Assessing the Vulnerability of Power Systems Using Multilevel Programming: A Literature Review
Abstract
Vulnerability studies in power systems allow to identify critical elements, in order to take protective measures against scenarios that may lead the system to load shedding. These scenarios can be caused by natural events or deliberate attacks. This paper presents a literature review for the latter case, which is known as the interdiction problem. In this problem, it is assumed that there is a disruptive agent whose objective is to maximize the damage to the system, while the network operator acts as a defensive agent. The nonsimultaneous interaction of these two agents results in a multilevel optimization problem. Various interdiction models and solution methods have been reported in the technical literature; as a main contribution, this paper presents the considerations to be taken into account when analyzing, modeling and solving the interdiction problem including the main solution techniques, the applied methodologies and future research. In the literature review, it was found that a large part of the studies focuses on the analysis of transmission systems considering linear network approximations. On the other hand, few interdiction studies use the AC model of the network or directly address distribution networks from a multilevel perspective. Future challenges in this research field lie in modeling and incorporating new defense strategies for the network operator such as the use of distributed generation, demand response and the topological reconfiguration of the system.

References
[1] J.M. Arroyo, and F.D. Galiana, "On the Solution of the Bilevel Programming Formulation of the Terrorist Threat Problem," IEEE Trans. Power Syst., vol. 20, pp. 789–797, 2005. DOI:10.1109/TPWRS.2005.846198.
[2] C.M. Rocco, J.E. RamirezMarquez, D.E. Salazar, and C. Yajure, "Assessing the Vulnerability of a Power System Through a Multiple Objective Contingency Screening Approach," IEEE Trans. Reliab., vol. 60, pp. 394–403, 2011. DOI:10.1109/TR.2011.2135490.
[3] J. Fang, C. Su, Z. Chen, H. Sun, and P. Lund, "Power System Structural Vulnerability Assessment Based on an Improved Maximum Flow Approach," IEEE Trans. Smart Grid, vol. 9, pp. 777–785, 2018. DOI:10.1109/TSG.2016.2565619.
[4] E. Bompard, R. Napoli, and F. Xue, "Analysis of structural vulnerabilities in power transmission grids," Int. J. Crit. Infrastruct. Prot., vol. 2, pp. 5–12, 2009. DOI:10.1016/j.ijcip.2009.02.002.
[5] J.M. Arroyo, and F.J. Fernández, A Genetic Algorithm for Power System Vulnerability Analysis under Multiple Contingencies.in: Springer, Berlin, Heidelberg, 2013, 41–68 p. DOI:10.1007/9783642378386_2.
[6] H. Davarikia, and M. Barati, "A trilevel programming model for attackresilient control of power grids," J. Mod. Power Syst. Clean Energy, vol. 6, pp. 918–929, 2018. DOI:10.1007/s405650180436y.
[7] J. Salmeron, K. Wood, and R. Baldick, "Analysis of Electric Grid Security Under Terrorist Threat," IEEE Trans. Power Syst., vol. 19, pp. 905–912, 2004. DOI:10.1109/TPWRS.2004.825888.
[8] A. Delgadillo, J.M. Arroyo, and N. Alguacil, "Analysis of Electric Grid Interdiction With Line Switching," IEEE Trans. Power Syst., vol. 25, pp. 633–641, 2010. DOI:10.1109/TPWRS.2009.2032232.
[9] Y. Lin, and Z. Bie, "Trilevel optimal hardening plan for a resilient distribution system considering reconfiguration and DG islanding," Appl. Energy, vol. 210, pp. 1266–1279, 2018. DOI:10.1016/j.apenergy.2017.06.059.
[10] Z. Bie, Y. Lin, G. Li, and F. Li, "Battling the Extreme: A Study on the Power System Resilience," Proc. IEEE, vol. 105, pp. 1253–1266, 2017. DOI:10.1109/JPROC.2017.2679040.
[11] M. Ouyang, Z. Pan, L. Hong, and L. Zhao, "Correlation analysis of different vulnerability metrics on power grids," Phys. A Stat. Mech. Its Appl., vol. 396, pp. 204–211, 2014. DOI:10.1016/J.PHYSA.2013.10.041.
