Computing critical k-tuples in power networks

IEEE Transactions on Power Systems

Volumn 27, Issue 3, 2012, Pages 1511-1520

  Sou, Kin Cheong ^a   Sandberg, Henrik ^a   Johansson, Karl Henrik ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Combinatorial optimization; critical k tuples; minimum cut; mixed integer linear programming; state estimation

Indexed keywords

APPROXIMATE SOLUTION; CARDINALITIES; CRITICAL K -TUPLES; CRITICAL MEASUREMENTS; MIN-CUT; MINIMUM CUT; MIXED INTEGER LINEAR PROGRAMMING; NUMERICAL STUDIES; OPTIMAL SOLUTIONS; POWER NETWORKS; PROBLEM-BASED; TOPOLOGICAL NETWORKS; WEAK POINTS;

COMBINATORIAL OPTIMIZATION; STATE ESTIMATION;

PROBLEM SOLVING;

EID: 84864284962     PISSN: 08858950     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPWRS.2012.2187685     Document Type: Article

References (45)

1. A. Monticelli and F. Wu, "Network observability: Theory," IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp. 1042-1048, May 1985.
2. G. Krumpholz, K. Clements, and P. Davis, "Power system observability: A practical algorithm using network topology," IEEE Trans. Power App. Syst., vol. PAS-99, no. 4, pp. 1534-1542, Jul./Aug. 1980. (Pubitemid 11472481)
3. A. Abur and A. Expósito, Power System State Estimation. NewYork: Marcel Dekker, 2004.
4. A. Monticelli, State Estimation in Electric Power Systems a Generalized Approach. Norwell, MA: Kluwer, 1999.
5. M. de Almeida, E. Asada, and A. Garcia, "On the use of gram matrix in observability analysis," IEEE Trans. Power Syst., vol. 23, no. 1, pp. 249-251, Feb. 2008. (Pubitemid 351292108)
6. B. Gou, "Jacobian matrix-based observability analysis for state estimation," IEEE Trans. Power Syst., vol. 21, no. 1, pp. 348-356, Feb. 2006. (Pubitemid 43204733)
7. R. Pruneda, C. Solares, A. Conejo, and E. Castillo, "An efficient algebraic approach to observability analysis in state estimation," Elect. Power Syst. Res., vol. 80, no. 3, pp. 277-286, 2010.
8. C. Solares, A. Conejo, E. Castillo, and R. Pruneda, "Binary- Arithmetic approach to observability checking in state estimation," IET Gen., Transm., Distrib., vol. 3, no. 4, pp. 336-345, 2009.
9. E. Castillo, A. Conejo, R. Pruneda, and C. Solares, "Observability analysis in state estimation: A unified numerical approach," IEEE Trans. Power Syst., vol. 21, no. 2, pp. 877-886, May 2006.
10. A.Monticelli, F.Wu, and M. Yen, "Multiple bad data identification for state estimation by combinatorial optimization," IEEE Trans. Power Del., vol. 1, no. 3, pp. 361-369, Jul. 1986.
11. K. Clements and P. Davis, "Multiple bad data detectability and identification: A geometric approach," IEEE Trans. Power Del., vol. 1, no. 3, pp. 355-360, Jul. 1986. (Pubitemid 16629654)
12. T. Van Cutsem, M. Ribbens-Pavella, and L. Mili, "Bad data identification methods in power system state estimation-A comparative study," IEEE Trans. Power App. Syst., vol. PAS-104, no. 11, pp. 3037-3049, Nov. 1985. (Pubitemid 16524642)
13. G. Korres and G. Contaxis, "Identification and updating of minimally dependent sets of measurements in state estimation," IEEE Trans. Power Syst., vol. 6, no. 3, pp. 999-1005, Aug. 1991. (Pubitemid 21690195)
14. M. de Almeida, E. Asada, and A. Garcia, "Identifying critical sets in state estimation using gram matrix," in Proc. IEEE PowerTech, 2009, Bucharest, Romania, Jun. 28, 2009-Jul. 2, 2009, pp. 1-5.
15. M. Ayres and P. H. Haley, "Bad data groups in power system state estimation," IEEE Trans. Power Syst., vol. 1, no. 3, pp. 1-7, Aug. 1986.
16. K. Clements, G. Krumpholz, and P. Davis, "Power system state estimation residual analysis: An algorithm using network topology," IEEE Trans. Power App. Syst., vol. PAS-100, no. 4, pp. 1779-1787, Apr. 1981. (Pubitemid 11498054)
17. J. B. A. London, Jr., A. S. Bretas, and N. G. Bretas, "Algorithms to solve qualitative problems in power system state estimation," Int. J. Elect. Power Energy Syst., vol. 26, no. 8, pp. 583-592, 2004.
18. J. London, J. B. A. , L. Alberto, and N. Bretas, "Network observability: Identification of the measurements redundancy level," in Proc. Int. Conf. Power System Technology (PowerCon 2000), 2000, vol. 2, pp. 577-582.
