An ADMM-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow

References

• Andreani R, Birgin EG, Martínez JM, Schuverdt ML (2008a) Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Programming 111(1):5–32.Google Scholar
• Andreani R, Birgin EG, Martínez JM, Schuverdt ML (2008b) On augmented lagrangian methods with general lower-level constraints. SIAM J. Optim. 18(4):1286–1309.Crossref, Google Scholar
• Aravena I, Molzahn DK, Zhang S, Petra CG, Curtis FE, Tu S, Wächter A, et al. (2022) Recent developments in security-constrained AC optimal power flow: Overview of challenge 1 in the ARPA-E grid optimization competition. Preprint, submitted June 15, https://arxiv.org/abs/2206.07843.Google Scholar
• ARPA-E (2019a) Grid optimization competition: Challenge 1 datasets. Accessed June 8, 2023, https://gocompetition.energy.gov/challenges/22/datasets.Google Scholar
• ARPA-E (2019b) SCOPF problem formulation. Challenge. Accessed June 8, 2023, https://gocompetition.energy.gov/sites/default/files/SCOPF_Problem_Formulation__Challenge_1_20190412.pdf.Google Scholar
• Bai X, Wei H, Fujisawa K, Wang Y (2008) Semidefinite programming for optimal power flow problems. Internat. J. Electric. Power Energy Systems 30(6–7):383–392.Crossref, Google Scholar
• Baldick R, Kim BH, Chase C, Luo Y (1999) A fast distributed implementation of optimal power flow. IEEE Trans. Power Systems 14(3):858–864.Crossref, Google Scholar
• Bertsekas DP (2014) Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York).Google Scholar
• Bienstock D, Verma A (2019) Strong NP-hardness of AC power flows feasibility. Oper. Res. Lett. 47(6):494–501.Crossref, Google Scholar
• Capitanescu F (2016) Critical review of recent advances and further developments needed in AC optimal power flow. Electric Power Systems Res. 136:57–68.Crossref, Google Scholar
• Capitanescu F, Glavic M, Ernst D, Wehenkel L (2007) Contingency filtering techniques for preventive security-constrained optimal power flow. IEEE Trans. Power Systems 22(4):1690–1697.Crossref, Google Scholar
• Capitanescu F, Martinez Ramos JL, Panciatici P, Kirschen D, Marano Marcolini A, Platbrood L, Wehenkel L (2011) State-of-the-art, challenges, and future trends in security constrained optimal power flow. Electric Power Systems Res. 81(8):1731–1741.Crossref, Google Scholar
• Carpentier J (1962) Contribution to the economic dispatch problem. Bull. Soc. French Électr. 3(8):431–447.Google Scholar
• Chen C, Mangasarian OL (1996) A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5(2):97–138.Crossref, Google Scholar
• Chen X (2012) Smoothing methods for nonsmooth, nonconvex minimization. Math. Programming 134(1):71–99.Crossref, Google Scholar
• Chung K, Kim B, Hur D (2011) Multi-area generation scheduling algorithm with regionally distributed optimal power flow using alternating direction method. Internat. J. Electric Power Energy Systems 33(9):1527–1535.Crossref, Google Scholar
• Chung K, Kim BH, Song KB (2005) Implementing distributed optimal power flow using the alternating direction method. KIEE Internat. Trans. Power Engrg. 5(4):412–415.Google Scholar
• Coffrin C (2019) A PowerModels extension for security constrained optimization problems. Accessed June 8, 2023, https://github.com/lanl-ansi/PowerModelsSecurityConstrained.jl.Google Scholar
• Coffrin C, Van Hentenryck P (2014) A linear-programming approximation of AC power flows. INFORMS J. Comput. 26(4):718–734.Link, Google Scholar
• Conforti M, Cornuéjols G, Zambelli G (2014) Integer Programming, vol. 271 (Springer, Berlin).Crossref, Google Scholar
• Erseghe T (2014) Distributed optimal power flow using ADMM. IEEE Trans. Power Systems 29(5):2370–2380.Crossref, Google Scholar
• Fliscounakis S, Panciatici P, Capitanescu F, Wehenkel L (2013) Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions. IEEE Trans. Power Systems 28(4):4909–4917.Crossref, Google Scholar
• Hong M, Luo ZQ, Razaviyayn M (2016) Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems. SIAM J. Optim. 26(1):337–364.Crossref, Google Scholar
• HSL A collection of Fortran codes for large scale scientific computation. Accessed June 8, 2023, http://www.hsl.rl.ac.uk/.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, Coonick AH, Cory BJ (2002) A primal-dual interior point method for optimal power flow dispatching. IEEE Trans. Power Systems 17(3):654–662.Crossref, Google Scholar
• Jiang B, Ma S, Zhang S (2014) Alternating direction method of multipliers for real and complex polynomial optimization models. Optimization 63(6):883–898.Crossref, Google Scholar