[12] Y. Lin, Z. Bie, and A. Qiu, "A review of key strategies in realizing power system resilience," Glob. Energy Interconnect., vol. 1, pp. 70–78, 2018. DOI:10.14171/j.20965117.gei.2018.01.009.
[13] M. Ouyang, M. Xu, C. Zhang, and S. Huang, "Mitigating electric power system vulnerability to worstcase spatially localized attacks," Reliab. Eng. Syst. Saf., vol. 165, pp. 144–154, 2017. DOI:10.1016/J.RESS.2017.03.031.
[14] A. Wang, Y. Luo, G. Tu, and P. Liu, "Vulnerability assessment scheme for power system transmission networks based on the fault chain theory," IEEE Trans. Power Syst., vol. 26, pp. 442–450, 2011. DOI:10.1109/TPWRS.2010.2052291.
[15] C.C. MarínCano, J.E. SierraAguilar, J.M. LópezLezama, Á. JaramilloDuque, and W.M. VillaAcevedo, "Implementation of User Cuts and Linear Sensitivity Factors to Improve the Computational Performance of the SecurityConstrained Unit Commitment Problem," Energies, vol. 12, pp. 1399, 2019. DOI:10.3390/en12071399.
[16] Y. Zhu, J. Yan, Y. Tang, Y.L. Sun, and H. He, "Resilience Analysis of Power Grids Under the Sequential Attack," IEEE Trans. Inf. Forensics Secur., vol. 9, pp. 2340–2354, 2014. DOI:10.1109/TIFS.2014.2363786.
[17] P.E. Roege, Z.A. Collier, J. Mancillas, J.A. McDonagh, and I. Linkov, "Metrics for energy resilience," Energy Policy, vol. 72, pp. 249–256, 2014. DOI:10.1016/J.ENPOL.2014.04.012.
[18] S. Wang, J. Zhang, M. Zhao, and X. Min, "Vulnerability analysis and critical areas identification of the power systems under terrorist attacks," Phys. A Stat. Mech. Its Appl., vol. 473, pp. 156–165, 2017. DOI:10.1016/j.physa.2017.01.003.
[19] S. Wang, J. Zhang, and N. Duan, "Multiple perspective vulnerability analysis of the power network," Phys. A Stat. Mech. Its Appl., vol. 492, pp. 1581–1590, 2018. DOI:10.1016/J.PHYSA.2017.11.083.
[20] S. Arianos, E. Bompard, A. Carbone, and F. Xue, "Power grid vulnerability: A complex network approach," Chaos An Interdiscip. J. Nonlinear Sci., vol. 19, pp. 013119, 2009. DOI:10.1063/1.3077229.
[21] Y.P. Fang, and G. Sansavini, "Optimum postdisruption restoration under uncertainty for enhancing critical infrastructure resilience," Reliab. Eng. Syst. Saf., vol. 185, pp. 1–11, 2019. DOI:10.1016/j.ress.2018.12.002.
[22] S. Mousavizadeh, M.R. Haghifam, and M.H. Shariatkhah, "A linear twostage method for resiliency analysis in distribution systems considering renewable energy and demand response resources," Appl. Energy, vol. 211, pp. 443–460, 2018. DOI:10.1016/J.APENERGY.2017.11.067.
[23] J.Z. Zhu, "Optimal reconfiguration of electrical distribution network using the refined genetic algorithm," Electr. Power Syst. Res., vol. 62, pp. 37–42, 2002. DOI:10.1016/S03787796(02)00041X.
[24] A. Costa, D. Georgiadis, T.S. Ng, and M. Sim, "An optimization model for power grid fortification to maximize attack immunity," Int. J. Electr. Power Energy Syst., vol. 99, pp. 594–602, 2018. DOI:10.1016/j.ijepes.2018.01.020.
[25] H. Mo, M. Xie, and G. Levitin, "Optimal resource distribution between protection and redundancy considering the time and uncertainties of attacks," Eur. J. Oper. Res., vol. 243, pp. 200–210, 2015. DOI:10.1016/J.EJOR.2014.12.006.
