Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming Approach

References

• Abel A, Parfomak PW, Shea DA (2004) Electric utility infrastructure vulnerabilities: Transformers towers and terrorism. Technical Report R42795, Congressional Research Service, Washington, DC.Google Scholar
• Arab A, Khodaei A, Khator SK, Ding K, Emesih VA, Han Z (2015) Stochastic pre-hurricane restoration planning for electric power systems infrastructure. IEEE Trans. Smart Grid 6(2):1046–1054.Crossref, Google Scholar
• Babaei S, Jiang R, Zhao C (2020) Distributionally robust distribution network configuration under random contingency. IEEE Trans. Power Systems 35(5):3332–3341.Google Scholar
• Baran ME, Wu FF (1989a) Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Delivery 4(2):1401–1407.Crossref, Google Scholar
• Baran ME, Wu FF (1989b) Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans. Power Delivery 4(1):735–743.Crossref, Google Scholar
• Barnes A, Nagarajan H, Yamangil E, Bent R, Backhaus S (2019) Resilient design of large-scale distribution feeders with networked microgrids. Electric Power Systems Res. 171:150–157.Crossref, Google Scholar
• Bienstock D (2015) Electrical Transmission System Cascades and Vulnerability: An Operations Research Viewpoint (SIAM, Philadelphia).Crossref, Google Scholar
• Bienstock D, Matke C, Muñoz G, Yang S (2016) Robust linear control of nonconvex battery operation in transmission systems. Preprint, submitted March 16, https://arxiv.org/abs/1610.09432.Google Scholar
• Birge JR, Louveaux FV (1988) A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. 34(3):384–392.Crossref, Google Scholar
• Brown GG, Carlyle WM, Salmerón J, Wood K (2005) Analyzing the Vulnerability of Critical Infrastructure to Attack and Planning Defenses (INFORMS TutORials), Oper. Res. 102–123.Link, Google Scholar
• Byeon G, Van Hentenryck P, Bent R, Nagarajan H (2020) Communication-constrained expansion planning for resilient distribution systems. INFORMS J. Comput. 32(4):968–985.Abstract, Google Scholar
• Cain MB, O’Neill RP, Castillo A (2012) History of optimal power flow and formulations. Technical report, Federal Energy Regulatory Commission, Washington, DC.Google Scholar
• Cardoso G, Heleno M, DeForest N (2019) Remote off-grid microgrid design support tool (ROMDST)—An optimal design support tool for remote, resilient, and reliable microgrids (Phase II, Final Report). Technical report, Lawrence Berkeley National Laboratory, Berkeley, CA.Google Scholar
• Chalil Madathil S, Yamangil E, Nagarajan H, Barnes A, Bent R, Backhaus S, Mason SJ, Mashayekh S, Stadler M (2018) Resilient off-grid microgrids: Capacity planning and N-1 security. IEEE Trans. Smart Grid 9(6):6511–6521.Crossref, Google Scholar
• Chen Q (2004) The probability, identification, and prevention of rare events in power systems. Unpublished PhD thesis, Iowa State University, Ames.Google Scholar
• Chen Z, Powell WB (1999) Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse. J. Optim. Theory Appl. 102:497–524.Crossref, Google Scholar
• Choi J, Mount TD, Thomas RJ (2007) Transmission expansion planning using contingency criteria. IEEE Trans. Power Systems 22(4):2249–2261.Crossref, Google Scholar
• Dantzig GB, Infanger G (1993) Approaches to stochastic programming with application to electric power systems. Frauendorfer K, Glavitsch H, Bacher R, eds. Optimization in Planning and Operation of Electric Power Systems (Springer, Heidelberg, Germany), 125–138.Crossref, Google Scholar
• Dempster MAH (2006) Sequential importance sampling algorithms for dynamic stochastic programming. J. Math. Sci. (N.Y.). 133(4):1422–1444.Crossref, Google Scholar
• Ding L, Ahmed S, Shapiro A (2019) A python package for multi-stage stochastic programming. Optimization Online. Accessed March 16, 2020, http://www.optimization-online.org/DB_FILE/2019/05/7199.pdf.Google Scholar
• Dowson O (2020) The policy graph decomposition of multistage stochastic optimization problems. Networks 76(1):3–23.Google Scholar
• Dowson O, Kapelevich L (2021) SDDP.jl: A Julia package for stochastic dual dynamic programming. INFORMS J. Comput. 33(1):27–33.Google Scholar
• Dunning I, Huchette J, Lubin M (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev. 59(2):295–320.Crossref, Google Scholar
• Executive Office of the President (2013) Economic benefits of increasing electric grid resilience to weather outages. Technical report, Executive Office of the President, Washington, DC.Google Scholar
• Frangioni A, Gentile C (2006) Solving nonlinear single-unit commitment problems with ramping constraints. Oper. Res. 54(4):767–775.Link, Google Scholar
• Gan L, Li N, Topcu U, Low SH (2014) Exact convex relaxation of optimal power flow in radial networks. IEEE Trans. Automatic Control 60(1):72–87.Crossref, Google Scholar
• Girardeau P, Leclère V, Philpott AB (2014) On the convergence of decomposition methods for multistage stochastic convex programs. Math. Oper. Res. 40(1):130–145.Link, Google Scholar
