Economic Analysis of the N-k Power Grid Contingency Selection and Evaluation

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 32)

Abstract

Contingency analysis is important for providing information about the vulnerability of power grids. Many methods have been purposed to use topological structures of power grids for analyzing contingency states. Considering failures of buses and lines, we present and compare several graph methods for selecting contingencies in this chapter. A new method, called critical node detection, is introduced for selecting contingencies consisting of failures on buses. Besides these methods, we include an interdiction model which provides the worst case contingency selection. Our measurement for contingency evaluation is to maximize the social benefit, or to minimize the generating and load shedding cost. Comparing with other measurements for contingency selection, our model is based on economic analysis and is reasonable for evaluating the selected contingency state. Additionally, a contingency consisting of both buses and lines is also studied.

Keywords

Contingency and economic analysis Buses and lines vulnerability of power grids Critical node detection Social benet Load shedding cost 

References

  1. 1.
    Abhinav Verm, D.B.: Power grid security analysis: An optimization approach (2009). Ph.D DissertationGoogle Scholar
  2. 2.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002). DOI 10.1103/RevModPhys.74.47. URL http://link.aps.org/doi/10.1103/RevModPhys.74.47 Google Scholar
  3. 3.
    Alguacil, N., Conejo, A.: Multiperiod optimal power flow using benders decomposition. IEEE T. Power Syst. 15(1), 196–201 (2000). DOI 10.1109/59.852121CrossRefGoogle Scholar
  4. 4.
    Alsac, O., Bright, J., Prais, M., Stott, B.: Further developments in lp-based optimal power flow. IEEE T. Power Syst. 5(3), 697–711 (1990). DOI 10.1109/59.65896CrossRefGoogle Scholar
  5. 5.
    Amin, M.: North america’s electricity infrastructure: Are we ready for more perfect storms? Security Privacy, IEEE 1(5), 19–25 (2003). DOI 10.1109/MSECP.2003.1236231Google Scholar
  6. 6.
    Andersson, G., Donalek, P., Farmer, R., Hatziargyriou, N., Kamwa, I., Kundur, P., Martins, N., Paserba, J., Pourbeik, P., Sanchez-Gasca, J., Schulz, R., Stankovic, A., Taylor, C., Vittal, V.: Causes of the 2003 major grid blackouts in north america and europe, and recommended means to improve system dynamic performance. IEEE T. Power Syst. 20(4), 1922–1928 (2005). DOI 10.1109/TPWRS.2005.857942CrossRefGoogle Scholar
  7. 7.
    Anghel, M., Werley, K.A., Motter, A.E.: Stochastic model for power grid dynamics. In: System Sciences, 2007. HICSS 2007. 40th Annual Hawaii International Conference on, pp. 113 (2007). DOI 10.1109/HICSS.2007.500Google Scholar
  8. 8.
    Aoki, K., Fan, M., Nishikori, A.: Optimal var planning by approximation method for recursive mixed-integer linear programming. IEEE T. Power Syst. 3(4), 1741–1747 (1988). DOI 10.1109/59.192990CrossRefGoogle Scholar
  9. 9.
    Arroyo, J., Galiana, F.: On the solution of the bilevel programming formulation of the terrorist threat problem. IEEE T. Power Syst. 20(2), 789–797 (2005). DOI 10.1109/TPWRS.2005.846198CrossRefGoogle Scholar
  10. 10.
    Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009). DOI 10.1016/j.cor.2008.08.016. URL http://www.sciencedirect.com/science/article/pii/S0305054808001494 Google Scholar
  11. 11.
    Athay, T.: Generation scheduling and control. P. IEEE 75(12), 1592–1606 (1987). DOI 10.1109/PROC.1987.13929CrossRefGoogle Scholar
  12. 12.
    Bae, K., Thorp, J.S.: A stochastic study of hidden failures in power system protection. Decis. Support Syst. 24(3–4), 259–268 (1999). DOI 10.1016/S0167-9236(98)00069-4. URL http://www.sciencedirect.com/science/article/pii/S0167923698000694
  13. 13.
    Bienstock, D., Mattia, S.: Using mixed-integer programming to solve power grid blackout problems. Discrete Optim.4(1), 115–141 (2007). DOI 10.1016/j.disopt.2006.10.007. URL http://www.sciencedirect.com/science/article/pii/S1572528606000867 Google Scholar
  14. 14.
