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3 - Resilience Models and Metrics

Published online by Cambridge University Press:  04 January 2024

Alexis Kwasinski
University of Pittsburgh
Andres Kwasinski
Rochester Institute of Technology, New York
Vaidyanathan Krishnamurthy
University of Pittsburgh
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This chapter is divided into two main parts. The first part presents various resilience modeling approaches for critical infrastructures, with a focus on power grids and communication networks. However, as is explained, a main modeling framework relying on graph theory is applicable to most other critical infrastructure systems. The second part discusses various resilience metric approaches, with special attention to those applied to power grids. Metrics for concepts related to resilience that have also been used in the literature are also discussed in this chapter. Discussion of both resilience modeling and metrics is expanded in later chapters, particularly in Chapter 4, where dependencies and interdependencies are taken into consideration.

Resilience Engineering for Power and Communications Systems
Networked Infrastructure in Extreme Events
, pp. 119 - 160
Publisher: Cambridge University Press
Print publication year: 2024

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Kwasinski, A., Trainor, J., Wolshon, B., and Lavelle, F. M., “A Conceptual Framework for Assessing Resilience at the Community Scale,” NIST GCR 16–001, Jan. 2016.CrossRefGoogle Scholar
Nan, C. and Sansavini, G., “A quantitative method for assessing resilience of interdependent infrastructures.” Reliability Engineering and System Safety, vol. 157, pp. 3553, Jan. 2017.CrossRefGoogle Scholar
Yodo, N., Wang, P., and Rafi, M., “Enabling resilience of complex engineered systems using control theory.” IEEE Transactions on Reliability, vol. 67, no. 1, pp. 5365, Mar. 2018.CrossRefGoogle Scholar
Long Vu, T. and Turitsyn, K., “A framework for robust assessment of power grid stability and resiliency.” IEEE Transactions on Automatic Control, vol. 62, no. 3, pp. 11651177, Mar. 2017.Google Scholar
Rocchetta, R. and Patelli, E., “Assessment of power grid vulnerabilities accounting for stochastic loads and model imprecision.” International Journal of Electrical Power & Energy Systems, vol. 98, pp. 219232, June 2018.CrossRefGoogle Scholar
Fang, Y., Pedroni, N., and Zio, E., “Optimization of cascade-resilient electrical infrastructures and its validation by power flow modeling.” Risk Analysis, vol. 35, no. 4, pp. 594607, Apr. 2015.CrossRefGoogle ScholarPubMed
Watson, E. B. and Etemadi, A. H., “Modeling electrical grid resilience under hurricane wind conditions with increased solar and wind power generation.” IEEE Transactions on Power Systems, vol. 35, no. 2, pp. 929937, Mar. 2020.CrossRefGoogle Scholar
Krishnamurthy, V., Huang, B., Kwasinski, A., Pierce, E., and Baldick, R., “Generalized resilience models for power systems and dependent infrastructure during extreme events.” IET Smart Grid, vol. 3, no. 2, pp. 194206, Apr. 2020.CrossRefGoogle Scholar
Kwasinski, A., “Modeling of Cyber-physical Intra-dependencies in Electric Power Grids and Their Effect on Resilience,” in Proceedings of the 2020 8th Workshop on Modeling and Simulation of Cyber-Physical Energy Systems, Sydney, Australia, Apr. 2020.CrossRefGoogle Scholar
Kwasinski, A. and Krishnamurthy, V., “Generalized Integrated Framework for Modeling Communications and Electric Power Infrastructure Resilience,” in Proceedings of the INTELEC 2017, Gold Coast, Australia, pp. 18, Oct. 2017.CrossRefGoogle Scholar
Kim, M. and Leskovec, J., “Multiplicative attribute graph model of real-world networks.” Internet Mathematics, vol. 8, nos. 1–2, pp. 113160, 2012.CrossRefGoogle Scholar
