Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

References

• Aigner KM, Clarner JP, Liers F, Martin A (2022) Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty. Eur. J. Oper. Res. 301(1):318–333.Google Scholar
• ARPA-E (2018) Grid optimization competition. https://gocompetition.energy.gov/.Google Scholar
• Bai X, Weihua H, Fujisawa K, Wang Y (2008) Semidefinite programming for optimal power flow problems. Internat. J. Electrical Power Energy Systems 30(6–7):383–392.Crossref, Google Scholar
• Bai Y, Zhong H, Xia Q, Kang C (2016) A two-level approach to AC optimal transmission switching with an accelerating technique. IEEE Trans. Power Systems 32(2):1616–1625.Google Scholar
• Balas E, Jeroslow R (1972) Canonical cuts on the unit hypercube. SIAM J. Appl. Math. 23(1):61–69.Crossref, Google Scholar
• Bärmann A, Liers F, Martin A, Merkert M, Thurner C, Weninger D (2015) Solving network design problems via iterative aggregation. Math. Programming Comput. 7:189–217.Crossref, Google Scholar
• Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Software 24(4–5):597–634.Crossref, Google Scholar
• Bienstock D, Verma A (2015) Strong NP-hardness of AC power flows feasibility. Oper. Res. Lett. 47(6):494–501.Crossref, Google Scholar
• Bienstock D, Chertkov M, Harnett S (2014) Chance-constrained optimal power flow: Risk-aware network control under uncertainty. SIAM Rev. 56(3):461–495.Crossref, Google Scholar
• Bienstock D, Escobar M, Gentile C, Liberti L (2020) Mathematical programming formulations for the alternating current optimal power flow problem. 4OR-Quart. J. Oper. Res. 18:249–292.Google Scholar
• Burlacu R, Geißler B, Schewe L (2020) Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes. Optim. Methods Software 35(1):37–64.Crossref, Google Scholar
• Burlacu R, Egger H, Groß M, Martin A, Pfetsch ME, Schewe L, Sirvent M, Skutella M (2019) Maximizing the storage capacity of gas networks: A global MINLP approach. Optim. Engrg. 20:543–573.Crossref, Google Scholar
• Cain MB, O’Neill RP, Castillo A (2012) History of optimal power flow and formulations, Federal Energy Regulatory Commission, Washington, DC.Google Scholar
• Carpentier J (1962) Contribution a l’etude du dispatching economique. Bull. Soc. Francaise Electricians 3:431–447.Google Scholar
• Castillo A, Laird C, Silva-Monroy CA, Watson J, O’Neill RP (2016) The unit commitment problem with AC optimal power flow constraints. IEEE Trans. Power Systems 31(6):4853–4866.Crossref, Google Scholar
• Christie RD, Wollenberg BF, Wangensteen I (2000) Transmission management in the deregulated environment. Proc. IEEE 88(2):170–195.Crossref, Google Scholar
• Coffrin C, Gordon D, Scott P (2014) NESTA, the NICTA energy system test case archive. Preprint, submitted November 3, https://arxiv.org/abs/1411.0359.Google Scholar
• Coffrin C, Hijazi HL, Van Hentenryck P (2016) The QC relaxation: A theoretical and computational study on optimal power flow. IEEE Trans. Power Systems 31(4):3008–3018.Crossref, Google Scholar
• Correa-Posada CM, Sánchez-Martín P (2014) Gas network optimization: A comparison of piecewise linear models. http://www.optimization-online.org/DB_HTML/2014/10/4580.html.Google Scholar
• D’Ambrosio C, Lodi A, Wiese S, Bragalli C (2015) Mathematical programming techniques in water network optimization. Eur. J. Oper. Res. 243(3):774–788.Crossref, Google Scholar
• Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math. Programming 91(2):201–213.Crossref, Google Scholar
• Domschke P, Geißler B, Kolb O, Lang J, Martin A, Morsi A (2011) Combination of nonlinear and linear optimization of transient gas networks. INFORMS J. Comput. 23(4):605–617.Link, Google Scholar
• Frank S, Steponavice I, Rebennack S (2012a) Optimal power flow: A bibliographic survey I. Energy Systems 3:221–258.Crossref, Google Scholar
• Frank S, Steponavice I, Rebennack S (2012b) Optimal power flow: A bibliographic survey II. Energy Systems 3:259–289.Crossref, Google Scholar
• Gambella C, Marecek J, Mevissen M, Fernández Ortega J, Djukic S, Pezic M (2018) Transmission-constrained unit commitment. Preprint, submitted June 25, https://arxiv.org/abs/1806.09408.Google Scholar
• Gamrath G, Anderson D, Bestuzheva K, Chen WK, Eifler L, Gasse M, Gemander P, et al. (2020) The SCIP Optimization Suite 7.0. ZIB-Report 20-10, Zuse Institute Berlin. http://nbn-resolving.de/urn:nbn:de:0297-zib-78023.Google Scholar
• GAMS (2020) General Algebraic Modeling System (GAMS) Release 31.2.0. Washington, DC, USA, URL http://www.gams.com/.Google Scholar
• Geißler B (2011) Toward globally optimal solutions of MINLPs by discretization techniques with applications in gas network optimization. Unpublished PhD thesis, FAU Erlangen-Nürnberg, Germany.Google Scholar
• Gleixner A, Berthold T, Müller B, Weltge S (2017) Three enhancements for optimization-based bound tightening. J. Global Optim. 67(4):731–757.Crossref, Google Scholar
