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Optimal power flow: a bibliographic survey I

Formulations and deterministic methods

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Abstract

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

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Notes

  1. DC power flow is so named because the resulting equations resemble the behavior of direct current systems. However, it still represents the operation of an AC electrical network.

Abbreviations

AC:

Alternating Current

ASP:

Active Set and Penalty

BFGS:

Broyden-Fletcher-Goldfarb-Shanno (quasi-Newton method)

CG:

Conjugate Gradient

DC:

Direct Current

DFP:

Davidon-Fletcher-Powell (quasi-Newton method)

ECQ:

Extended Conic-Quadratic

HVDC:

High-Voltage Direct Current

FACTS:

Flexible AC Transmission Systems

GRG:

Generalized Reduced Gradient

IPM:

Interior Point Method

KKT:

Karush-Kuhn-Tucker (conditions for optimality)

LP:

Linear Programming

MBAL:

Modified Barrier-Augmented Lagrangian

MCC:

Multiple Centrality Corrections

MILP:

Mixed Integer Linear Programming

MINLP:

Mixed Integer-Nonlinear Programming

MW:

Megawatt

NC:

Nonlinear Complementarity

NLP:

Nonlinear Programming

OPF:

Optimal Power Flow

ORPF:

Optimal Reactive Power Flow

PC:

Predictor-Corrector

PD:

Primal-Dual

PDIPM:

Primal-Dual Interior Point Method

PDLB:

Primal-Dual Logarithmic Barrier

QP:

Quadratic Programming

RG:

Reduced Gradient

SCED:

Security-Constrained Economic Dispatch

SCIPM:

Step-Controlled Interior Point Method

SCUC:

Security-Constrained Unit Commitment

SDP:

Semi-Definite Programming

SLP:

Sequential Linear Programming

SQP:

Sequential Quadratic Programming

TRIPM:

Trust Region Interior Point Method

UPFC:

Unified Power Flow Controller

VAR:

Volt-Ampere Reactive

References

  1. Abadie, J., Carpentier, J.: Generalization of the wolfe reduced gradient method to the case of nonlinear constraints. In: Fletcher, R. (ed.) Optimization, Proceedings of a Symposium Held at University of Keele, 1968, pp. 37–47. Academic Press, London (1969)

    Google Scholar 

  2. Acha, E., Fuerte-Esquivel, C., Ambriz-Pérez, H., Angeles-Camacho, C.: FACTS: Modeling and Simulation in Power Networks. Wiley, New York (2004)

    Book  Google Scholar 

  3. Adibi, M., Polyak, R., Griva, I., Mili, L., Ammari, S.: Optimal transformer tap selection using modified barrier-augmented Lagrangian method. IEEE Trans. Power Syst. 18, 251–257 (2003)

    Article  Google Scholar 

  4. Alguacil, N., Conejo, A.: Multiperiod optimal power flow using benders decomposition. IEEE Trans. Power Syst. 15(1), 196–201 (2000)

    Article  Google Scholar 

  5. Almeida, K., Galiana, F.: Critical cases in the optimal power flow. IEEE Trans. Power Syst. 11(3), 1509–1518 (1996)

    Article  Google Scholar 

  6. Alsac, O., Stott, B.: Optimal load flow with steady-state security. IEEE Trans. Power Appar. Syst. PAS-93(3), 745–751 (1974)

    Article  Google Scholar 

  7. Alsac, O., Bright, J., Praise, M., Stott, B.: Further developments in LP-based optimal power flow. IEEE Trans. Power Syst. 5(3), 697–711 (1990)

    Article  Google Scholar 

  8. Avalos, R., Canizares, C., Anjos, M.: A practical voltage-stability-constrained optimal power flow. In: IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–6 (2008)

    Chapter  Google Scholar 

  9. Azevedo, A., Oliveira, A., Rider, M., Soares, S.: How to efficiently incorporate facts devices in optimal active power flow model. J. Ind. Manag. Optim. 6(2), 315–331 (2010)

    Article  MATH  Google Scholar 

  10. Azmy, A.: Optimal power flow to manage voltage profiles in interconnected networks using expert systems. IEEE Trans. Power Syst. 22(4), 1622–1628 (2007)

    Article  Google Scholar 

  11. Bai, X., Wei, H.: Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints. IET Gener. Transm. Distrib. 3(2), 182–197 (2009)

