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A bilevel approach for identifying the worst contingencies for nonconvex alternating current power systems. (English) Zbl 07319280
MSC:
90C11 Mixed integer programming
90C26 Nonconvex programming, global optimization
90C17 Robustness in mathematical programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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[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 07165832
[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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