Garlaschelli, D., “The weighted random graph model.” New Journal of Physics, vol. 11, 9 pages, July 2009.CrossRefGoogle Scholar
Li, Y., Kong, X., Jia, C., and Li, J., “Clustering uncertain graphs with node attributes.” ACML Proceedings of Machine Learning Research, vol. 95, pp. 232247, 2018.Google Scholar
Attoh-Okine, N. A., Resilience Engineering: Models and Analysis, Cambridge University Press, New York, NY, 2016.Google Scholar
Nazemi, M. and Dehghanian, P., “Seismic-resilient bulk power grids: hazard characterization, modeling, and mitigation.” IEEE Transactions on Engineering Management, vol. 67, no. 3, pp. 614630, Nov. 2019.CrossRefGoogle Scholar
Panteli, M. and Mancarella, P., “Modelling and evaluating the resilience of critical electrical power infrastructure to extreme weather events.” IEEE Systems Journal, vol. 11, no. 3, pp. 17331742, Sept. 2017.CrossRefGoogle Scholar
Galbusera, L., Giannopoulos, G., Argyroudis, S., and Kakderi, K., “A Boolean networks approach to modeling and resilience analysis of interdependent critical infrastructures.” Computer-Aided Civil and Infrastructure Engineering, vol. 33, pp. 10411055, July 2018.CrossRefGoogle Scholar
Abimbola, M. and Khan, F., “Resilience modeling of engineering systems using dynamic object-oriented Bayesian network approach.” Computers and Industrial Engineering, vol. 130, pp. 108118, Apr. 2019.CrossRefGoogle Scholar
Ji, C., Wei, Y., and Poor, V., “Resilience of energy infrastructure and services: modeling, data analytics, and metrics.” Proceedings of the IEEE, vol. 105, no. 7, pp. 13541366, July 2017.CrossRefGoogle Scholar
Nateghi, R., “Multi-dimensional infrastructure resilience modeling: an application to hurricane-prone electric power distribution systems.” IEEE Access, vol. 6, pp. 1347813489, Jan. 2018.CrossRefGoogle Scholar
Liu, X., Ferrario, E., and Zio, E., “Resilience analysis framework for interconnected critical infrastructures.” ASCE-ASME Journal of Risk and Uncertainty, vol. 3, no. 2, 10 pages, Feb. 2017.Google Scholar
Linkov, I. and Kott, A. (eds.), Fundamental Concepts of Cyber Resilience: Introduction and Overview, Springer, Cham, 2019.Google Scholar
Netkachov, O., Popov, P., and Salako, K., “Model-Based Evaluation of the Resilience of Critical Infrastructures under Cyber Attacks,” in Proceedings of the 2014 International Conference on Critical Information Infrastructures Security, pp. 231243.CrossRefGoogle Scholar
Spiegler, V. L. M., Naim, M. M., and Wikner, J., “A control engineering approach to the assessment of supply chain resilience.” International Journal of Production Research, vol. 50, no. 21, pp. 61626187, Aug. 2012.CrossRefGoogle Scholar
Soupionis, Y. and Benoist, T., “Cyber Attacks in Power Grid ICT Systems Leading to Financial Disturbance,” in Proceedings of the 2014 International Conference on Critical Information Infrastructures Security, pp. 256267.CrossRefGoogle Scholar
European Network and Information Security Agency (ENISA), “Measurement Frameworks and Metrics for Resilient Networks and Services: Challenges and Recommendations,” European Network and Information Security Agency (ENISA),2010.Google Scholar
Watson, J.-P., Guttromson, R, Silva-Monroy, C et al., “Conceptual Framework for Developing Resilience Metrics for the Electricity, Oil, and Gas Sectors in the United States,” Sandia National Laboratories Report SAND2014-18019, Sept. 2015.CrossRefGoogle Scholar
Auer, S., Kleis, K., Schultz, P., Kurths, J., and Hellmann, F., “The impact of model detail on power grid resilience measures.” The European Physical Journal Special Topics, vol. 225, pp. 609625, May 2016.CrossRefGoogle Scholar