[26] T. Kim, S.J. Wright, D. Bienstock, and S. Harnett, "Vulnerability Analysis of Power Systems," ArXiv Prepr., 2015. Disponible: http://arxiv.org/abs/1503.02360.
[27] V.M. Bier, E.R. Gratz, N.J. Haphuriwat, W. Magua, and K.R. Wierzbicki, "Methodology for identifying nearoptimal interdiction strategies for a power transmission system," Reliab. Eng. Syst. Saf., vol. 92, pp. 1155–1161, 2007. DOI:10.1016/J.RESS.2006.08.007.
[28] M. Ouyang, L. Zhao, Z. Pan, and L. Hong, "Comparisons of complex network based models and direct current power flow model to analyze power grid vulnerability under intentional attacks," Phys. A Stat. Mech. Its Appl., vol. 403, pp. 45–53, 2014. DOI:10.1016/J.PHYSA.2014.01.070.
[29] A.B.M. Nasiruzzaman, H.R. Pota, and M.N. Akter, "Vulnerability of the largescale future smart electric power grid," Phys. A Stat. Mech. Its Appl., vol. 413, pp. 11–24, 2014. DOI:10.1016/j.physa.2014.06.024.
[30] N. Alguacil, A. Delgadillo, and J.M. Arroyo, "A trilevel programming approach for electric grid defense planning," Comput. Oper. Res., vol. 41, pp. 282–290, 2014. DOI:10.1016/j.cor.2013.06.009.
[31] T. Lu, Z. Wang, J. Wang, Q. Ai, and C. Wang, "A DataDriven Stackelberg Market Strategy for Demand ResponseEnabled Distribution Systems," IEEE Trans. Smart Grid, vol. 10, pp. 2345–2357, 2019. DOI:10.1109/TSG.2018.2795007.
[32] J. Zhang, and J. Zhuang, "Modeling a multitarget attackerdefender game with multiple attack types," Reliab. Eng. Syst. Saf., vol. 185, pp. 465–475, 2019. DOI:10.1016/j.ress.2019.01.015.
[33] J.M. Arroyo, "Bilevel programming applied to power system vulnerability analysis under multiple contingencies," IET Gener. Transm. Distrib., vol. 4, pp. 178, 2010. DOI:10.1049/ietgtd.2009.0098.
[34] J.M. Arroyo, and F.J. Fernandez, A Genetic Algorithm Approach for the Analysis of Electric Grid Interdiction with Line Switching.in: 2009 15th Int. Conf. Intell. Syst. Appl. to Power Syst. IEEE, 2009, 1–6 p. DOI:10.1109/ISAP.2009.5352849.
[35] L. Agudelo, J.M. LópezLezama, and N. Muñoz Galeano, "Vulnerability Assessment of Power Systems to Intentional Attacks using a Specialized Genetic Algorithm," DYNA, vol. 82, pp. 78–84, 2015. DOI:10.15446/dyna.v82n192.48578.
[36] J.M. LópezLezama, J. CortinaGómez, and N. MuñozGaleano, "Assessment of the Electric Grid Interdiction Problem using a nonlinear modeling approach," Electr. Power Syst. Res., vol. 144, pp. 243–254, 2017. DOI:10.1016/j.epsr.2016.12.017.
[37] J.J. Cortina, J.M. LópezLezama, and N. MuñozGaleano, "Metaheurísticas Aplicadas al Problema de Interdicción en Sistemas de Potencia," Inf. Tecnológica, vol. 29, pp. 73–88, 2018. DOI:10.4067/s071807642018000200073.
[38] J. Salmeron, K. Wood, and R. Baldick, "WorstCase Interdiction Analysis of LargeScale Electric Power Grids," IEEE Trans. Power Syst., vol. 24, pp. 96–104, 2009. DOI:10.1109/TPWRS.2008.2004825.
[39] S. Sayyadipour, G.R. Yousefi, and M.A. Latify, "Midterm vulnerability analysis of power systems under intentional attacks," IET Gener. Transm. Distrib., vol. 10, pp. 3745–3755, 2016. DOI:10.1049/ietgtd.2016.0052.
