A bilevel approach for identifying the worst contingencies for nonconvex alternating current power systems. (English) Zbl 1461.90080


90C11 Mixed integer programming
90C26 Nonconvex programming, global optimization
90C17 Robustness in mathematical programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Full Text: DOI


[1] T. Achterberg, T. Koch, and A. Martin, Branching rules revisited, Oper. Res. Lett., 33 (2005), pp. 42-54. · Zbl 1076.90037
[2] N. Alguacil, A. Delgadillo, and J. M. Arroyo, A trilevel programming approach for electric grid defense planning, Comput. Oper. Res., 41 (2014), pp. 282-290. · Zbl 1348.90378
[3] J. M. Arroyo, Bilevel programming applied to power system vulnerability analysis under multiple contingencies, IET Gener. Transm. Dis., 4 (2010), pp. 178-190.
[4] J. M. Arroyo and F. J. Fernández, Application of a genetic algorithm to \(n-K\) power system security assessment, Int. J. Electr. Power Energy Syst., 49 (2013), pp. 114-121.
[5] X. Bai, H. Wei, K. Fujisawa, and Y. Wang, Semidefinite programming for optimal power flow problems, Int. J. Electr. Power Energy Syst., 30 (2008), pp. 383-392.
[6] J. Bezanson, A. Edelman, S. Karpinski, and V. Shah, Julia: A fresh approach to numerical computing, SIAM Rev., 59 (2017), pp. 65-98, https://doi.org/10.1137/141000671. · Zbl 1356.68030
[7] D. Bienstock and A. Verma, The \(N-k\) problem in power grids: New models, formulations, and numerical experiments, SIAM J. Optim., 20 (2010), pp. 2352-2380, https://doi.org/10.1137/08073562X. · Zbl 1211.90140
[8] D. Bienstock and A. Verma, Strong \(NP\)-hardness of AC power flows feasibility, Oper. Res. Lett., 47 (2019), pp. 494-501. · Zbl 1476.90070
[9] F. Capitanescu, J. L. M. Ramos, P. Panciatici, D. Kirschen, A. M. Marcolini, L. Platbrood, and L. Wehenkel, State-of-the-art, challenges, and future trends in security constrained optimal power flow, Electr. Pow. Syst. Res., 81 (2011), pp. 1731-1741.
[10] F. Capitanescu and L. Wehenkel, Computation of worst operation scenarios under uncertainty for static security management, IEEE Trans. Power Syst., 28 (2013), pp. 1697-1705.
[11] C. Chen, A. Atamtürk, and S. Oren, A spatial branch-and-cut method for nonconvex QCQP with bounded complex variables, Math. Program., 165 (2017), pp. 549-577. · Zbl 1380.65102
[12] C. Chen, A. Atamtürk, and S. S. Oren, Bound tightening for the alternating current optimal power flow problem, IEEE Trans. Power Syst., 31 (2016), pp. 3729-3736.
[13] R. Chen, N. Fan, A. Pinar, and J.-P. Watson, Contingency-constrained unit commitment with post-contingency corrective recourse, Ann. Oper. Res., 249 (2017), pp. 381-407. · Zbl 1357.90095
[14] C. Coffrin, R. Bent, K. Sundar, Y. Ng, and M. Lubin, PowerModels.jl: An open-source framework for exploring power flow formulations, in Power Systems Computation Conference (PSCC), 2018, pp. 1-8, https://doi.org/10.23919/PSCC.2018.8442948.
[15] C. Coffrin, H. L. Hijazi, and P. V. Hentenryck, The QC relaxation: A theoretical and computational study on optimal power flow, IEEE Trans. Power Syst., 31 (2016), pp. 3008-3018.
[16] P. Cuffe, A comparison of malicious interdiction strategies against electrical networks, IEEE Trans. Emerg. Sel. Topics Circuits Syst., 7 (2017), pp. 205-217.
[17] B. Dandurand, K. Kim, S.-i. Yim, and M. Schanen, Julia Software Package: MaximinOPF.jl, 2020, https://github.com/Argonne-National-Laboratory/MaximinOPF.jl.