19. E. Castillo, A. Conejo, R. Pruneda, C. Solares, and J. Menendez, "m-k robust observability in state estimation," IEEE Trans. Power Syst., vol. 23, no. 2, pp. 296-305, May 2008. (Pubitemid 351695807)
20. B. Gou and A. Abur, "An improved measurement placement algorithm for network observability," IEEE Power Eng. Rev., vol. 21, no. 10, p. 61, Oct. 2001.
21. O. Kosut, L. Jia, R. Thomas, and L. Tong, "Malicious data attacks on smart grid state estimation: Attack strategies and countermeasures," in Proc. IEEE SmartGridComm, 2010.
22. Y. Liu, M. Reiter, and P. Ning, "False data injection attacks against state estimation in electric power grids," in Proc. 16th ACMConf. Computer and Communication Security, New York, 2009, pp. 21-32.
23. R. Bobba, K. Rogers, Q. Wang, H. Khurana, K. Nahrstedt, and T. Overbye, "Detecting false data injection attacks on dc state estimation," in Proc. 1st Workshop Secure Control Systems (CPSWEEK 2010), 2010.
24. A. Teixeira, S. Amin, H. Sandberg, K. H. Johansson, and S. Sastry, "Cyber security analysis of state estimators in electric power systems," in Proc. IEEE Conf. Decision and Control, Dec. 2010.
25. G. Dan and H. Sandberg, "Stealth attacks and protection schemes for state estimators in power systems," in Proc. IEEE SmartGridComm, 2010.
26. K. C. Sou, H. Sandberg, and K. H. Johansson, "Electric power network security analysis via minimum cut relaxation," in Proc. IEEE Conf. Decision and Control, Dec. 2011. [Online]. Available: https://eeweb01.ee.kth.se/ upload/publications/reports/2011/IREERT-2011-089.pdf, report version.
27. J. Tsitsiklis and D. Bertsimas, Introduction to Linear Optimization. Nashua, NH: Athena Scientific, 1997.
28. M. Stoer and F. Wagner, "A simple min-cut algorithm," J. ACM, vol. 44, pp. 585-591, Jul. 1997. (Pubitemid 127617705)
29. L. Ford and D. Fulkerson, "Maximal flow through a network," Can. J. Math., vol. 8, pp. 399-404, 1956.
30. J.-C. Picard and M. Queyranne, "On the structure of all minimum cuts in a network and applications," Combinatorial Optimization II, ser. Mathematical Programming Studies, vol. 13, pp. 8-16, 1980.
31. L. Schrage and K. R. Baker, "Dynamic programming solution of sequencing problems with precedence constraints," Oper. Res., vol. 26, no. 3, pp. 444-449, 1978. (Pubitemid 8611378)
32. E. L. Lawler, Efficient Implementation of Dynamic Programming Algorithms for Sequencing Problems: (Preprint), CWI Technical Report Stichting Mathematisch Centrum. Mathematische Besliskunde-BW 106/79, 1979. [Online]. Available: http://oai.cwi.nl/oai/asset/9663/9663A.pdf.
33. W. H. Cunningham, "On submodular function minimization," Combinatorica, vol. 5, pp. 185-192, 1985.
34. S. T. Mccormick, Submodular Function Minimization Based on Chapter 7 of the Handbook on Discrete Optimization [54] Version 3, 2007.
35. R. G. Bland, D. Goldfarb, and M. J. Todd, "The ellipsoid method: A survey," Oper. Res., vol. 29, no. 6, pp. 1039-1091, Nov./Dec. 1981.
36. S. Iwata and J. B. Orlin, "A simple combinatorial algorithm for submodular function minimization," in Proc. 20th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA'09), 2009, pp. 1230-1237.
37. S. Mallat and Z. Zhang, "Matching pursuit with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
38. H. Sandberg, A. Teixeira, and K. H. Johansson, "On security indices for state estimators in power networks," in Proc. 1st Workshop Secure Control Systems (CPSWEEK 2010), 2010.
39. R. Tibshirani, "Regression shrinkage and selection via the LASSO," J. Royal. Statist. Soc. B, vol. 58, no. 1, pp. 267-288, 1996.
40. Cplex. [Online]. Available: http://www-01.ibm.com/software/integration/ optimization/cplexoptimizer/.
41. Gurobi. [Online]. Available: http://www.gurobi.com/.
42. D. Gleich, Contents Matlab BGL v4.0, 2006. [Online]. Available: http://www.stanford.edu/dgleich/programs/matlab-bgl/.
43. The Boost Graph Library: User Guide and Reference Manual. Boston, MA: Addison-Wesley Longman, 2002.
44. W. Yin, Gurobi Mex: A MATLAB Interface for Gurobi. [Online]. Available: http://convexoptimization.com/wikimization/index.php/gurobi mex.
45. R. Zimmerman, C. Murillo-Sánchez, and R. Thomas, "MATPOWER steady-state operations, planning and analysis tools for power systems research and education," IEEE Trans. Power Syst., vol. 26, no. 1, pp. 12-19, Feb. 2011.