    Article  Google Scholar 

  12. Bakirtzis, A., Biskas, P.: A decentralized solution to the dc-opf of interconnected power systems. IEEE Trans. Power Syst. 18(3), 1007–1013 (2003)

    Article  Google Scholar 

  13. Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming: Theory and Algorithms. Wiley New York (2006)

    Book  MATH  Google Scholar 

  14. Bell, B.: Nonsmooth Optimization by Successive Quadratic Programming. University of Washington (1984)

  15. Berizzi, A., Delfanti, M., Marannino, P., Pasquadibisceglie, M., Silvestri, A.: Enhanced security-constrained OPF with FACTS devices. IEEE Trans. Power Syst. 20(3), 1597–1605 (2005)

    Article  Google Scholar 

  16. Biskas, P., Ziogos, N., Tellidou, A., Zoumas, C., Bakirtzis, A., Petridis, V., Tsakoumis, A.: Comparison of two metaheuristics with mathematical programming methods for the solution of OPF. In: Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems (2005)

    Google Scholar 

  17. Bollt, S.: Nonlinear Programming by Successive Linear Programming Approximations. Massachusetts Institute of Technology, Dept. of Economics (1964)

  18. Burchett, R., Happ, H., Vierath, D., Wirgau, K.: Developments in optimal power flow. IEEE Trans. Power Appar. Syst. PAS-101(2), 406–414 (1982). doi:10.1109/TPAS.1982.317121

    Article  Google Scholar 

  19. Burchett, R., Happ, H., Wirgau, K.: Large scale optimal power flow. IEEE Trans. Power Appar. Syst. 101(10), 3722–3732 (1982)

    Article  Google Scholar 

  20. Burchett, R., Happ, H., Veirath, D.: Quadratically convergent optimal power flow. IEEE Trans. Power Appar. Syst. 103(11), 3267–3275 (1984)

    Article  Google Scholar 

  21. Capitanescu, F., Wehenkel, L.: Sensitivity-based approaches for handling discrete variables in optimal power flow computations. IEEE Trans. Power Syst. 25(4), 1780–1789 (2010). doi:10.1109/TPWRS.2010.2044426

    Article  Google Scholar 

  22. Capitanescu, F., Glavic, M., Wehenkel, L.: Experience with the multiple centrality corrections interior-point algorithm for optimal power flow. In: CEE Conference, Coimbra, Portugal (2005)

    Google Scholar 

  23. Capitanescu, F., Glavic, M., Ernst, D., Wehenkel, L.: Interior-point based algorithms for the solution of optimal power flow problems. Electr. Power Syst. Res. 77(5–6), 508–517 (2007)

    Article  Google Scholar 

  24. Capitanescu, F., Rosehart, W., Wehenkel, L.: Optimal power flow computations with constraints limiting the number of control actions. In: IEEE Bucharest Power Tech Conference, Bucharest, Romania, pp. 1–8 (2009)

    Chapter  Google Scholar 

  25. Carpenter, T.J., Lusting, I.J., Mulvey, J.M., Shanno, D.F.: Higher-order predictor-corrector interior point methods with application to quadratic objectives. SIAM J. Optim. 3(4), 696–725 (1993). doi:10.1137/0803036

    Article  MathSciNet  MATH  Google Scholar 

  26. Carpentier: Contribution to the economic dispatch problem. Bull. Soc. Fr. Electr. 8(3), 431–447 (1962)

    Google Scholar 

  27. Carpentier, J.: Optimal power flows. Electr. Power Energy Syst. 1(1), 3–15 (1979). doi:10.1016/0142-0615(79)90026-7

    Article  Google Scholar 

  28. de Carvalho, E., dos Santos, A., Mac, T.: Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem. Appl. Math. Comput. 200, 529–536 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Castronuovo, E., Campagnolo, J., Salgado, R.: In: Proceedings of the IEEE/PES T&D 2002 Latin America, São Paulo, Brazil (2002)

    Google Scholar 

  30. Chang, S.K., Albuyeh, F., Gilles, M., Marks, G., Kato, K.: Optimal real-time voltage control. IEEE Trans. Power Syst. 5(3), 750–758 (1990)

    Article  Google Scholar 

  31. Chattopadhyay, D., Gan, D.: Market dispatch incorporating stability constraints. Int. J. Electr. Power Energy Syst. 23(6), 459–469 (2001)