• Grid Integration Group (2020) The distributed energy resources customer adoption model (der-cam). Accessed March 16, 2020, https://gridintegration.lbl.gov/der-cam.Google Scholar
• Gurobi Optimization, Inc. (2016) Gurobi reference manual. Accessed March 16, 2020, http://www.gurobi.com.Google Scholar
• Hari SKK, Sundar K, Nagarajan H, Bent R, Backhaus S (2018) Hierarchical predictive control algorithms for optimal design and operation of microgrids. Power Systems Comput. Conference. (IEEE), 1–7.Google Scholar
• Hedman KW, O’Neill RP, Fisher EB, Oren SS (2009) Optimal transmission switching with contingency analysis. IEEE Trans. Power Systems 24(3):1577–1586.Crossref, Google Scholar
• Infanger G (1992) Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann. Oper. Res. 39(1):69–95.Crossref, Google Scholar
• Lei S, Chen C, Li Y, Hou Y (2019) Resilient disaster recovery logistics of distribution systems: Co-optimize service restoration with repair crew and mobile power source dispatch. IEEE Trans. Smart Grid 10(6):6187–6202.Crossref, Google Scholar
• Lin Z, Hu Z, Song Y (2019) Distribution network expansion planning considering N-1 criterion. IEEE Trans. Power Systems 34(3):2476–2478.Crossref, Google Scholar
• Linowsky K, Philpott AB (2005) On the convergence of sampling-based decomposition algorithms for multistage stochastic programs. J. Optim. Theory Appl. 125(2):349–366.Crossref, Google Scholar
• Ma S, Li S, Wang Z, Qiu F (2019) Resilience-oriented design of distribution systems. IEEE Trans. Power Systems 34(4):2880–2891.Crossref, Google Scholar
• Mashayekh S, Stadler M, Cardoso G, Heleno M, Madathil SC, Nagarajan H, Bent R, Mueller-Stoffels M, Lu X, Wang J (2017) Security-constrained design of isolated multi-energy microgrids. IEEE Trans. Power Systems 33(3):2452–2462.Crossref, Google Scholar
• Nagarajan H, Yamangil E, Bent R, Van Hentenryck P, Backhaus S (2016) Optimal resilient transmission grid design. Power Systems Comput. Conf. (IEEE, Piscataway, NJ), 1–7.Google Scholar
• Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math. Programming 52(1–3):359–375.Crossref, Google Scholar
• Philpott AB, Guan Z (2008) On the convergence of stochastic dual dynamic programming and related methods. Oper. Res. Lett. 36(4):450–455.Crossref, Google Scholar
• Rebennack S (2016) Combining sampling-based and scenario-based nested Benders decomposition methods: Application to stochastic dual dynamic programming. Math. Programming 156(1):343–389.Crossref, Google Scholar
• Rockafellar RT, Wets RJB (1976) Stochastic convex programming: Relatively complete recourse and induced feasibility. SIAM J. Control Optim. 14(3):574–589.Crossref, Google Scholar
• Salmerón J, Wood RK, Morton DP (2009) A stochastic program for optimizing military sealift subject to attack. Military Oper. Res. 14(2):19–39.Crossref, Google Scholar
• Schneider KP, Mather BA, Pal BC, Ten C, Shirek GJ, Zhu H, Fuller JC, et al. (2018) Analytic considerations and design basis for the IEEE distribution test feeders. IEEE Trans. Power Systems 33(3):3181–3188.Crossref, Google Scholar
• Shapiro A (2011) Analysis of stochastic dual dynamic programming method. Eur. J. Oper. Res. 209(1):63–72.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).Crossref, Google Scholar
• Ton DT, Wang WTP (2015) A more resilient grid: The US department of energy joins with stakeholders in an R&D plan. IEEE Power Energy Magazine 13(3):26–34.Crossref, Google Scholar
• Vanin M, Ergun H, D’hulst R, Van Hertem D (2020) Comparison of linear and conic power flow formulations for unbalanced low voltage network optimization. Electric Power Systems Res. 189:106699.Crossref, Google Scholar
• Yamangil E, Bent R, Backhaus S (2015) Resilient upgrade of electrical distribution grids. 29th AAAI Conf. Artificial Intelligence (PKP Publishing Services Network).Google Scholar
• Yan J, Hu B, Xie K, Tang J, Tai H (2019) Data-driven transmission defense planning against extreme weather events. IEEE Trans. Smart Grid 11(3):2257–2270.Crossref, Google Scholar
• Yang H, Morton DP (2021) Optimal crashing of an activity network with disruptions. Math. Programming. Forthcoming.Google Scholar
• Yang H, Nagarajan H (2020) Optimal power flow in distribution networks under stochastic N-1 disruptions. Electric Power Systems Res. 189:106689.Crossref, Google Scholar
• Yang H, Morton DP, Bandi C, Dvijotham K (2021) Robust optimization for electricity generation. INFORMS J. Comput. 33(1):336–351.Link, Google Scholar
• Yuan W, Wang J, Qiu F, Chen C, Kang C, Zeng B (2016) Robust optimization-based resilient distribution network planning against natural disasters. IEEE Trans. Smart Grid 7(6):2817–2826.Crossref, Google Scholar
• Zhou H, Zheng JH, Li Z, Wu QH, Zhou XX (2019) Multi-stage contingency-constrained co-planning for electricity-gas systems interconnected with gas-fired units and power-to-gas plants using iterative benders decomposition. Energy 180:689–701.Crossref, Google Scholar