Belaid, J. N., Coudray, P, Sanchez-Torres, J et al., “Resilience quantification of smart distribution networks: a bird’s eye view perspective.” Energies, vol. 14, no. 10, 29 pages, May 2021.Google Scholar
O’Rourke, T. D., “Critical infrastructure, interdependencies, and resilience.” The Bridge, vol. 37, no. 1, pp. 2229, Spring 2007.Google Scholar
Papadopoulos, T., Gunasekaran, A, Dubey, R et al., “The role of big data in explaining disaster resilience in supply chains for sustainability.” Journal of Cleaner Production, vol. 142, part 2, pp. 11081118, Jan. 2017.CrossRefGoogle Scholar
Reed, D. A., Kapur, K. C., and Christie, R. D., “Methodology for assessing the resilience of networked infrastructure.” IEEE Systems Journal, vol. 3, no. 2, pp. 174179, June 2009.CrossRefGoogle Scholar
Srivastava, A., Liu, C.-C., and Chanda, S. (editors), Resilience of Power Distribution Systems. Kwasinski, A (author), Chapter 7: Quantitative Model and Metrics for Distribution System Resiliency, Wiley, West Sussex,2021.Google Scholar
Ayyub, B. M., “Practical resilience metrics for planning, design, and decision making.” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, vol. 1, no. 3, 11 pages, Sept. 2015.Google Scholar
Friedberg, I., McLaughlin, K., Smith, P., and Wurzenberger, M., “Towards a Resilience Metric Framework for Cyber-Physical Systems,” in Proceedings of the 4th International Symposium for ICS and SCADA Cyber Security Research, 2016.CrossRefGoogle Scholar
Gholami, A., Shekari, T., Amirioun, M. H. et al., “Toward a consensus on the definition and taxonomy of power system resilience.” IEEE Access, vol. 6, pp. 3203532053, June 2018.CrossRefGoogle Scholar
Albasrawi, M. N., Jarus, N., Joshi, K. A., and Sarvestani, S. S., “Analysis of Reliability and Resilience for Smart Grids,” in Proceedings of the 2014 IEEE 38th Annual Computer Software and Applications Conference, 6 pages.CrossRefGoogle Scholar
Ouyang, M. and Dueñas-Ozorio, L., “Resilience modeling and simulation of smart grids,” in Proceedings of the 2011 ASCE Structures Congress, 14 pages.CrossRefGoogle Scholar
Clark, A. and Zonouz, S., “Cyber-physical resilience: definition and assessment metric.” IEEE Transactions on Smart Grid, vol. 10, no. 2, pp. 16711684, Mar. 2019.CrossRefGoogle Scholar
Wei, Y., Ji, C., Galvan, F. et al., “Non-stationary random process for large-scale failure and recovery of power distributions,” 2012. Scholar
Vugrin, E. D. and Turgeon, J., Advancing Cyber Resilience Analysis with Performance-Based Metrics from Infrastructures Assessments, IGI Global, Hershey, PA, 2014.CrossRefGoogle Scholar
Francis, R. and Bekera, B., “A metric and frameworks for resilience analysis of engineered and infrastructure systems.” Reliability Engineering and Systems Journal, vol. 121, pp. 90103, Jan. 2014.CrossRefGoogle Scholar
Litvinov, E. and Zhao, F., “Survivability of the Electric Grid,” in Proceedings of the 2017 Bulk Power System Dynamics and Control (iREP) – X (iREP) Symposium, 9 pages.Google Scholar
Kwasinski, A., Weaver, W., and Balog, R., Micro-grids in Local Area Power and Energy Systems, Cambridge University Press, Cambridge, 2016.CrossRefGoogle Scholar
Kwasinski, A., “Quantitative model and metrics of electrical grids’ resilience evaluated at a power distribution level.Energies, vol. 9, 93, 2016.CrossRefGoogle Scholar
Keogh, M. and Cody, C., “Resilience in Regulated Utilities,” National Association of Regulatory Utility Commissioners report, Nov. 2013.Google Scholar
Cholda, P., Tapolcai, J., Cinkler, T., Wajda, K., and Jajszczyk, A., “Quality of resilience as a network reliability characterization tool authorized licensed.” IEEE Network, vol. 23, no. 2, pp. 1119, Mar. 2009.CrossRefGoogle Scholar