    Article  Google Scholar 

  32. Chen, L., Tada, Y., Okamoto, H., Tanabe, R., Ono, A.: Optimal operation solutions of power systems with transient stability constraints. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 327–329 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  33. Chiang, H.D., Wang, B., Jiang, Q.Y.: Applications of TRUST-TECH methodology in optimal power flow of power systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optimization in the Energy Industry, Energy Systems, vol. 1, pp. 297–318. Springer, Berlin (2009). Chap. 13

    Chapter  Google Scholar 

  34. Chowdhury, E.H., Rahrnan, S.: A review of recent advances in economic dispatch. IEEE Trans. Power Syst. 5(4), 1248–1259 (1990)

    Article  Google Scholar 

  35. Conejo, A., Aguado, J.: Multi-area coordinated decentralized dc optimal power flow. Power Syst. 13(4), 1272–1278 (1998)

    Article  Google Scholar 

  36. Conejo, A.J., Nogales, F.J., Prieto, F.J.: A decomposition procedure based on approximate Newton directions. Math. Program. 93, 495–515 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  37. Contaxis, G., Delkis, C., Korres, G.: Decoupled optimal load flow using linear or quadratic programming. IEEE Trans. Power Syst. PWRS-I, 1–7 (1986)

    Article  Google Scholar 

  38. da Costa, G.: Optimal reactive dispatch through primal-dual method. IEEE Trans. Power Syst. 12(2), 669–674 (1997). doi:10.1109/59.589644

    Article  Google Scholar 

  39. da Costa, G., Costa, C., de Souza, A.: Comparative studies of optimization methods for the optimal power flow problem. Electr. Power Syst. Res. 56, 249–254 (2000)

    Article  Google Scholar 

  40. Crisan, D., Mohtadi, M.: Efficient identification of binding inequality constraints in the optimal power flow Newton approach. In: IEE PROCEEDINGS-C, vol. 139, pp. 365–370 (1992)

    Google Scholar 

  41. Dai, Y., McCalley, J., Vittal, V.: Simplification, expansion and enhancement of direct interior point algorithm for power system maximum loadability. IEEE Trans. Power Syst. 15(3), 1014–1021 (2000)

    Article  Google Scholar 

  42. Das, J.: Power System Analysis: Short-Circuit Load Flow and Harmonics. CRC Press, Boca Raton (2002)

    Google Scholar 

  43. Dent, C., Ochoa, L., Harrison, G., Bialek, J.: Efficient secure AC OPF for network generation capacity assessment. IEEE Trans. Power Syst. 25, 575–583 (2010)

    Article  Google Scholar 

  44. Deuflhard, P.: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms. Springer, Berlin (2004)

    MATH  Google Scholar 

  45. Dommel, H., Tinney, W.: Optimal power flow solutions. IEEE Trans. Power Appar. Syst. 87(10), 1866–1876 (1968)

    Article  Google Scholar 

  46. El-Hawary, M.: Optimal economic operation of large scale electric power systems: a review. In: Proceedings Joint International Power Conference Athens Power Tech., vol. 1, pp. 206–210 (1993)

    Chapter  Google Scholar 

  47. Fernandes, R., Happ, H., Wirgau, K.: Optimal reactive power flow for improved system operations. Int. J. Electr. Power Energy Syst. 2(3), 133–139 (1980)

    Article  Google Scholar 

  48. Franch, T., Scheidt, M., Stock, G.: Current and future challenges for production planning systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optmization in the Energy Industry, Energy Systems, vol. 1, pp. 5–18. Springer, Berlin (2009). Chap. 1

    Chapter  Google Scholar 

  49. Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: A bibliographic survey, II., Non-deterministic and hybrid methods. Energy Syst. (2012). 10.1007/s12667-012-0057-x

    Google Scholar 

  50. Gan, D., Thomas, R., Zimmerman, R.: Stability-constrained optimal power flow. IEEE Trans. Power Syst. 15(2), 535–540 (2000)

    Article  Google Scholar 

  51. Garzillo, A., Innorrta, M., Ricci, M.: The problem of the active and reactive optimum power dispatching solved by utilizing a primal-dual interior point method. Int. J. Electr. Power Energy Syst. 20(6), 427–434 (1998)

    Article  Google Scholar 

  52. Geidl, M., Andersson, G.: Optimal power flow of multiple energy carriers. IEEE Trans. Power Syst. 22(1), 145–155 (2007)

    Article  Google Scholar 

  53. Glavitsch, H., Spoerry, M.: Quadratic loss formula for reactive dispatch. IEEE Trans. Power Appar. Syst. 102(12), 3850–3858 (1983)