    Bienstock, D., Verm, A.: The n − k problem in power grids: New models, formulations and numerical experiments. SIAM J. Optim. 20(5), 2352–2380 (2010)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    van den Bosch, P., Honderd, G.: A solution of the unit commitment problem via decomposition and dynamic programming. IEEE T. Power Ap. Syst. PAS-104(7), 1684–1690 (1985). DOI 10.1109/TPAS.1985.319199CrossRefGoogle Scholar
  16. 16.
    Carpentie, J.: Contribution a l’etude du dispatching economique. Bulletin de la Societe Francoise des Electriciens (1962). http://130.203.133.150/showciting;jsessionid=D109D27681C74B7BB9008E5E112DAABA?cid=5923854
  17. 17.
    Carreras, B., Newman, D., Dobson, I., Poole, A.: Evidence for self-organized criticality in a time series of electric power system blackouts. Circuits and Systems I: IEEE Transactions on Regular Papers, 51(9), 1733–1740 (2004). DOI 10.1109/TCSI.2004.834513CrossRefGoogle Scholar
  18. 18.
    Carreras, B.A., Lynch, V.E., Dobson, I., Newman, D.E.: Critical points and transitions in an electric power transmission model for cascading failure blackouts. Chaos 12(4), 985–994 (2002). DOI DOI:10.1063/1.150581MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Carreras, B.A., Lynch, V.E., Dobson, I., Newman, D.E.: Complex dynamics of blackouts in power transmission systems. Chaos 14(3), 643–652 (2004). DOI DOI:10.1063/1.1781391. URL http://dx.doi.org/doi/10.1063/1.1781391 Google Scholar
  20. 20.
    Chebbo, A., Irving, M.: Combined active and reactive dispatch. i. problem formulation and solution algorithm. IEE P.-Gener. Transm. D. 142(4), 393–400 (1995). DOI 10.1049/ip-gtd:19951976Google Scholar
  21. 21.
    Chebbo, A., Irving, M., Dandachi, N.: Combined active reactive dispatch. part 2: Test results. IEE P.-Gener. Transm. D. 142(4), 401–405 (1995). DOI 10.1049/ip-gtd:19951977Google Scholar
  22. 22.
    Chen, J., Thorp, J.S., Dobson, I.: Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model. Int. J. Elec. Power 27(4), 318–326 (2005). DOI 10.1016/j.ijepes.2004.12.003. URL http://www.sciencedirect.com/science/article/pii/S0142061505000232
  23. 23.
    Chen, Q., McCalley, J.: Identifying high risk n-k contingencies for online security assessment. IEEE T. Power Syst. 20(2), 823–834 (2005). DOI 10.1109/TPWRS.2005.846065CrossRefGoogle Scholar
  24. 24.
    Chowdhury, B., Baravc, S.: Creating cascading failure scenarios in interconnected power systems. In: Power Engineering Society General Meeting, 2006. IEEE, pp. 8 (2006). DOI 10.1109/PES.2006.1709061Google Scholar
  25. 25.
    Chung, T., Shaoyun, G.: A recursive lp-based approach for optimal capacitor allocation with cost-benefit consideration. Electr. Pow. Syst. Res. 39(2), 129–136 (1996). DOI 10.1016/S0378-7796(96)01103-0 URL http://www.sciencedirect.com/science/article/pii/S0378779696011030.
  26. 26.
    Cohen, A., Yoshimura, M.: A branch-and-bound algorithm for unit commitment. IEEE T. Power Ap. Syst. PAS-102(2), 444–451 (1983). DOI 10.1109/TPAS.1983.317714CrossRefGoogle Scholar
  27. 27.
    Debs, A.S.: Modern Power System Control and Operation. Springer, Berlin (1988)CrossRefGoogle Scholar
  28. 28.
    Deeb, N., Shahidehpour, S.: Linear reactive power optimization in a large power network using the decomposition approach. IEEE T. Power Syst. 5(2), 428–438 (1990). DOI 10.1109/59.54549CrossRefGoogle Scholar
  29. 29.
    Dillon, T.S., Edwin, K.W., Kochs, H.D., Taud, R.J.: Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination. IEEE T. Power Ap. Syst. PAS-97(6), 2154–2166 (1978). DOI 10.1109/TPAS.1978.354719CrossRefGoogle Scholar
  30. 30.