• Kim BH, Baldick R (1997) Coarse-grained distributed optimal power flow. IEEE Trans. Power Systems 12(2):932–939.Crossref, Google Scholar
• Kim BH, Baldick R (2000) A comparison of distributed optimal power flow algorithms. IEEE Trans. Power Systems 15(2):599–604.Crossref, Google Scholar
• Kocuk B, Dey SS, Sun XA (2016) Strong SOCP relaxations for the optimal power flow problem. Oper. Res. 64(6):1177–1196.Link, Google Scholar
• Lavaei J, Low SH (2011) Zero duality gap in optimal power flow problem. IEEE Trans. Power Systems 27(1):92–107.Crossref, Google Scholar
• Lee YJ, Mangasarian OL (2001) Ssvm: A smooth support vector machine for classification. Comput. Optim. Appl. 20(1):5–22.Crossref, Google Scholar
• Lehmann K, Grastien A, Van Hentenryck P (2015) AC-feasibility on tree networks is NP-hard. IEEE Trans. Power Systems 31(1):798–801.Crossref, Google Scholar
• Low SH (2014a) Convex relaxation of optimal power flow. Part I: Formulations and equivalence. IEEE Trans. Control Network Systems 1(1):15–27.Crossref, Google Scholar
• Low SH (2014b) Convex relaxation of optimal power flow. Part II: Exactness. IEEE Trans. Control Network Systems 1(2):177–189.Crossref, Google Scholar
• Majidi-Qadikolai M, Baldick R (2016) Stochastic transmission capacity expansion planning with special scenario selection for integrating n − 1 contingency analysis. IEEE Trans. Power Systems 31(6):4901–4912.Crossref, Google Scholar
• Mhanna S, Verbic G, Chapman AC (2019) Adaptive ADMM for distributed AC optimal power flow. IEEE Trans. Power Systems 34(3):2025–2035.Crossref, Google Scholar
• Molzahn DK, Hiskens IA (2019) A survey of relaxations and approximations of the power flow equations. Foundations Trends Electric Energy Systems 4(1):1–221.Crossref, Google Scholar
• Peng Q, Low SH (2014) Distributed algorithm for optimal power flow on a radial network. 53rd IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 167–172.Google Scholar
• Peng Q, Low SH (2015) Distributed algorithm for optimal power flow on an unbalanced radial network. 54th IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 6915–6920.Google Scholar
• Peng Q, Low SH (2016) Distributed optimal power flow algorithm for radial networks. I. Balanced single phase case. IEEE Trans. Smart Grid 9(1):111–121.Crossref, Google Scholar
• Phan D, Kalagnanam J (2013) Some efficient optimization methods for solving the security-constrained optimal power flow problem. IEEE Trans. Power Systems 29(2):863–872.Crossref, Google Scholar
• Platbrood L, Capitanescu F, Merckx C, Crisciu H, Wehenkel L (2013) A generic approach for solving nonlinear-discrete security-constrained optimal power flow problems in large-scale systems. IEEE Trans. Power Systems 29(3):1194–1203.Crossref, Google Scholar
• Rockafellar RT, Wets RJB (2009) Variational Analysis, vol. 317 (Springer Science & Business Media, New York).Google Scholar
• Schmidt M, Fung G, Rosales R (2007) Fast optimization methods for l1 regularization: A comparative study and two new approaches. Eur. Conf. Machine Learn. (Springer, Berlin), 286–297.Google Scholar
• Stott B, Jardim J, Alsac O (2009) DC power flow revisited. IEEE Trans. Power Systems 24(3):1290–1300.Crossref, Google Scholar
• Sun AX, Phan DT, Ghosh S (2013) Fully decentralized AC optimal power flow algorithms. 2013 IEEE Power Energy Soc. General Meeting (IEEE, Piscataway, NJ), 1–5.Google Scholar
• Sun K, Sun XA (2021) A two-level ADMM algorithm for AC OPF with global convergence guarantees. IEEE Trans. Power Systems 36(6):5271–5281.Crossref, Google Scholar
• Sun K, Sun XA (2023) A two-level distributed algorithm for nonconvex constrained optimization. Comput. Optim. Appl. 84(2):609–649.Crossref, Google Scholar
• Torres GL, Quintana VH (1998) An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Trans. Power Systems 13(4):1211–1218.Crossref, Google Scholar
• Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming 106(1):25–57.Crossref, Google Scholar
• Wang H, Murillo-Sanchez CE, Zimmerman RD, Thomas RJ (2007) On computational issues of market-based optimal power flow. IEEE Trans. Power Systems 22(3):1185–1193.Crossref, Google Scholar
• Wang Y, Yin W, Zeng J (2019) Global convergence of ADMM in nonconvex nonsmooth optimization. J. Sci. Comput. 78:29–63.Crossref, Google Scholar
• Wu YC, Debs AS, Marsten RE (1994) A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Trans. Power Systems 9(2):876–883.Crossref, Google Scholar
• Zimmerman RD, Murillo-Sánchez CE (2020) MATPOWER user’s manual. Accessed June 8, 2023, https://matpower.org/docs/manual.pdf.Google Scholar