Chance-constrained optimal power flow: Risk-aware network control under uncertainty

SIAM Review

Volumn 56, Issue 3, 2014, Pages 461-495

  Bienstock, Daniel ^a   Chertkov, Michael ^b   Harnett, Sean ^a,b  

^a Department of Earth and Environmental Sciences   (United States)

^b CENTER FOR NONLINEAR STUDIES   (United States)

Author keywords

Networks; Optimization; Power flows; Uncertainty; Wind farms

Indexed keywords

ACOUSTIC GENERATORS; COAL DEPOSITS; ELECTRIC INDUSTRY; ELECTRIC LOAD FLOW; ELECTRIC POWER TRANSMISSION NETWORKS; ELECTRIC UTILITIES; NETWORKS (CIRCUITS); OPTIMIZATION; WEATHER FORECASTING; WIND POWER;

CHANCE-CONSTRAINED; EFFICIENT IMPLEMENTATION; ELECTRIC POWER INDUSTRIES; OPERATIONAL PROCEDURES; OPTIMAL POWER FLOWS; POWER FLOWS; UNCERTAINTY; WIND FARM;

OUTAGES;

EID: 84905985454     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/130910312     Document Type: Article

References (56)

1. 20% of Wind Energy by 2030: Increasing Wind Energy's Contribution to U.S. Electricity Supply, DOE/GO-102008-2567, Department of Energy (DOE), Energy Efficiency and Renewable Energy, 2008.
2. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1965.
3. D. Apostolopoulou, P. W. Sauer, and A. D. Dominguez-Garcia, Automatic generation control and its implementation in real time, in Proceedings of the 47th Hawaii International Conference on System Sciences (HICSS), 2014, pp. 2444-2452.
4. S. Baghsorkhi and I. Hiskens, Analysis tools for assessing the impact of wind power on weak grids, in Proceedings of the 6th Annual IEEE Systems Conference (SysCon), 2012, pp. 1-8.
5. R. Ben-Tal and A. Nemirovski, Robust solutions of linear programming problems contaminated with uncertain data, Math. Programming, 88 (2000), pp. 411-424.
6. R. Bent, G. Toole, and A. Berscheid, Transmission network expansion planning with complex power flow models, IEEE Trans. Power Systems, 27 (2012), pp. 904-912.
7. A. Bergen and V. Vittal, Power System Analysis, Prentice-Hall, 2000.
8. A. Bernstein, D. Hay, M. Uzunoglu, and G. Zussman, Power Grid Vulnerability to Geographically Correlated Failures: Analysis and Control Implications, preprint, 2012; available online from http://arxiv.org/abs/1206. 1099.
9. D. Bertsimas and M. Sim, Price of robustness, Oper. Res., 52 (2004), pp. 35-53.
10. D. Bienstock, Potential Function Methods for Approximately Solving Linear Programming Problems, Theory and Practice, Kluwer Academic, 2002.
11. D. Bienstock, Adaptive online control of cascading blackouts, in Proceedings of the 2011 IEEE Power and Energy Society General Meeting, IEEE, 2011, pp. 1-8.
12. D. Bienstock, Optimal control of cascading power grid failures, in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, pp. 2166-2173.
13. D. Bienstock and G. Iyengar, Approximating fractional packings and coverings in 0(1/-) iterations, SIAM J. Comput., 35 (2006), pp. 825-854.
14. H. Bludszuweit, J. Dominguez-Navarro, and A. Llombart, Statistical analysis of wind power forecast error, IEEE Trans. Power Systems, 23 (2008), pp. 983-991.
15. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
16. A. Charnes, W. Cooper, and G. Symonds, Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil, Management Sci., 4 (1958), pp. 235- 263.
17. J. Chen, J. Thorp, and I. Dobson, Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model, Internat. J. Electrical Power Energy Systems, 27 (2005), pp. 318-326.
18. M. Chertkov, F. Pan, and M. Stepanov, Predicting failures in power grids: The case of static overloads, IEEE Trans. Smart Grids, 2 (2010), p. 150.
19. M. Chertkov, M. Stepanov, F. Pan, and R. Baldick, Exact and efficient algorithm to discover extreme stochastic events in wind generation over transmission power grids, in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, pp. 2174-2180.
20. F. D̈orfler, M. Chertkov, and F. Bullo, Synchronization in complex oscillator networks and smart grids, Proc. Natl. Acad. Sci. USA, 10.1073/pnas.1212134110 (2013).
21. Energy Management Planning for the Integration of Wind Energy into the Grid in Germany, Onshore and Offshore by 2020, Deutsche Energie-Agentur GmbH (DENA), 2005.
22. M. Eppstein and P. Hines, A "random chemistry" algorithm for identifying collections of multiple contingencies that initiate cascading failure, IEEE Trans. Power Systems, 27 (2012), pp. 1698-1705.
23. E. Erdogan and G. Iyengar, Ambiguous chance constrained problems and robust optimization, Math. Programming, 107 (2007), pp. 37-61.
24. D. Goldfarb and F. Alizadeh, Second-order cone programming, Math. Programming, 95 (2003), pp. 3-51.
25. D. Goldfarb and G. Iyengar, Robust portfolio selection problems, Math. Programming, 28 (2001), pp. 1-38.