    Dobson, I., Wierzbicki, K., Carreras, B., Lynch, V., Newman, D.: An estimator of propagation of cascading failure. In: System Sciences, 2006. HICSS ’06. Proceedings of the 39th Annual Hawaii International Conference on, vol. 10, pp. 245c (2006). DOI 10.1109/HICSS.2006.54Google Scholar
  31. 31.
    Dola, H., Chowdhury, B.: Intentional islanding and adaptive load shedding to avoid cascading outages. In: Power Engineering Society General Meeting, 2006. IEEE, pp. 8 (2006). DOI 10.1109/PES.2006.1709349Google Scholar
  32. 32.
    Donde, V., Lopez, V., Lesieutre, B., Pinar, A., Yang, C., Meza, J.: Identification of severe multiple contingencies in electric power networks. In: Power Symposium, 2005. Proceedings of the 37th Annual North American, pp. 59–66 (2005). DOI 10.1109/NAPS.2005.1560502Google Scholar
  33. 33.
    Dopazo, J., Merrill, H.: Optimal generator maintenance scheduling using integer programming. IEEE T. Power Ap. Syst 94(5), 1537–1545 (1975). DOI 10.1109/T-PAS.1975.31996CrossRefGoogle Scholar
  34. 34.
    Nedic, D.P., Kirchen, D.S.: Discovering mechanisms of large disturbance development. In: Bulk Power System Dynamics and Control - VI, pp. 751–757 (2004)Google Scholar
  35. 35.
    Enacheanu, B., Fontela, M., Andrieu, C., Pham, H., Martin, A., Gie-Idea, Y.B.: New control strategies to prevent blackouts: Intentional islanding operation in distribution networks. In: Electricity Distribution, 2005. CIRED 2005. 18th International Conference and Exhibition on, pp. 1–5 (2005)Google Scholar
  36. 36.
    Fan, N., Xu, H., Pan, F., Pardalos, P.M.: Economic analysis of the n − k power grid contingency selection and evaluation by graph algorithms and interdiction methods. Energy Sys. 2(3), 313–324 (2011). DOI 10.1007/s12667-011-0038-5CrossRefGoogle Scholar
  37. 37.
    Farag, A., Al-Baiyat, S., Cheng, T.: Economic load dispatch multiobjective optimization procedures using linear programming techniques. IEEE T. Power Syst. 10(2), 731–738 (1995). DOI 10.1109/59.387910CrossRefGoogle Scholar
  38. 38.
    G\ddot{o}nen, T., Foote, B.: Distribution-system planning using mixed-integer programming. IEE Proc. C 128(2), 70–79 (1981). DOI 10.1049/ip-c:19810010Google Scholar
  39. 39.
    Gou, B., Zheng, H., Wu, W., Yu, X.: Probability distribution of power system blackouts. In: Power Engineering Society General Meeting, 2007. IEEE, pp. 1–8 (2007). DOI 10.1109/PES.2007.385471Google Scholar
  40. 40.
    Granelli, G., Montagna, M.: Security-constrained economic dispatch using dual quadratic programming. Electr. Pow. Syst. Res. 56(1), 71–80 (2000). DOI 10.1016/S0378-7796(00)00097-3. URL http://www.sciencedirect.com/science/article/pii/S0378779600000973
  41. 41.
    Granville, S.: Optimal reactive dispatch through interior point methods. IEEE T. Power Syst. 9(1), 136–146 (1994). DOI 10.1109/59.317548CrossRefGoogle Scholar
  42. 42.
    Gross, C.A.: Optimal Economic Operation of Electric Power Systems. Wiely, New York (1986)Google Scholar
  43. 43.
    Grudinin, N.: Reactive power optimization using successive quadratic programming method. IEEE T. Power Syst. 13(4), 1219–1225 (1998). DOI 10.1109/59.736232CrossRefGoogle Scholar
  44. 44.
    Guy, J.: Security constrained unit commitment. IEEE T. Power Ap. Syst. PAS-90(3), 1385–1390 (1971). DOI 10.1109/TPAS.1971.292942MathSciNetCrossRefGoogle Scholar
  45. 45.
