Skip to main content
SpringerLink
Log in

Empirical Electrical-Based Framework to Judge the Ability of Centrality Measures in Predicting Grid Vulnerability

  • Original Article
  • Published:
Journal of Electrical Engineering & Technology Aims and scope Submit manuscript

Abstract

We develop an empirical electrical-based framework to compare between centrality measures as to judge their ability to predict the vulnerability of smart grids and their elements under various attacks. The centrality measures considered are based on a weighted graph adjacency matrix representing the real power flows. The vulnerability is measured by the post-attack unsatisfied load (UL), which is determined through steady-state simulation using the MatPower v6.0. We introduce a generalized vulnerability curve as a plot of measures of electrical damage (e.g., the UL), versus physical damage. We consider various measures of physical damage such as the Fraction of Elements (FOE) removed and sums of centrality scores of elements removed. The area under the vulnerability curve (denoted as VPM) is shown to be a logical, reliable, and consistent indicator of the predictive power of a centrality measure. The VPM is simulated for several attacks including the Remove Most Central Elements First (RMCEF) attack. We show that degree centrality is the most predictive, when compared to eigenvector and betweenness centralities. Moreover, the degree-based RMCEF attack is the worst among the RMCEF and 5400 random attacks. The FOE-degree centrality VPM is the most predictive as well as the most computationally efficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Mili L, Qiu Q (2004) Risk assessment of catastrophic failures in electric power systems. Int J Crit Infrastruct 1(1):38–63

    Article  Google Scholar 

  2. Sweet B (2012) A post-mortem on India’s blackout. IEEE spectrum, 2012. Available: http://spectrum.ieee.org/energy wise/energy/the-smarter-grid/a-postmortem-on-indias-blackout. Accessed 17 Dec 2016

  3. Ordacgi JM (2010) Brazilian blackout 2009 blackout watch. PAC world magazine, Vol. 2010, No. March 2010, pp 36–37

  4. U.S.-Canada Power System Outage Task Force (2004) Final report on the August 14, 2003 blackout in the United States and Canada: causes and recommendations, 2004

  5. Newman ME (2003) The structure and function of complex networks. SIAM Rev 45:167–256

    Article  MathSciNet  Google Scholar 

  6. Bompard E, Huang T, Wu Y, Cremenescu M (2013) Classification and trend analysis of threats origins to the security of power systems. Int J Electr Power Energy Syst 50:50–64

    Article  Google Scholar 

  7. Zhu Y, Yan J, Sun Y, He H (2014) Revealing cascading failure vulnerability in power grids using risk-graph. IEEE Trans Parallel Distrib Syst 25:3274–3284

    Article  Google Scholar 

  8. Zhao L, Park K, Lai YC, Ye N (2005) Tolerance of scale-free networks against attack-induced cascades. Phys Rev E 72:025104

    Article  Google Scholar 

  9. Holmgren J (2006) Using graph models to analyze the vulnerability of electric power networks. Risk Anal 26(4):955–969

    Article  Google Scholar 

  10. Pagani GA, Aiello M (2013) The power grid as a complex network: a survey. Phys A Stat Mech Appl 392(11):2688–2700

    Article  MathSciNet  Google Scholar 

  11. Kim CJ, Obah OB (2007) Vulnerability assessment of power grid using graph topological indices. Int J Emerg Electr Power Syst 8(6):4

    Google Scholar 

  12. Rosas-Casals MM, Valverde S, Sole RV (2007) Topological vulnerability of the European power grid under errors and attacks. Int J Bifurc Chaos 17(7):2465–2475

    Article  Google Scholar 

  13. Sole RV, Rosas-Casals M, Corominas-Murtra B, Valverde S (2008) Robustness of the European power grids under intentional attack. Phys Rev E 77:026102

    Article  Google Scholar 

  14. Rosato V, Bologna S, Tiriticco F (2007) Topological properties of high-voltage electrical transmission networks. Electr Res Power Syst 77:99–105

    Article  Google Scholar 

  15. Crucitti P, Latora V, Marchiori M (2005) Locating critical lines in high-voltage electrical power grids. Fluct Noise Lett 5:L201–L208

    Article  Google Scholar 

  16. Mei S, Zhang X, Cao M (2011) Power grid complexity. Springer, Berlin, Germany

    Book  Google Scholar 

  17. Bompard E, Wu D, Xue F (2010) The concept of betweenness in the analysis of power grid vulnerability. In: Proceedings of the complexity in engineering, 2010 (COMPENG’10), Rome, Italy, 22–24 Feb, pp 52–54

  18. Holmgren AJ, Jenelius E, Westin J (2007) Evaluating strategies for defending electric power networks against antagonistic attacks. IEEE Trans Power Syst 22:76–84

    Article  Google Scholar 

  19. Verma T, Ellens W, Kooij RE (2013) Context-independent centrality measures underestimate the vulnerability of power grids. ArXiv

  20. Ernster TA, AK (2012) Power system vulnerability analysis - Towards validation of centrality measures. In: Proceedings of IEEE power engineering and society transmission and distribution conference, pp 1–6

  21. Gutierrez F, Barocio E, Uribe F, Zuniga P (2013) Vulnerability analysis of power grids using modified centrality measures. Discrete Dynamics in Nature and Society

  22. Wang Z, Scaglione A, Thomas RJ (2010) Electrical centrality measures for electric power grid vulnerability analysis. In: Proceedings of IEEE conference decision and control, pp 5792–5797

  23. Cuadra L, Salcedo-Sanz S, Del Ser J, - Fernandez S, Geem ZW (2015) A critical review of robustness in power grids using complex networks concepts. Energies 8(9):9211–9265

  24. Reka A, Barabasi A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

    Article  MathSciNet  Google Scholar 

  25. Bompard E, Napoli R, Xue F (2009) Analysis of structural vulnerabilities in power transmission grids. Int J Crit Infrastruct Prot 2(1–2):5–12

    Article  Google Scholar 

  26. Bompard E, Luo L, Pons E (2015) A perspective overview of topological approaches for vulnerability analysis of power transmission grids. Int J Crit Infrastruct 11(1):15–26

  27. Bompard E, Napoli R, Xue F (2010) Extended topological approach for the assessment of structural vulnerability in transmission networks. IET Gener Transm Distrib 4(6):716

    Article  Google Scholar 

  28. Caldarelli G, Vespignani A (2007) Large scale structure and dynamics of complex networks: from information technology to finance and natural science, Vol 2. World Scientific: Singapore

  29. Chopade P, Bikdash M (2016) New centrality measures for assessing smart grid vulnerabilities and predicting brownouts and blackouts. Int J Crit Infrastruct Prot 12:29–45

  30. Wang Z, Scaglione A, Thomas RJ (2010) Electrical centrality measures for electric power grid vulnerability analysis. In: 49th IEEE conference on decision and control (CDC). GA, Atlanta, pp 5792–5797

  31. Arianos S, Bompard E, Carbone A, Xue F (2009) Power grid vulnerability: a complex network approach. Chaos Interdiscip J Nonlinear Sci 19:013119

    Article  Google Scholar 

  32. Koc Y, Warnier M, Kooij RE, Brazier FMT (2014) Structural vulnerability assessment of electric power grids. In: Proceedings of 11th IEEE international conference on networking, sensing and control, Aug 2016, pp 386–391

  33. Wang X, Koç Y, Kooij RE, Van Mieghem P (2015) A network approach for power grid robustness against cascading failures. In: 2015 7th international workshop on reliable networks design and modeling (RNDM), pp 208–214

  34. Jin S, Huang Z, Chen Y, Chavarria-Miranda D, Feo J, Wong PC (2010) A novel application of parallel betweenness centrality to power grid contingency analysis. In: 2010 IEEE international symposium on parallel and distributed processing, pp 1–7

  35. MATLAB http://www.mathworks.com/

  36. Zimmerman RD, Murillo-Sanchez CE, TRJ (2015) MatPower 5.1 user’s manual

  37. Pahwa S, Hodges A , Scoglio C, Wood S (2010) Topological analysis of the power grid and mitigation strategies against cascading failures. In: Proceedings of the 4th annual IEEE systems conference, San Diego, CA, USA, 5–8 April, pp 272–276

  38. Wang JW, Rong LL (2009) Cascade-based attack vulnerability on the US power grid. Saf Sci 2009(47):1332–1336. XXXX

  39. Qi X, Fuller E, Wu Q, Wu Y, Zhang CQ (2012) Laplacian centrality: a new centrality measure for weighted networks. Inf Sci 194:240–253

    Article  MathSciNet  Google Scholar 

  40. Hotelling H calculation of principal components. Psychometrika 1(1):27–35

  41. Warshall S (1962) A theorem on Boolean matrices. J ACM 9(1):11–12

    Article  MathSciNet  Google Scholar 

  42. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177

    Article  Google Scholar 

  43. Albarakati A, Bikdash M (2018) Vulnerabilities of power grid due to line failures based on power traffic centrality of the line graph, SoutheastCon 2018, St. Petersburg, FL, 2018, pp 1–7

  44. Albarakati A, Bikdash M, Dai X (2017) Line-graph based modeling for assessing the vulnerability of transmission lines. In: 2017 proceedings of IEEE Southeastcon

Download references

Author information

Authors and Affiliations

  1. College of Computer and Information Science, Majmaah University, Majmaah, Saudi Arabia

    Aiman Albarakati

  2. Computational Data Science and Engineering, North Carolina A&T State University, Greensboro, NC, USA

    Marwan Bikdash

Authors
  1. Aiman Albarakati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marwan Bikdash
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aiman Albarakati.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albarakati, A., Bikdash, M. Empirical Electrical-Based Framework to Judge the Ability of Centrality Measures in Predicting Grid Vulnerability. J. Electr. Eng. Technol. 16, 1917–1927 (2021). https://doi.org/10.1007/s42835-021-00742-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42835-021-00742-4

Keywords

Search

Navigation