[18] H. Davarikia and M. Barati, A tri-level programming model for attack-resilient control of power grids, J. Mod. Power Syst. Cle., 6 (2018), pp. 918-929.
[19] S. Dempe, V. Kalashnikov, G. Pérez-Valdés, and N. Kalashnykova, Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks, Springer-Verlag, Berlin, Heidelberg, 2015. · Zbl 1338.90005
[20] T. Ding, C. Li, C. Yan, F. Li, and Z. Bie, A bilevel optimization model for risk assessment and contingency ranking in transmission system reliability evaluation, IEEE Trans. Power Syst., 32 (2017), pp. 3803-3813.
[21] I. Dunning, J. Huchette, and M. Lubin, JuMP: A modeling language for mathematical optimization, SIAM Rev., 59 (2017), pp. 295-320, https://doi.org/10.1137/15M1020575. · Zbl 1368.90002
[22] V.-P. Eronen, M. M. Mäkelä, and T. Westerlund, On the generalization of ECP and OA methods to nonsmooth convex MINLP problems, Optimization, 63 (2014), pp. 1057-1073. · Zbl 1295.90022
[23] Gurobi Optimization, Gurobi Optimizer Reference Manual, 2020, http://www.gurobi.com.
[24] HSL, A Collection of Fortran Codes for Large Scale Scientific Computation, http://www.hsl.rl.ac.uk/.
[25] IBM Corporation, IBM ILOG CPLEX V12.7, https://www.cplex.com (accessed 1 Nov. 2018).
[26] R. A. Jabr, Radial distribution load flow using conic programming, IEEE Trans. Power Syst., 21 (2006), pp. 1458-1459.
[27] K. Kim, An Optimization Approach for Identifying and Prioritizing Critical Components in a Power System, Tech. Report ANL/MCS-P7076-0717, Argonne National Laboratory, Lemont, IL, 2017, available at https://kibaekkim.github.io/papers/P7076-0717.pdf.
[28] B. Kocuk, S. S. Dey, and X. A. Sun, Inexactness of SDP relaxation and valid inequalities for optimal power flow, IEEE Trans. Power Syst., 31 (2016), pp. 642-651.
[29] K. Lai, M. Illindala, and K. Subramaniam, A tri-level optimization model to mitigate coordinated attacks on electric power systems in a cyber-physical environment, Appl. Energy, 235 (2019), pp. 204-218.
[30] J. Lavaei and S. H. Low, Zero duality gap in optimal power flow problem, IEEE Trans. Power Syst., 27 (2012), pp. 92-107.
[31] J. López-Lezama, J. Cortina-Gómez, and N. M. noz Galeano, Assessment of the electric grid interdiction problem using a nonlinear modeling approach, Electr. Pow. Syst. Res., 144 (2017), pp. 243-254.
[32] S. H. Low, Convex relaxation of optimal power flow-Part I: Formulations and equivalence, IEEE Trans. Control Netw. Syst., 1 (2014), pp. 15-27. · Zbl 1370.90043
[33] S. H. Low, Convex relaxation of optimal power flow-Part II: Exactness, IEEE Trans. Control Netw. Syst., 1 (2014), pp. 177-189. · Zbl 1370.90044
[34] R. Madani, S. Sojoudi, and J. Lavaei, Convex relaxation for optimal power flow problem: Mesh networks, IEEE Trans. Power Syst., 30 (2015), pp. 199-211.
[35] D. K. Molzahn, J. T. Holzer, B. C. Lesieutre, and C. L. DeMarco, Implementation of a large-scale optimal power flow solver based on semidefinite programming, IEEE Trans. Power Syst., 28 (2013), pp. 3987-3998.
[36] D. R. Morrison, S. H. Jacobson, J. J. Sauppe, and E. C. Sewell, Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning, Discrete Optim., 19 (2016), pp. 79-102. · Zbl 1387.90010
[37] MOSEK ApS, MOSEK Optimizer API for C 9.0.105, 2019, https://docs.mosek.com/9.0/capi/index.html.