    Hardiman, R., Kumbale, M., Makarov, Y.: An advanced tool for analyzing multiple cascading failures. In: Probabilistic Methods Applied to Power Systems, 2004 International Conference on, pp. 629–634 (2004). DOI 10.1109/PMAPS.2004.242665Google Scholar
  46. 46.
    Hedman, K., Ferris, M., O’Neill, R., Fisher, E., Oren, S.: Co-optimization of generation unit commitment and transmission switching with n-1 reliability. IEEE T. Power Syst.25(2), 1052–1063 (2010). DOI 10.1109/TPWRS.2009.2037232CrossRefGoogle Scholar
  47. 47.
    Hedman, K., O’Neill, R., Fisher, E., Oren, S.: Optimal transmission switching with contingency analysis. IEEE T. Power Syst. 24(3), 1577–1586 (2009). DOI 10.1109/TPWRS.2009.2020530CrossRefGoogle Scholar
  48. 48.
    Hines, P., Cotilla-Sanchez, E., Blumsack, S.: Do topological models provide good information about electricity infrastructure vulnerability? CHAOS 20(3), 033, 122 (2010) DOI DOI:10.1063/1.3489887. URL http://dx.doi.org/doi/10.1063/1.3489887
  49. 49.
    Hobbs, W., Hermon, G., Warner, S., Shelbe, G.: An enhanced dynamic programming approach for unit commitment. IEEE T. Power Syst. 3(3), 1201–1205 (1988). DOI 10.1109/59.14582CrossRefGoogle Scholar
  50. 50.
    Holmgren, A.J., Molin, S.: Using disturbance data to assess vulnerability of electric power delivery systems. J. Infrastruct. Syst. 12(4), 243–251 (2006). DOI DOI:10.1061/(ASCE)1076-0342(2006)12:4(243). URL http://dx.doi.org/doi/10.1061/(ASCE)1076-0342(2006)12:4(243) Google Scholar
  51. 51.
    Hsu, Y.Y., Su, C.C., Liang, C.C., Lin, C.J., Huang, C.T.: Dynamic security constrained multi-area unit commitment. IEEE T. Power Syst. 6(3), 1049–1055 (1991). DOI 10.1109/59.119245CrossRefGoogle Scholar
  52. 52.
    Huaiwei Liao Jay Apt, S.T.: Phase transitions in the probability of cascading failures (2004). Supported by ABB, NSF and CEICGoogle Scholar
  53. 53.
    Irving, M., Song, Y.H.: Optimisation techniques for electrical power systems. part 1: Mathematical optimisation methods. Power Eng. J. 14(5), 245–254 (2000). DOI 10.1049/pe:20000509. URL http://link.aip.org/link/abstract/PEJOEE/v14/i5/p245/s1
  54. 54.
    Bakke, J.Ø.H., Hansen, A., Kertész, J.: Failures and avalanches in complex network. Europhys. Lett. 76(4), 717–723 (2006). URL http://iopscience.iop.org/0295-5075/76/4/717 Google Scholar
  55. 55.
    Wierzbicki, K.R., Dobson, I. : An approach to statistical estimation of cascading failure propagation in blackouts. In: CRIS, Third International Conference on Critical Infrastructures, 2006., pp. 1–7 (2006)Google Scholar
  56. 56.
    Mili, L.M., Phadke, A.G., Qiu, Q.: Risk assessment of catastrophic failures in electric power systems. Int. J. Crit. Infrastructures 1(1), 38–63 (2004)CrossRefGoogle Scholar
  57. 57.
    Lee, F.: Short-term thermal unit commitment-a new method. IEEE T. Power Syst. 3(2), 421–428 (1988). DOI 10.1109/59.192892CrossRefGoogle Scholar
  58. 58.
    Lin, W.M., Chen, S.J., Su, Y.S.: An application of interior-point based opf for system expansion with facts devices in a deregulated environment. In: Power System Technology, 2000. Proceedings. PowerCon 2000. International Conference on, vol. 3, pp. 1407–1412 (2000). DOI 10.1109/ICPST.2000.898175Google Scholar
  59. 59.
    Liu, Y., Liu, Y.: Aspects on power system islanding for preventing widespread blackout. In: Networking, Sensing and Control, 2006. ICNSC ’06. Proceedings of the 2006 IEEE International Conference on, pp. 1090–1095 (2006). DOI 10.1109/ICNSC.2006.1673304Google Scholar
  60. 60.