Montoya, G. A., “Assessing Resilience in Power Grids as a Particular Case of Supply Chain Management,” master’s thesis, Air Force Institute of Technology, Mar. 2010.Google Scholar
Smith, P., Hutchison, D., Sterbenz, J. P. G. et al., “Network resilience: a systematic approach.” IEEE Communications Magazine, vol. 47, no. 7, pp. 8897, July 2011.CrossRefGoogle Scholar
Sterbenz, J. P. G., Çetinkaya, E. K., Hameed, M. A. et al., “Modeling and Analysis of Network Resilience,” in Proceedings of the 2011 Third International Conference on Communication Systems and Networks (COMSNETS 2011), 10 pages, 2011.CrossRefGoogle Scholar
Vugrin, E., Castillo, A., and Silva-Monroy, C., “Resilience Metrics for the Electric Power System: A Performance-Based Approach,” Sandia National Lab report SAND2017-1493, Feb. 2017.CrossRefGoogle Scholar
Pant, R., Barker, K., and Zobel, C. W., “Static and dynamic metrics of economic resilience for interdependent infrastructure and industry sectors.” Reliability Engineering and System Safety, vol. 125, pp. 92102, May 2014.CrossRefGoogle Scholar
Ji, C. and Wei, Y., “Dynamic Resilience for Power Distribution and Customers,” in Proceedings of the 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm): Architectures, Control and Operation for Smart Grids and Microgrids, 6 pages, 2015.CrossRefGoogle Scholar
Fisher, R. E., Bassett, G., Buehring, W. A. et al., “Constructing a Resilience Index for the Enhanced Critical Infrastructure Protection Program,” Argonne National Lab report ANL/DIS-10–9, Aug. 2010.CrossRefGoogle Scholar
Soni, U., Jain, V., and Kumar, S., “Measuring supply chain resilience using a deterministic modeling approach.” Computers & Industrial Engineering, vol. 74, pp. 1125, Aug. 2014.CrossRefGoogle Scholar
Panteli, M., Mancarella, P., Trakas, D. N. et al., “Metrics and quantification of operational and infrastructure resilience in power systems.” IEEE Transactions on Power Systems, vol. 32, no. 6, pp. 47324742, Nov. 2017.CrossRefGoogle Scholar
Bajpai, P., Chanda, S., and Srivastava, A. K., “A novel metric to quantify and enable resilient distribution system using graph theory and Choquet integral.” IEEE Transactions on Smart Grid, vol. 9, no. 4, pp. 29182929, July 2018.CrossRefGoogle Scholar
Chanda, S. and Srivastava, A. K., “Defining and enabling resiliency of electric distribution systems with multiple microgrids,” IEEE Transactions on Smart Grid, vol. 7, no. 6, pp. 28592868, Nov. 2016.CrossRefGoogle Scholar
Kwasinski, A., “Technology planning for electric power supply in critical events considering a bulk grid, backup power plants, and micro-grids.” IEEE Systems Journal, vol. 4, no. 2, pp. 167178, June 2010.CrossRefGoogle Scholar
ITU-T Focus Group on Disaster Relief Systems, Network Resilience and Recovery, “Terms and definitions for disaster relief systems, network resilience and recovery,” International Telecommunications Union, Standardization Sector technical report FG-DR&NRR, ver. 1, May 2014.Google Scholar
Filippini, R. and Silva, A., “A modeling framework for the resilience analysis of networked systems-of-systems based on functional dependencies.” Reliability Engineering and Systems Safety, vol. 125, pp. 8291, May 2014.CrossRefGoogle Scholar
Der Sarkissian, R., Abdallah, C., Zaninetti, J.-M., and Najem, S., “Modelling intra-dependencies to assess road network resilience to natural hazards.Natural Hazards, vol. 103, pp. 121137, May 2020.CrossRefGoogle Scholar
Kwasinski, A., “Analysis of a Microgrid Availability and Resilience with Distributed Energy Storage Embedded in Active Power Distribution Nodes,” in Proceedings of the IEEE 11th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 6 pages, 2020.CrossRefGoogle Scholar

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