    Article  Google Scholar 

  54. Gomez, T., Perez-Arriaga, I., Lumbreras, J., Parra, V.: A security-constrained decomposition approach to optimal reactive power planning. IEEE Trans. Power Syst. 6(3), 1069–1076 (1991)

    Article  Google Scholar 

  55. Gondzio, J.: Multiple centrality corrections in a primal-dual method for linear programming. Comput. Optim. Appl. 6(2), 137–156 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  56. Granelli, G., Montagna, M.: Security constrained economic dispatch using dual quadratic programming. Electr. Power Syst. Res. 56, 71–80 (2000)

    Article  Google Scholar 

  57. Granville, S.: Optimal reactive dispatch through interior point method. IEEE Trans. Power Syst. 9(1), 136–146 (1994)

    Article  Google Scholar 

  58. Griffith, R., Stewart, R.: A nonlinear programming technique for optimization of continuous processing systems. Manag. Sci. 7, 379–392 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  59. Grigsby, L.: The Electric Power Engineering Handbook. CRC Press, Boca Raton (2000)

    Book  Google Scholar 

  60. Gross, G., Bompard, E.: Optimal power flow application issues in the pool paradigm. Int. J. Electr. Power Energy Syst. 26(10), 787–796 (2004)

    Google Scholar 

  61. Grudinin, N.: Combined Quadratic-Separable programming OPF algorithm for economic dispatch and security control. IEEE Trans. Power Syst. 12(4), 1682–1688 (1997)

    Article  Google Scholar 

  62. Grudinin, N.: Reactive power optimization using successive quadratic programming method. IEEE Trans. Power Syst. 13(4), 1219–1225 (1998)

    Article  Google Scholar 

  63. Happ, H.: Optimal power dispatch—a comprehensive survey. IEEE Trans. Power Appar. Syst. 96(3), 841–854 (1977). doi:10.1109/T-PAS.1977.32397

    Article  Google Scholar 

  64. Hong, Y.: Enhanced Newton optimal power flow approach: experiences in Taiwan power system. In: IEE Proceedings, vol. 139 (1992)

    Google Scholar 

  65. Horst, R., Pardalos, P., Thoai, N.V.: Introduction to Global Optimization, 2nd edn. Springer, Berlin (2000)

    MATH  Google Scholar 

  66. Housos, E., Irisarri, G.: A sparse variable metric optimization method applied to the solution of power system problems. IEEE Trans. Power Appar. Syst. 101(1), 195–202 (1982)

    Article  Google Scholar 

  67. Huneault, M., Galiana, F.: A survey of the optimal power flow literature. IEEE Trans. Power Syst. 6(2), 762–770 (1991)

    Article  Google Scholar 

  68. Iba, K., Suzuki, H., Suzuki, K.I., Suzuki, K.: Practical reactive power allocation/operation planning using successive linear programming. IEEE Trans. Power Appar. Syst. 3(2), 558–566 (1988)

    Article  Google Scholar 

  69. Irisarri, G., Wang, X., Tong, J., Mokhtari, S.: Maximum loadability of power systems using interior point non-linear optimization method. IEEE Trans. Power Syst. 12(1), 162–172 (1997). doi:10.1109/59.574936

    Article  Google Scholar 

  70. Jabr, R.: Primal-dual interior-point method to solve the optimal power flow dispatching problem. Optim. Eng. 4(4), 309–336 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  71. Jabr, R.: Optimal power flow using an extended conic quadratic formulation. IEEE Trans. Power Syst. 23(3), 1000–1008 (2008)

    Article  Google Scholar 

  72. Jabr, R.: Recent developments in optimal power flow modeling techniques. In: Rebennack, S., Pardalos, P., Pereira, M., Iliadis, N. (eds.) Handbook of Power Systems, Energy Systems, vol. II, pp. 3–29. Springer, Berlin (2010)

    Chapter  Google Scholar 

  73. Jabr, R., Coonick, A., Cory, B.: A primal-dual interior point method for optimal power flow dispatching. IEEE Trans. Power Syst. 17(3), 654–662 (2002)

    Article  Google Scholar 

  74. Jamoulle, E., Dupont, G.: A reduced gradient method with variable base using second order information, applied to the constrained- and optimal power flow (2004). www.systemseurope.be/pdf/nap_article-E.pdf. Unpublished, accessed in December 2011