[40] L. Agudelo, J.M. Lópezlezama, and N. Muñoz, "Análisis de Vulnerabilidad de Sistemas de Potencia Mediante Programación Binivel Vulnerability Analysis of Power Systems using Bilevel Programing," Inf. Tecnol., vol. 25, pp. 103–114, 2014. DOI:10.4067/S071807642014000300013.
[41] T. Kim, S.J. Wright, D. Bienstock, and S. Harnett, "Analyzing Vulnerability of Power Systems with Continuous Optimization Formulations," IEEE Trans. Netw. Sci. Eng., vol. 3, pp. 132–146, 2016. DOI:10.1109/TNSE.2016.2587484.
[42] L. Shi, Q. Dai, and Y. Ni, "Cyber–physical interactions in power systems: A review of models, methods, and applications," Electr. Power Syst. Res., vol. 163, pp. 396–412, 2018. DOI:10.1016/j.epsr.2018.07.015.
[43] Y. Xiang, L. Wang, and N. Liu, "Coordinated attacks on electric power systems in a cyberphysical environment," Electr. Power Syst. Res., vol. 149, pp. 156–168, 2017. DOI:10.1016/j.epsr.2017.04.023.
[44] H. Nemati, M.A. Latify, and G.R. Yousefi, "Trilevel transmission expansion planning under intentional attacks: virtual attacker approach – part I: formulation," IET Gener. Transm. Distrib., vol. 13, pp. 390–398, 2019. DOI:10.1049/ietgtd.2018.6104.
[45] H. Nemati, M.A. Latify, and G.R. Yousefi, "Trilevel transmission Expansion planning under intentional attacks: virtual attacker approachpart II: Case studies," IET Gener. Transm. Distrib., vol. 13, pp. 399–408, 2019. DOI:10.1049/ietgtd.2018.6105.
[46] X. Wu, and A.J. Conejo, "An Efficient TriLevel Optimization Model for Electric Grid Defense Planning," IEEE Trans. Power Syst., vol. 32, pp. 2984–2994, 2017. DOI:10.1109/TPWRS.2016.2628887.
[47] K. Lai, M. Illindala, and K. Subramaniam, "A trilevel optimization model to mitigate coordinated attacks on electric power systems in a cyberphysical environment," Appl. Energy, vol. 235, pp. 204–218, 2019. DOI:10.1016/J.APENERGY.2018.10.077.
[48] Z. Ding, Y. Xiang, and L. Wang, Incorporating Unidentifiable Cyberattacks into Power System Reliability Assessment.in: IEEE Power Energy Soc. Gen. Meet. IEEE, 2018, 1–5 p. DOI:10.1109/PESGM.2018.8585884.
[49] W. Yuan, L. Zhao, and B. Zeng, "Optimal power grid protection through a defender–attacker–defender model," Reliab. Eng. Syst. Saf., vol. 121, pp. 83–89, 2014. DOI:10.1016/J.RESS.2013.08.003.
[50] T. Ding, L. Yao, and F. Li, "A multiuncertaintyset based twostage robust optimization to defender–attacker–defender model for power system protection," Reliab. Eng. Syst. Saf., vol. 169, pp. 179–186, 2018. DOI:10.1016/j.ress.2017.08.020.
[51] Y. Wang, and R. Baldick, "Interdiction Analysis of Electric Grids Combining Cascading Outage and MediumTerm Impacts," IEEE Trans. Power Syst., vol. 29, pp. 2160–2168, 2014. DOI:10.1109/TPWRS.2014.2300695.

Author Biography
Jesus Maria LopezLezama, Universidad de AntioquiaProfesor del Departamento de Ingeniería Eléctrica de la Universidad de Antioquia
Downloads
Copyright (c) 2020 Revista Ingenierías Universidad de Medellín
This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.
The total or partial reproduction of the contents of the journal for educational, research, or academic purposes is authorized as long as the source is cited. For reproduction for other purposes, express authorization from the Sello Editorial Universidad de Medellín is required.