26. G. Gonzalez et al., Experience integrating and operating wind power in the peninsular Spanish power system. Point of view of the transmission system operator and a wind power producer, CIGRE, 2006.
27. Grid Integration of Wind Generation, Technical brochure 450, International Conference on Large High Voltage Electric Systems, CIGRE, 2009.
28. M. Gr̈otschel, L. Lov́asz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, 1998.
29. Gurobi Optimizer, http://www.gurobi.com/, 2012.
30. B.-M. Hodge and M. Milligan, Wind power forecasting error distributions over multiple timescales, in Detroit Power Engineering Society Meeting, 2011, pp. 1-8.
31. M. Huneault and F. D. Galiana, A survey of the optimal power flow literature, IEEE Trans. Power Systems, 6 (1991), pp. 762-770.
32. ILOG CPLEX Optimizer, http://www-01.ibm.com/software/integration/ optimization/cplexoptimizer/, IBM, 2012.
33. Integration of Renewable Resources: Transmission and Operating Issues and Recommendations for Integrating Renewable Resources on the California ISO-Controlled Grid, http://www.caiso.com/1ca5/1ca5a7a026270.pdf, CAISO, 2007.
34. J. E. Kelley, The cutting-plane method for solving convex programs, J. Soc. Indust. Appl. Math., 8 (1960), pp. 703-712.
35. M. Kraning, E. Chu, J. Lavaei, and S. Boyd, Message Passing for Dynamic Network Energy Management, http://www.stanford.edu/?boyd/papers/decen dyn opt.html, 2012.
36. P. Kundur, Power System Stability and Control, McGraw-Hill, New York, 1994.
37. Y. Makarov, C. Loutan, J. Ma, and P. De Mello, Operational impacts of wind generation on California power systems, IEEE Trans. Power Systems, 24 (2009), pp. 1039-1050.
38. L. Miller and H. Wagner, Chance-constrained programming with joint constraints, Oper. Res., 13 (1965), pp. 930-945.
39. MOSEK Optimizer, http://www.mosek.com/, 2012.
40. D. Nedic, I. Dobson, D. Kirschen, B. Carreras, and V. E. Lynch, Criticality in a cascading failure blackout model, Internat. J. Electrical Power Energy Systems, 28 (2006), pp. 627- 633.
41. A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), pp. 969-996.
42. U. Ozturk and M. Mazumdar, A solution to the stochastic unit commitment problem using chance constrained programming, IEEE Trans. Power Systems, 19 (2004), pp. 1589-1598.
43. R. Pfitzner, K. Turitsyn, and M. Chertkov, Controlled Tripping of Overheated Lines Mitigates Power Outages, preprint, arxiv:1104.4558, 2011.
44. R. Pfitzner, K. Turitsyn, and M. Chertkov, Statistical classification of cascading failures in power grids, in Proceedings of the 2011 IEEE Power and Energy Society General Meeting, 2011, pp. 1-8.
45. A. Pŕekopa, On probabilistic constrained programming, in Proceedings of the Princeton Symposium on Mathematical Programming, 1970, pp. 113-138.
46. L. Roald, F. Oldewurtel, T. Krause, and G. Andersson, Analytical reformulation of security constrained optimal power flow with probabilistic constraints, in Proceedings of the Grenoble PowerTech, Grenoble, France, 2013.
47. A. Sjodin, D. Gayme, and U. Topcu, Risk-Mitigated Optimal Power Flow with High Wind Penetration, http://smart.caltech.edu/papers/riskoptimal.pdf, 2012.
48. U.S.-Canada Power System Outage Task Force. Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations, Tech. report, https://reports.energy.gov, Department of Energy (DOE), 2004.
49. M. Vrakopoulou, K. Margellos, J. Lygeros, and G. Andersson, A probabilistic framework for security constrained reserve scheduling of networks with wind power generation, in Proceedings of the 2012 IEEE International Energy Conference and Exhibition (ENERGYCON), 2012, pp. 452-457.
50. G. Wang, M. Negrete-Pincetic, A. Kowli, E. Shafieepoorfard, S. Meyn, and U. Shanbhag, Dynamic competitive equilibria in electricity markets, in Control and Optimization Theory for Electric Smart Grids, A. Chakrabortty and M. Illic, eds., Springer, 2011.
51. J. Wang, M. Shahidehpour, and Z. Li, Security-constrained unit commitment with volatile wind power generation, IEEE Trans. Power Systems, 23 (2008), pp. 1319-1327.
52. Wind Generation & Total Load in the BPA Balancing Authority, http://transmission.bpa.gov/business/operations/wind/, Bonneville Power Administration, 2012.
53. A. J. Wood and B. Wollenberg, Power Generation, Operation and Control, John Wiley and Sons, 1983.
54. H. Zhang, Chance Constrained Programming for Optimal Power Flow under Uncertainty, IEEE Trans. Power Systems, 26 (2011), pp. 2417-2424.
55. S. Zhang, Y. Song, Z. Hu, and L. Yao, Robust optimization method based on scenario analysis for unit commitment considering wind uncertainties, in Proceedings of the 2011 IEEE Power and Energy Society General Meeting, 2011, pp. 1-7.
56. R. Zimmerman, C. Murillo-Sanchez, and R. Thomas, MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education, IEEE Trans. Power Systems, 26 (2011), pp. 12-19.