    Lobato, E., Rouco, L., Navarrete, M., Casanova, R., Lopez, G.: An lp-based optimal power flow for transmission losses and generator reactive margins minimization. In: Power Tech Proceedings, 2001 IEEE Porto, vol 3., p. 5 (2001). DOI 10.1109/PTC.2001.964894Google Scholar
  61. 61.
    Lowery, P.: Generating unit commitment by dynamic programming. IEEE T. Power Ap. Syst. PAS-85(5), 422–426 (1966). DOI 10.1109/TPAS.1966.291679CrossRefGoogle Scholar
  62. 62.
    El-Hawary, M.E., Christensen G.S.: Power System Analysis. Academic Press, New York (1979)Google Scholar
  63. 63.
    Ma, H.T., Chowdhury, B.: Dynamic simulations of cascading failures. In: Power Symposium, 2006. NAPS 2006. 38th North American, pp. 619–623 (2006). DOI 10.1109/NAPS.2006.359636Google Scholar
  64. 64.
    Megahed, I., Abou-Taleb, N., Iskandrani, E., Moussa, A.: A modified method for solving the economic dispatching problem. IEEE T. Power Ap. Syst. 96(1), 124–133 (1977). DOI 10.1109/T-PAS.1977.32315CrossRefGoogle Scholar
  65. 65.
    wei Mei, S., Yadana, feng Weng, X., cheng Xue, A.: Blackout model based on opf and its self-organized criticality. In: Control Conference, 2006. CCC 2006. Chinese, pp. 1673–1678 (2006). DOI 10.1109/CHICC.2006.280819Google Scholar
  66. 66.
    Milano, F., Ca\ddot{n}izares, C.A., Invernizzi, M.: Voltage stability constrained opf market models considering contingency criteria. Electr. Pow. Syst. Res.74(1), 27–36 (2005). DOI 10.1016/j.epsr.2004.07.012. URL http://www.sciencedirect.com/science/article/pii/S0378779604002081 Google Scholar
  67. 67.
    Momoh, J.: A generalized quadratic-based model for optimal power flow. In: Systems, Man and Cybernetics, 1989. Conference Proceedings., IEEE International Conference on, pp. 261–271, vol. 1 (1989). DOI 10.1109/ICSMC.1989.71294Google Scholar
  68. 68.
    Momoh, J., Adapa, R., El-Hawary, M.: A review of selected optimal power flow literature to 1993. i. nonlinear and quadratic programming approaches. IEEE T. Power Syst. 14(1), 96–104 (1999). DOI 10.1109/59.744492Google Scholar
  69. 69.
    Momoh, J., Guo, S., Ogbuobiri, E., Adapa, R.: The quadratic interior point method solving power system optimization problems. IEEE T. Power Syst. 9(3), 1327–1336 (1994). DOI 10.1109/59.336133CrossRefGoogle Scholar
  70. 70.
    Montagna, M., Granelli, G.: Detection of jacobian singularity and network islanding in power flow computations. IEE P-Gener. Transm. D. 142(6), 589–594 (1995). DOI 10.1049/ip-gtd:19952232Google Scholar
  71. 71.
    Hatziargyriou, N., Strbac, G.: A possible future energy configuration? (2004) PresentationGoogle Scholar
  72. 72.
    Nanda, J., Kothari, D., Srivastava, S.: New optimal power-dispatch algorithm using fletcher’s quadratic programming method. IEE Proc. C 136(3), 153–161 (1989)Google Scholar
  73. 73.
    Nedic, D.P., Dobson, I., Kirschen, D.S., Carreras, B.A., Lynch, V.E.: Criticality in a cascading failure blackout model. Int. J. Elec. Power 28(9), 627–633 (2006). DOI 10.1016/j.ijepes.2006.03.006. URL http://www.sciencedirect.com/science/article/pii/S0142061506000810 Google Scholar
  74. 74.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003). URL http://www.jstor.org/stable/25054401 Google Scholar
  75. 75.
    Opoku, G.: Optimal power system var planning. IEEE T. Power Syst. 5(1), 53 –60 (1990). DOI 10.1109/59.49086CrossRefGoogle Scholar
  76. 76.
