & Zong Woo Geem, 2015. "A Critical Review of Robustness in Power Grids Using Complex Networks Concepts," Energies, MDPI, vol. 8(9), pages 1-55, August.
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