  75. Jiang, Q., Han, Z.: Solvability identification and feasibility restoring of divergent optimal power flow problems. Sci. China Ser. E, Technol. Sci. 52(4), 944–954 (2009)

    Article  MATH  Google Scholar 

  76. Jiang, Q., Chiang, H., Guo, C., Cao, Y.: Power-current hybrid rectangular formulation for interior-point optimal power flow. IET Gener. Transm. Distrib. 3(8), 748–756 (2009)

    Article  Google Scholar 

  77. Karmarkar, N.: A new polynomial time algorithm for linear programming. Combinatorica 4, 373–395 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  78. Karoui, K., Platbrood, L., Crisciu, H., Waltz, R.: New large-scale security constrained optimal power flow program using a new interior point algorithm. In: 5th International Conference on European Electricity Market, pp. 1–6 (2008). eEM

    Chapter  Google Scholar 

  79. Kirschen, D., Meeteren, H.V.: MW/voltage control in a linear programming based optimal power flow. IEEE Trans. Power Syst. 3(2), 481–489 (1988)

    Article  Google Scholar 

  80. Klee, V., Minty, J.G.: How good is the simplex algorithm? Tech. Rep., Washington University (1970)

  81. Kundur, P.: Power System Stability and Control. McGraw Hill, New York (1994)

    Google Scholar 

  82. Lavaei, J.: Zero duality gap for classical OPF problem convexifies fundamental nonlinear power problems. In: American Control Conference (2011)

    Google Scholar 

  83. Lavaei, J., Low, S.H.: Zero duality gap in optimal power flow problem. IEEE Transactions on Power Systems 27(1), 92–107 (2012)

    Article  Google Scholar 

  84. Lehmköster, C.: Security constrained optimal power flow for an economical operation of FACTS-devices in liberalized energy markets. IEEE Trans. Power Deliv. 17(2), 603–608 (2002)

    Article  Google Scholar 

  85. Li, M., Tang, W., Tang, W., Wu, Q., Saunders, J.: Bacterial foraging algorithm with varying population for optimal power flow. In: Applications of Evolutinary Computing. Lectures Notes in Computer Science, pp. 32–41. Springer, Berlin (2007)

    Chapter  Google Scholar 

  86. Li, X., Li, Y., Zhang, S.: Analysis of probabilistic optimal power flow taking account of the variation of load power. IEEE Trans. Power Syst. 23(3), 992–999 (2008)

    Article  Google Scholar 

  87. Li, Y., McCalley, J.: Risk-based optimal power flow and system operation state. In: IEEE PES General Meeting (2009)

    Google Scholar 

  88. Lima, F., Galiana, F., Kockar, I., Munoz, J.: Phase shifter placement in Large-Scale systems via mixed integer linear programming. IEEE Trans. Power Syst. 18(3), 1029–1034 (2003)

    Article  Google Scholar 

  89. Lin, C.H., Lin, S.Y.: Distributed optimal power flow with discrete control variables of large distributed power systems. IEEE Trans. Power Syst. 23(3), 1383–1393 (2008)

    Article  Google Scholar 

  90. Lin, W.M., Huang, C.H., Zhan, T.S.: A hybrid current-power optimal power flow technique. IEEE Trans. Power Syst. 23(1), 177–185 (2008)

    Article  Google Scholar 

  91. Lin, X., David, A., Yu, C.: Reactive power optimization with voltage stability consideration in power market systems. In: IEE Proceedings—Genereration, Transmission and Distribution, vol. 150, pp. 305–310 (2003)

    Google Scholar 

  92. 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: Proceedings of IEEE Porto Power Tech Conference, Portugal (2001)

    Google Scholar 

  93. Lu, N., Unum, M.: Network constrained security control using an interior point algorithm. IEEE Trans. Power Syst. 8(3), 1068–1076 (1993)

    Article  Google Scholar 

  94. Maria, G., Findlay, J.: A Newton optimal power flow program for Ontario hydro EMS. IEEE Trans. Power Syst. 2(3), 576–582 (1987)

    Article  Google Scholar 

  95. Martinez-Crespo, J., Usaola, J., Fernandez, J.: Security-constrained optimal generation scheduling in large-scale power systems. IEEE Trans. Power Syst. 21(1), 321–332 (2006)

    Article  Google Scholar 

  96. Mehrotra, S.: On the implementation of a primal-dual interior-point method. SIAM J. Optim. 2(4), 575–601 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  97. Min, W., Shengsong, L.: A trust region interior point algorithm for optimal power flow problems. Int. J. Electr. Power Energy Syst. 27(4), 293–300 (2005)