    Ouyang, Z., Shahidehpour, S.: An intelligent dynamic programming for unit commitment application. IEEE T. Power Syst. 6(3), 1203–1209 (1991). DOI 10.1109/59.119267CrossRefGoogle Scholar
  77. 77.
    Pang, C., Sheble, G., Albuyeh, F.: Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments. IEEE T. Power Ap. Syst. PAS-100(3), 1212–1218 (1981). DOI 10.1109/TPAS.1981.316592CrossRefGoogle Scholar
  78. 78.
    Parten, J.: A simplified modified dynamic programming algorithm for sizing location and feeder reinforcements. IEEE Trans on Power Delivery. 5(1), 227–283 (1990)Google Scholar
  79. 79.
    Peiravi, A., Ildarabadi, R.: A fast algorithm for intentional islanding of power systems using the multilevel kernel k-means approach. J. Appl. Sci. 12(9), 2247–2255 (2009)Google Scholar
  80. 80.
    Pinar, A., Meza, J., Donde, V., Lesieutre, B.: Optimization strategies for the vulnerability analysis of the electric power grid. J. Optim. 20(4), 1786–1810 (2010). DOI DOI:10.1137/070708275. URL http://dx.doi.org/doi/10.1137/070708275
  81. 81.
    Pudjianto, D., Ahmed, S., Strbac, G.: Allocation of var support using lp and nlp based optimal power flows. IEE P.-Gener. Transm. D. 149(4), 377–383 (2002). DOI 10.1049/ip-gtd:20020200Google Scholar
  82. 82.
    Adams, N.R., Laughton, M.A.: Optimal planning of power networks using mixed integer programming. IEE Proc. 121(2), 139–147 (1974)CrossRefGoogle Scholar
  83. 83.
    R\acute{e}ka Albert, H.J., Barab\acute{a}si, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000). DOI 10.1038/35019019Google Scholar
  84. 84.
    Ranade, S., Kolluru, R., Mitra, J.: Identification of chains of events leading to catastrophic failures of power systems. In: Circuits and Systems, 2005. ISCAS 2005. IEEE International Symposium on, pp. 4187–4190, vol. 5 (2005). DOI 10.1109/ISCAS.2005.1465554Google Scholar
  85. 85.
    Rios, M., Kirschen, D., Jayaweera, D., Nedic, D., Allan, R.: Value of security: modeling time-dependent phenomena and weather conditions. IEEE T. Power Syst. 17(3), 543–548 (2002). DOI 10.1109/TPWRS.2002.800872CrossRefGoogle Scholar
  86. 86.
    Salmeron, J., Wood, K., Baldick, R.: Analysis of electric grid security under terrorist threat. IEEE T. Power Syst. 19(2), 905–912 (2004). DOI 10.1109/TPWRS.2004.825888CrossRefGoogle Scholar
  87. 87.
    Shahnawaz Ahmed, S., Sarker, N.C., Khairuddin, A.B., Ghani, M.R.B.A., Ahmad, H.: A scheme for controlled islanding to prevent subsequent blackout. Power Eng. Rev. IEEE 22(11), 55 (2002). DOI 10.1109/MPER.2002.4311812CrossRefGoogle Scholar
  88. 88.
    Simonoff, J.S., Restrepo, C.E., Zimmerman, R.: Risk-management and risk-analysis-based decision tools for attacks on electric power. Risk Anal. 27(3), 547–570 (2007). DOI 10.1111/j.1539-6924.2007.00905.x. URL http://dx.doi.org/10.1111/j.1539-6924.2007.00905.x
  89. 89.
    Snyder, W.L., Powell, H.D., Rayburn, J.C.: Dynamic programming approach to unit commitment. IEEE T. Power Syst. 2(2), 339–348 (1987). DOI 10.1109/TPWRS.1987.4335130CrossRefGoogle Scholar
  90. 90.
    Stott, B., Marinho, J.: Linear programming for power-system network security applications. IEEE T. Power Ap. Syst. PAS-98(3), 837–848 (1979). DOI 10.1109/TPAS.1979.319296CrossRefGoogle Scholar
  91. 91.
    Sun, D., Ashley, B., Brewer, B., Hughes, A., Tinney, W.: Optimal power flow by newton approach. IEEE T. Power Ap. Syst. PAS-103(10), 2864–2880 (1984). DOI 10.1109/TPAS.1984.318284CrossRefGoogle Scholar
  92. 92.