• Gopinath S, Hijazi H, Weisser T, Nagarajan H, Yetkin M, Sundar K, Bent R (2020) Proving global optimality of ACOPF solutions. Electric Power Systems Res, 189:106688.Crossref, Google Scholar
• Grimm V, Kleinert T, Liers F, Schmidt M, Zöttl G (2019) Optimal price zones of electricity markets: A mixed-integer multilevel model and global solution approaches. Optim. Methods Software 34(2):406–436.Crossref, Google Scholar
• Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D (2018) Toward simulation based mixed-integer optimization with differential equations. Networks 72(1):60–83.Crossref, Google Scholar
• Gurobi Optimization L (2020) Gurobi optimizer reference manual. http://www.gurobi.com.Google Scholar
• Hijazi H, Coffrin C, Van Hentenryck P (2013) Convex quadratic relaxations of mixed-integer nonlinear programs in power systems. Math. Programming Comput. 9:321–367.Crossref, Google Scholar
• Jabr RA (2006) Radial distribution load flow using conic programming. IEEE Trans. Power Systems 21(3):1458–1459.Crossref, Google Scholar
• Jabr RA (2008) Optimal power flow using an extended conic quadratic formulation. IEEE Trans. Power Systems 23(3):1000–1008.Crossref, Google Scholar
• Kocuk B, Dey S, Sun X (2016) Strong SOCP relaxations for the optimal power flow problem. Oper. Res. 64(6):1177–1196.Link, Google Scholar
• Kocuk B, Dey SS, Sun XA (2017) New formulation and strong MISOCP relaxations for AC optimal transmission switching problem. IEEE Trans. Power Systems 32(6):4161–4170.Crossref, Google Scholar
• Kocuk B, Dey SS, Sun XA (2018) Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem. Math. Programming Comput. 10(4):557–596.Crossref, Google Scholar
• Kuchlbauer M, Liers F, Stingl M (2022a) Adaptive bundle methods for nonlinear robust optimization. INFORMS J. Comput. 34(4):2106–2124.Link, Google Scholar
• Kuchlbauer M, Liers F, Stingl M (2022b) Outer approximation for mixed-integer nonlinear robust optimization. J. Optim. Theory Appl. 195:1056–1086.Crossref, Google Scholar
• Kuhn S (2011) Betriebsoptimierung von elektrischen energieerzeugungsanlagen und übertragungssystemen bei unvollständiger Information. Unpublished PhD thesis, Universität Duisburg-Essen, Germany.Google Scholar
• Liu J, Laird CD, Scott JK, Watson JP, Castillo A (2019) Global solution strategies for the network-constrained unit commitment problem with AC transmission constraints. IEEE Trans. Power Systems 34(2):1139–1150.Crossref, Google Scholar
• Lu M, Nagarajan H, Bent R, Eksioglu SD, Mason SJ (2018) Tight piecewise convex relaxations for global optimization of optimal power flow. 2018 Power Systems Comput. Conf., 1–7.Google Scholar
• McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Math. Programming 10(1):147–175.Crossref, Google Scholar
• Misener R, Floudas CA (2014) Antigone: Algorithms for continuous/integer global optimization of nonlinear equations. J. Global Optim. 59(2–3):503–526.Crossref, Google Scholar
• Morsi A (2013) Solving MINLPs on loosely-coupled networks with applications in water and gas network optimization. Unpublished PhD thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany.Google Scholar
• Nannicini G, Belotti P (2012) Rounding-based heuristics for nonconvex MINLPs. Math. Programming Comput. 4:1–31.Crossref, Google Scholar
• Purchala K, Meeus L, Dommelen DV, Belmans R (2005) Usefulness of DC power flow for active power flow analysis. IEEE Power Engrg. Soc. General Meeting, vol. 1, 454–459.Google Scholar
• Qiu Z, Deconinck G, Belmans R (2009) A literature survey of optimal power flow problems in the electricity market context. 2009 IEEE/PES Power Systems Conf. Exposition, 1–6.Google Scholar
• Salgado E, Scozzari A, Tardella F, Liberti L (2018) Alternating current optimal power flow with generator selection. Lee J, Rinaldi G, Mahjoub AR, eds. Combinatorial Optimization (Springer International Publishing), 364–375.Crossref, Google Scholar
• Saravanan B, Das S, Sikri S, Kothari DP (2013) A solution to the unit commitment problem—A review. Frontiers Energy 7(2):223–236.Crossref, Google Scholar
• Siqueira A, Gaia Costa da Silva R, Santos LR (2016) Perprof-py: A Python package for performance profile of mathematical optimization software. J. Open Res. Software 4(1):e12.Crossref, Google Scholar
• Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math. Programming 103:225–249.Crossref, Google Scholar
• Vieira B, Mayerle S, Campos L, Coelho L (2019) Optimizing drinking water distribution system operations. Eur. J. Oper. Res. 280(3):1035–1050.Crossref, Google Scholar
• Vielma JP, Ahmed S, Nemhauser GL (2010) Mixed-integer models for nonseparable piecewise-linear optimization: Unifying framework and extensions. Oper. Res. 58(2):303–315.Link, Google Scholar
• Vigerske S, Gleixner A (2018) SCIP: Global optimization of mixed-integer nonlinear programs in a branch-and-cut framework. Optim. Methods Software 33(3):563–593.Crossref, Google Scholar