    Article  Google Scholar 

  98. Momoh, J.: A generalized quadratic-based model for optimal power flow. In: Conference Proceedings IEEE International Conference on Systems, Man and Cybernetics, vol. 1, pp. 261–271 (1989)

    Chapter  Google Scholar 

  99. Momoh, J., Zhu, J.: Improved interior point method for OPF problems. IEEE Trans. Power Syst. 14(3), 1114–1120 (1999)

    Article  Google Scholar 

  100. Momoh, J., Guo, S., Ogbuobiri, E., Adapa, R.: The quadratic interior point method solving power system optimization problems. IEEE Trans. Power Syst. 9(3), 1327–1336 (1994)

    Article  Google Scholar 

  101. Momoh, J., Koessler, R., Bond, M.S., Sun, D., Papalexopoulos, A., Ristanovic, P.: Challenges to optimal power flow. IEEE Trans. Power Syst. 12(1), 444–447 (1997)

    Article  Google Scholar 

  102. Momoh, J.A., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part I. Non Linear and quadratic programming approaches. IEEE Trans. Power Syst. 14(1), 105–111 (1999)

    Article  Google Scholar 

  103. Momoh, J.A., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part II. Newton, linear programming and interior point methods. IEEE Trans. Power Syst. 14(1), 105–111 (1999)

    Article  Google Scholar 

  104. Monticelli, A., MVFPereira Granville, S.: Security-constrained optimal power flow with post-contingency corrective rescheduling. IEEE Trans. Power Syst. 2(1), 175–180 (1987)

    Article  Google Scholar 

  105. Mota-Palomino, R., Quintana, V.: Sparse reactive power scheduling by a penalty-function-linear programming technique. IEEE Trans. Power Syst. PWRS-I(3), 31–39 (1986)

    Article  Google Scholar 

  106. Moyano, C., Salgado, R.: Adjusted optimal power flow solutions via parameterized formulation. Electr. Power Syst. Res. 80(9), 1018–1023 (2010)

    Article  Google Scholar 

  107. Muchayi, M., El-Hawary, M.: A summary of algorithms in reactive power pricing. Int. J. Electr. Power Energy Syst. 21, 119–124 (1999)

    Article  Google Scholar 

  108. Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  109. Nogales, F.J., Prieto, F.J., Conejo, A.J.: A decomposition methodology applied to the multi-area optimal power flow problem. Ann. Oper. Res. 120, 99–116 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  110. Nualhong, D., Chusanapiputt, S., Phomvuttisarn, S., Jantarang, S.: Reactive tabu search for optimal power flow under constrained emission dispatch. In: IEEE Region 10 Conference 2004. TENCON, vol. 3, pp. 327–330 (2004)

    Chapter  Google Scholar 

  111. de Oliveira, L., Carneiro Jr., S.,de Oliveira, E.J., Pereira, J.L.R., Silva Jr., I.C.,Costa, J.S.: Optimal reconfiguration and capacitor allocation in radial distribution systems for energy losses minimization. Int. J. Electr. Power Energy Syst. 32(8), 840–848 (2010)

    Article  Google Scholar 

  112. Osman, M., Abo-Sinna, M., Mousa, A.: A solution to the optimal power flow using genetic algorithm. Appl. Math. Comput. 155(2), 391–405 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  113. Pandya, K., Joshi, S.: A survey of optimal power flow methods. J. Theor. Appl. Inf. Technol. 4(5), 450–458 (2008)

    Google Scholar 

  114. Papalexopoulos, A., Imparato, C., Wu, F.: Large-scale optimal power flow: effects of initialization, decoupling and discretization. IEEE Trans. Power Syst. 4(2), 748–759 (1989)

    Article  Google Scholar 

  115. Parker, C., Morrison, I., Sutanto, D.: Application of an optimisation method for determining the reactive margin from voltage collapse in reactive power planning. IEEE Trans. Power Syst. 11(3), 1473–1481 (1996)

    Article  Google Scholar 

  116. Patra, S., Goswamib, S.: A non-interior point approach to optimum power flow solution. Electr. Power Syst. Res. 74, 17–26 (2005)

    Article  Google Scholar 

  117. Peschon, J., Bree, D., Hajdu, L.: Optimal power-flow solutions for power system planning. Proc. IEEE 6(1), 64–70 (1972)