[38] G. Nemhauser and L. Wolsey, Integer and Combinatorial Optimization, Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, New York, 1999. · Zbl 0944.90001
[39] NERC Steering Group, Technical Analysis of the August 14, 2003, Blackout: What Happened, Why, and What Did We Learn?, Tech. report, North American Electric Reliability Council, Atlanta, GA, 2004.
[40] U. of Washington-Department of Electrical Engineering, Power Systems Test Case Archive, 1999, http://www.ee.washington.edu/research/pstca/ (accessed 7 Nov. 2018).
[41] A. Pinar, J. Meza, V. Donde, and B. Lesieutre, Optimization strategies for the vulnerability analysis of the electric power grid, SIAM J. Optim., 20 (2010), pp. 1786-1810, https://doi.org/10.1137/070708275. · Zbl 1201.90138
[42] D. Pozo, E. Sauma, and J. Contreras, Basic theoretical foundations and insights on bilevel models and their applications to power systems, Ann. Oper. Res., 254 (2017), pp. 303-334. · Zbl 1406.91027
[43] R. T. Rockafellar, Convex Analysis, Princeton Mathematical Series, Princeton University Press, Princeton, NJ, 1970.
[44] A. Ruszczyński, Nonlinear Optimization, Princeton University Press, Princeton, NJ, 2006. · Zbl 1108.90001
[45] J. Salmeron, K. Wood, and R. Baldick, Worst-case interdiction analysis of large-scale electric power grids, IEEE Trans. Power Syst., 24 (2009), pp. 96-104.
[46] S. Soltan, D. Mazauric, and G. Zussman, Analysis of failures in power grids, IEEE Trans. Control Netw. Syst., 4 (2017), pp. 288-300. · Zbl 1370.90051
[47] A. Street, F. Oliveira, and J. M. Arroyo, Contingency-constrained unit commitment with \(n - K\) security criterion: A robust optimization approach, IEEE Trans. Power Syst., 26 (2011), pp. 1581-1590.
[48] K. Sundar, C. Coffrin, H. Nagarajan, and R. Bent, Probabilistic \(N-k\) failure-identification for power systems, Networks, 71 (2018), pp. 302-321.
[49] O. Tange, GNU Parallel – The command-line power tool, ;login: The USENIX Magazine, 36 (2011), pp. 42-47, https://doi.org/10.5281/zenodo.16303, http://www.gnu.org/s/parallel.
[50] U.S./Canada Power System Outage Task Force, Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations, Tech. report, Office of Electricity Delivery & Energy Reliability-United States Department of Energy, Washington, DC, 2004.
[51] A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), pp. 25-57. · Zbl 1134.90542
[52] T. Westerlund and F. Pettersson, An extended cutting plane method for solving convex MINLP problems, Computers Chem. Engng., 19 (1995), pp. 131-136.
[53] X. Wu, A. Conejo, and N. Amjady, Robust security constrained ACOPF via conic programming: Identifying the worst contingencies, IEEE Trans. Power Syst., 33 (2018), pp. 5884-5891.
[54] Y. Xu, Scalable Algorithms for Parallel Tree Search, Ph.D. thesis, Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, 2007.
[55] L. Zhao and B. Zeng, Vulnerability analysis of power grids with line switching, IEEE Trans. Power Syst., 28 (2013), pp. 2727-2736.
[56] Y. Zheng, G. Fantuzzi, A. Papachristodoulou, P. Goulart, and A. Wynn, Fast ADMM for semidefinite programs with chordal sparsity, in Proceedings of the 2017 American Control Conference (ACC), IEEE, 2017, pp. 3335-3340.
[57] Y. Zheng, G. Fantuzzi, A. Papachristodoulou, P. Goulart, and A. Wynn, Chordal decomposition in operator-splitting methods for sparse semidefinite programs, Math. Program., 180 (2020), pp. 489-532. · Zbl 1434.90126
[58] R. Zimmermann and C. Murillo-Sánchez, Matpower 7.0b1 User’s Manual, Power Systems Engineering Research Center (PSerc), 2018, http://www.pserc.cornell.edu/matpower/manual.pdf.
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