    Thorp, J., Phadke, A., Horowitz, S., Tamronglak, S.: Anatomy of power system disturbances: Importance sampling. Int. J. Elec. Power 20(2), 147–152 (1998). DOI 10.1016/S0142-0615(97)00034-3. URL http://www.sciencedirect.com/science/article/pii/S0142061597000343 Google Scholar
  93. 93.
    Tinney, W., Hart, C.: Power flow solution by newton’s method. IEEE T. Power Ap. Syst. PAS-86(11), 1449–1460 (1967). DOI 10.1109/TPAS.1967.291823CrossRefGoogle Scholar
  94. 94.
    Vaithianathan (Mani) Venkatasubramanian, Y.L.: Analysis of 1996 western american electric blackouts. In: Bulk Power System Dynamics and Control - VI, pp. 685–721 (2004)Google Scholar
  95. 95.
    Van Meeteren, H.: Scheduling of generation and allocation of fuel, using dynamic and linear programming. IEEE T. Power Ap. Syst. PAS-103(7), 1562–1568 (1984). DOI 10.1109/TPAS.1984.318626CrossRefGoogle Scholar
  96. 96.
    Wang, J.W., Rong, L.L.: Cascade-based attack vulnerability on the us power grid. Safety Sci. 47(10), 1332–1336 (2009). DOI 10.1016/j.ssci.2009.02.002. URL http://www.sciencedirect.com/science/article/pii/S0925753509000174 Google Scholar
  97. 97.
    Wang, W.X., Chen, G.: Universal robustness characteristic of weighted networks against cascading failure. Phys. Rev. E 77, 026,101 (2008). DOI 10.1103/PhysRevE.77.026101. URL http://link.aps.org/doi/10.1103/PhysRevE.77.026101 Google Scholar
  98. 98.
    Watts Duncan, J., Strogatz, S.H.: Collective dynamics of /‘small-world/’ networks. Nature 393, 440–442 (1998). DOI 10.1038/30918CrossRefGoogle Scholar
  99. 99.
    Weng, X., Hong, Y., Xue, A., Mei, S.: Failure analysis on china power grid based on power law. J. Contr. Theor. Appl. 4, 235–238 (2006). URL http://dx.doi.org/10.1007/s11768-006-5082-7. 10.1007/s11768-006-5082-7Google Scholar
  100. 100.
    Weron, R., Simonsen, I.: Blackouts, risk, and fat-tailed distributions. In: Takayasu, H. (ed.) Practical Fruits of Econophysics, pp. 215–219. Springer, Tokyo (2006). URL http://dx.doi.org/10.1007/4-431-28915-1. 10.1007/4-431-28915-1
  101. 101.
    Wortze, L.M.: Chinas approach to cyber operations: Implications for the united states (2010). URL http://www.internationalrelations.house.gov/111/wor031010.pdf. Testimony before the Committee on Foreign Affairs House of Representatives
  102. 102.
    Yan, W., Yu, J., Yu, D., Bhattarai, K.: A new optimal reactive power flow model in rectangular form and its solution by predictor corrector primal dual interior point method. IEEE T. Power Syst. 21(1), 61–67 (2006). DOI 10.1109/TPWRS.2005.861978CrossRefGoogle Scholar
  103. 103.
    You, H., Vittal, V., Yang, Z.: Self-healing in power systems: An approach using islanding and rate of frequency decline-based load shedding. IEEE T. Power Syst. 18(1), 174–181 (2003). DOI 10.1109/TPWRS.2002.807111CrossRefGoogle Scholar
  104. 104.
    Zhao, Q., Sun, K., Zheng, D.Z., Ma, J., Lu, Q.: A study of system splitting strategies for island operation of power system: A two-phase method based on obdds. IEEE T. Power Syst. 18(4), 1556–1565 (2003). DOI 10.1109/TPWRS.2003.818747CrossRefGoogle Scholar
  105. 105.
    Zhu, J., Momoh, J.A.: Multi-area power systems economic dispatch using nonlinear convex network flow programming. Elect. Pow. Syst Res. 59(1), 13–20 (2001). DOI 10.1016/S0378-7796(01)00131-6. URL http://www.sciencedirect.com/science/article/pii/S0378779601001316

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Industrial and Systems EngineeringUniversity of FloridaFLUSA

Personalised recommendations