    Article  Google Scholar 

  118. Qiu, W., Flueck, A., Tu, F.: A new parallel algorithm for security constrained optimal power flow with a nonlinear interior point method. In: IEEE Power Engineering Society General Meeting, pp. 2422–2428 (2005)

    Chapter  Google Scholar 

  119. Qiu, Z., Deconinck, G., Belmans, R.: A literature survey of optimal power flow problems in the electricity market context. In: IEEE/PES Power Systems Conference and Exposition. PSCE’09, Seattle, WA, pp. 1–6 (2009)

    Google Scholar 

  120. Radziukynas, V., Radziukyniene, I.: Optimization methods application to optimal power flow systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optimization in the Energy Industry, Energy Systems, vol. 1, pp. 409–436. Springer, Berlin (2009). Chap. 18

    Chapter  Google Scholar 

  121. Ramos, R., Vallejos, J., Barn, B.: Multi-objective reactive power compensation with voltage security. In: Proceedings IEEE/PES Transmission and Distribution Conf. and Expo, Latin America, Brazil, pp. 302–307 (2004)

    Google Scholar 

  122. Rashidi, M.A., El-Hawary, M.: Hybrid particle swarm optimization approach for solving the discrete OPF problem considering the valve loading effects. IEEE Trans. Power Syst. 22(4), 2030–2038 (2007)

    Article  Google Scholar 

  123. Rau, N.: Issues in the path toward an RTO and standard markets. IEEE Trans. Power Syst. 18(2), 435–443 (2003)

    Article  Google Scholar 

  124. Rau, N.: Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry. Wiley/IEEE Press, Hoboken (2003)

    Google Scholar 

  125. Rider, M., Castro, C., Bedrinana, M., Garcia, A.: Towards a fast and robust interior point method for power system applications. IEE Proc., Gener. Transm. Distrib. 151, 575–581 (2004)

    Article  Google Scholar 

  126. Rider, M., Paucar, V., Garcia, A.: Enhanced higher-order interior-point method to minimise active power losses in electric energy systems. IEE Proc., Gener. Transm. Distrib. 151(4), 517–525 (2004)

    Article  Google Scholar 

  127. Rosehart, W., Canizares, C., Vannelli, A.: Sequential methods in solving economic power flow problems. In: IEEE Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 281–284 (1997)

    Google Scholar 

  128. Rosehart, W., Canizares, C., Quintana, V.: Optimal power flow incorporating voltage collapse constraints. In: Proceedings of the 1999 IEEE/PES Summer Meeting, Edmonton, Alberta, pp. 820–825 (1999)

    Google Scholar 

  129. Rosehart, W., Schellenberg, A., Roman, C.: New tools for power system dynamic performance management. In: IEEE Power Engineering Society General Meeting (2006)

    Google Scholar 

  130. Sadati, N., Amraee, T., Ranjbar, A.: A global particle Swarm-Based-Simulated annealing optimization technique for under-voltage load shedding problem. Appl. Soft Comput. 9, 652–657 (2009)

    Article  Google Scholar 

  131. Saha, T., Maitra, A.: Optimal power flow using the reduced Newton approach in rectangular coordinates. Int. J. Electr. Power Energy Syst. 20(6), 383–389 (1998)

    Article  Google Scholar 

  132. Salahi, M., Pengy, J., Terlaky, T.: On Mehrotra-type predictor-corrector algorithms. SIAM J. Optim. 18(4), 1377–1397 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  133. Santos, A., Deckmann, S. Jr., Soares, S.: A dual augmented Lagrangian approach for optimal power flow. IEEE Trans. Power Syst. 3, 1020–1025 (1988)

    Article  Google Scholar 

  134. Sasson, A., Viloria, F., Aboytes, F.: Optimal load flow solution using the Hessian matrix. IEEE Trans. Power Appar. Syst. PAS-92(1), 31–41 (1973). doi:10.1109/TPAS.1973.293590

    Article  Google Scholar 

  135. Scala, M.L., Trovato, M., Antonelli, C.: On-line dynamic preventive control: an algorithm for transient security constraints. IEEE Trans. Power Syst. 13(2), 601–610 (1998)

    Article  Google Scholar 

  136. Smale, S.: On the average number of steps of the simplex method of linear programming. Math. Program. 27, 241–262 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  137. Sojoudi, S., Lavaei, J.: Network topologies guaranteeing zero duality gap for optimal power flow problem (2011). Submitted for publication. Available https://www.cds.caltech.edu/~lavaei/TPS_S_L.pdf

  138. Sousa, A., Torres, G.: Globally convergent optimal power flow by trust-region interior-point methods. In: Power Tech 2007, Lausanne, Switzerland (2007)

    Google Scholar 

  139. Sousa, A., Torres, G., Cañizares, C.: Robust optimal power flow solution using trust region and interior-point methods. IEEE Trans. Power Syst. 26(2), 487–499 (2011). doi:10.1109/TPWRS.2010.2068568

    Article  Google Scholar 

  140. Stott, B., Hobson, E.: Power system security control calculation using linear programming. Parts I and II. IEEE Trans. Power Appar. Syst. PAS-97, 1713–1731 (1978). doi:10.1109/TPAS.1978.354664

    Article  Google Scholar 

  141. Stott, B., Marinho, J.: Linear programming for power system network security applications. IEEE Trans. Power Appar. Syst. PAS-98, 837–848 (1979)

    Article  Google Scholar 

  142. Stott, B., Alsac, O., Monticelli, A.: Security analysis and optimization. In: Proceedings of the, IEEE, vol. 75, pp. 1623–1644 (1987)

    Google Scholar 

  143. Stott, B., Jardim, J., Alsac, O.: DC power flow revisited. IEEE Trans. Power Syst. 24(3), 1290–1300 (2009). doi:10.1109/TPWRS.2009.2021235

    Article  Google Scholar 

  144. Subbaraj, P., Rajnarayanan, P.: Optimal reactive power dispatch using self-adaptive real coded genetic algorithm. Electr. Power Syst. Res. 79, 374–381 (2009)

    Article  Google Scholar 

  145. Sun, D., Ashley, B., Brewer, B., Hughes, A., Tinney, W.: Optimal power flow by Newton approach. IEEE Trans. Power Appar. Syst. 103(10), 2864–2880 (1984)

    Article  Google Scholar 

  146. Thomas, W., Dixon, A., Cheng, D., Dunnett, R., Schaff, G., Thorp, J.: Optimal reactive planning with security constraints. In: IEEE Power Industry Computer Application Conference, pp. 79–84 (1995)

    Google Scholar 

  147. Thukaram, D., Yesuratnam, G.: Fuzzy—expert approach for voltage-reactive power dispatch. In: IEEE Power India Conference (2006)

    Google Scholar 

  148. Tognola, G., Bacher, R.: Unlimited point algorithm for OPF problems. IEEE Trans. Power Syst. 14(3), 1046–1054 (1999)

    Article  Google Scholar 

  149. Tong, X., Zhang, Y., Wu, F.: A decoupled semismooth Newton method for optimal power flow. In: IEEE Power Engineering Society General Meeting (2006)

    Google Scholar 

  150. Torres, G., Quintana, V.: An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Trans. Power Syst. 13(4), 1211–1218 (1998)

    Article  Google Scholar 

  151. Torres, G., Quintana, V.: Optimal power flow by a nonlinear complementarity method. IEEE Trans. Power Syst. 15(3), 1028–1033 (2000)

    Article  Google Scholar 

  152. Torres, G., Quintana, V.: On a nonlinear multiple-centrality corrections interior-point method for optimal power flow. IEEE Trans. Power Syst. 16(2), 222–228 (2001)

    Article  Google Scholar 

  153. Torres, G., Quintana, V.: A Jacobian smoothing nonlinear complementarity method for solving optimal power flows. In: PSCC Conference, Sevilla, Spain (2002)

    Google Scholar 

  154. Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design, 3rd edn. Vanderplaats Research & Development (1999)

    Google Scholar 

  155. Vanti, M., Gonzaga, C.: On the Newton interior-point method for nonlinear optimal power flow. In: IEEE Bologna PowerTech Conference, Bologna, Italy (2003)

    Google Scholar 

  156. Vargas, L., Quintana, V., Vannelli, A.: A tutorial description of an interior point method and its applications to security-constrained economic dispatch. IEEE Trans. Power Syst. 8(3), 1315–1323 (1993)

    Article  Google Scholar 

  157. Verbič, G., Cañizares, C.: Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Trans. Power Syst. 21(4), 1883–1893 (2006)

    Article  Google Scholar 

  158. Wallace, S., Fleten, S.E.: Stochastic programming models in energy. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 637–677. North-Holland, Amsterdam (2003)

    Chapter  Google Scholar 

  159. