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Joint Cyber and Physical Attacks on Power Grids: Graph Theoretical Approaches for Information Recovery

Published: 15 June 2015 Publication History

Abstract

Recent events demonstrated the vulnerability of power grids to cyber attacks and to physical attacks. Therefore, we focus on joint cyber and physical attacks and develop methods to retrieve the grid state information following such an attack. We consider a model in which an adversary attacks a zone by physically disconnecting some of its power lines and blocking the information flow from the zone to the grid's control center. We use tools from linear algebra and graph theory and leverage the properties of the power flow DC approximation to develop methods for information recovery. Using information observed outside the attacked zone, these methods recover information about the disconnected lines and the phase angles at the buses. We identify sufficient conditions on the zone structure and constraints on the attack characteristics such that these methods can recover the information. We also show that it is NP-hard to find an approximate solution to the problem of partitioning the power grid into the minimum number of attack-resilient zones. However, since power grids can often be represented by planar graphs, we develop a constant approximation partitioning algorithm for these graphs. Finally, we numerically study the relationships between the grid's resilience and its structural properties, and demonstrate the partitioning algorithm on real power grids. The results can provide insights into the design of a secure control network for the smart grid.

References

[1]
Platts GIS Data. http://www.platts.com/Products/gisdata.
[2]
Power systems test case archive. Available at: http://www.ee.washington.edu/research/pstca/.
[3]
U.S.-Canada Power System Outage Task Force. Report on the August 14, 2003 blackout in the United States and Canada: Causes and recommendations. 2004.
[4]
Report of the enquiry committee on grid disturbance in Northern region on 30th July 2012 and in Northern, Eastern and North-Eastern region on 31st July 2012, Aug. 2012.
[5]
The Federal Energy Regulatory Comission (FERC) and the North American Electric Reliability Corporation (NERC). Arizona-Southern California Outages on September 8, 2011. 2012.
[6]
Assault on California power station raises alarm on potential for terrorism. Source: http://goo.gl/RiuhI1, 2014.
[7]
Cybersecurity and the North American electric grid: New policy approaches to address an evolving threat. Source: http://goo.gl/WgUbPI, 2014.
[8]
R. Albert, H. Jeong, and A.-L. Barabási. Error and attack tolerance of complex networks. Nature, 406(6794):378--382, 2000.
[9]
R. Bapat. Graphs and matrices. Springer, 2010.
[10]
A.-L. Barabási and R. Albert. Emergence of scaling in random networks. Science, 286(5439):509--512, 1999.
[11]
A. R. Bergen and V. Vittal. Power Systems Analysis. Prentice-Hall, 1999.
[12]
A. Bernstein, D. Bienstock, D. Hay, M. Uzunoglu, and G. Zussman. Sensitivity analysis of the power grid vulnerability to large-scale cascading failures. ACM SIGMETRICS Perform. Eval. Rev., 40(3):33--37, 2012.
[13]
A. Bernstein, D. Bienstock, D. Hay, M. Uzunoglu, and G. Zussman. Power grid vulnerability to geographically correlated failures - analysis and control implications. In Proc. IEEE INFOCOM'14, Apr. 2014.
[14]
D. Bienstock. Optimal control of cascading power grid failures. Proc. IEEE CDC-ECC, Dec. 2011.
[15]
D. Bienstock and A. Verma. The N-k problem in power grids: New models, formulations, and numerical experiments. SIAM J. Optimiz., 20(5):2352--2380, 2010.
[16]
J. A. Bondy and U. Murty. Graph theory, volume 244 of graduate texts in mathematics, 2008.
[17]
J. A. Bondy and U. S. R. Murty. Graph theory with applications. Macmillan London, 1976.
[18]
S. Buldyrev, R. Parshani, G. Paul, H. Stanley, and S. Havlin. Catastrophic cascade of failures in interdependent networks. Nature, 464(7291):1025--1028, 2010.
[19]
G. Chartrand, D. Geller, and S. Hedetniemi. Graphs with forbidden subgraphs. J. Combin. Theory Ser. B, 10(1):12--41, 1971.
[20]
D. P. Chassin and C. Posse. Evaluating North American electric grid reliability using the Barabási--Albert network model. Phys. A, 355(2--4):667 -- 677, 2005.
[21]
G. Dán and H. Sandberg. Stealth attacks and protection schemes for state estimators in power systems. In Proc. IEEE SmartGridComm'10, 2010.
[22]
I. Dobson, B. Carreras, V. Lynch, and D. Newman. Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization. Chaos, 17(2):026103, 2007.
[23]
D. Donoho and Y. Tsaig. Fast solution of l1-norm minimization problems when the solution may be sparse, 2006. Preprint at http://statweb.stanford.edu/donoho/Reports/2006/kstep-20061005.pdf.
[24]
P. Erd\Hos and A. Rényi. On random graphs. Publicationes Mathematicae Debrecen, 6:290--297, 1959.
[25]
L. Gan, A. Wierman, U. Topcu, N. Chen, and S. H. Low. Real-time deferrable load control: handling the uncertainties of renewable generation. In Proc. ACM e-Energy'13, May 2013.
[26]
M. R. Garey and D. S. Johnson. Computers and intractability: a guide to the theory of np-completeness. 1979.
[27]
Y. Ghiassi-Farrokhfal, S. Keshav, C. Rosenberg, and F. Ciucu. Firming solar power. In Proc. ACM SIGMETRICS'13 (poster description), June 2013.
[28]
Y.-F. Huang, S. Werner, J. Huang, N. Kashyap, and V. Gupta. State estimation in electric power grids: Meeting new challenges presented by the requirements of the future grid. IEEE Signal Process. Mag., 29(5):33--43, 2012.
[29]
K. Khandeparkar, P. Patre, S. Jain, K. Ramamritham, and R. Gupta. Efficient PMU data dissemination in smart grid. In Proc. ACM e-Energy'14 (poster description), June 2014.
[30]
J. Kim and L. Tong. On topology attack of a smart grid: undetectable attacks and countermeasures. IEEE J. Sel. Areas Commun, 31(7):1294--1305, 2013.
[31]
J. Kleinberg, M. Sandler, and A. Slivkins. Network failure detection and graph connectivity. In Proc. ACM-SIAM SODA'04, Jan. 2004.
[32]
J. Liu, C. H. Xia, N. B. Shroff, and H. D. Sherali. Distributed optimal load shedding for disaster recovery in smart electric power grids: A second-order approach. In Proc. ACM SIGMETRICS'14 (poster description), June 2014.
[33]
Y. Liu, P. Ning, and M. K. Reiter. False data injection attacks against state estimation in electric power grids. ACM Trans. Inf. Syst. Secur., 14(1):13, 2011.
[34]
L. Lu, J. Tu, C.-K. Chau, M. Chen, and X. Lin. Online energy generation scheduling for microgrids with intermittent energy sources and co-generation. In Proc. ACM SIGMETRICS'13, June 2013.
[35]
N. M. Manousakis, G. N. Korres, and P. S. Georgilakis. Taxonomy of PMU placement methodologies. IEEE Trans. Power Syst., 27(2):1070--1077, 2012.
[36]
C. Phillips. The network inhibition problem. In Proc. ACM STOC'93, May 1993.
[37]
A. Pinar, J. Meza, V. Donde, and B. Lesieutre. Optimization strategies for the vulnerability analysis of the electric power grid. SIAM J. Optimiz., 20(4):1786--1810, 2010.
[38]
W. Rudin. Real and complex analysis. Tata McGraw-Hill Education, 1987.
[39]
P. D. Seymour. On odd cuts and plane multicommodity flows. P. Lond. Math. Soc., 3(1):178--192, 1981.
[40]
S. Soltan, D. Mazauric, and G. Zussman. Cascading failures in power grids -- analysis and algorithms. In Proc. ACM e-Energy'14, June 2014.
[41]
S. Soltan and G. Zussman. A statistical method for synthetic power grid generation based on the U.S. Western Interconnection. Abstract presented at phSIAM NS'15, May 2015.
[42]
J. E. Tate and T. J. Overbye. Line outage detection using phasor angle measurements. IEEE Trans. Power Syst., 23(4):1644--1652, 2008.
[43]
J. E. Tate and T. J. Overbye. Double line outage detection using phasor angle measurements. In Proc. IEEE PES'09, July 2009.
[44]
O. Vukovic, K. C. Sou, G. Dán, and H. Sandberg. Network-layer protection schemes against stealth attacks on state estimators in power systems. In Proc. IEEE SmartGridComm'11, 2011.
[45]
X. Wang, X. Song, and J. Yuan. On matching cover of graphs. Math. Program., 147(1--2):499--518, 2014.
[46]
D. B. West et al. Introduction to graph theory, volume 2. Prentice hall Upper Saddle River, 2001.
[47]
H. Xiao and E. M. Yeh. Cascading link failure in the power grid: A percolation-based analysis. In Proc. IEEE Int. Work. on Smart Grid Commun., June 2011.
[48]
Y. Zhao, A. Goldsmith, and H. V. Poor. On PMU location selection for line outage detection in wide-area transmission networks. In Proc. IEEE PES'12, July 2012.
[49]
H. Zhu and G. B. Giannakis. Sparse overcomplete representations for efficient identification of power line outages. IEEE Trans. Power Syst., 27(4):2215--2224, 2012.
[50]
R. D. Zimmerman, C. E. Murillo-Sánchez, and R. J. Thomas. Matpower: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst., 26(1):12--19, 2011.
[51]
D. Zuckerman. Linear degree extractors and the inapproximability of max clique and chromatic number. In Proc. ACM STOC'06, May 2006.

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cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 43, Issue 1
Performance evaluation review
June 2015
468 pages
ISSN:0163-5999
DOI:10.1145/2796314
Issue’s Table of Contents
  • cover image ACM Conferences
    SIGMETRICS '15: Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems
    June 2015
    488 pages
    ISBN:9781450334860
    DOI:10.1145/2745844
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Publication History

Published: 15 June 2015
Published in SIGMETRICS Volume 43, Issue 1

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Author Tags

  1. algorithms
  2. cyber attacks
  3. graph theory
  4. information recovery
  5. physical attacks
  6. power grids

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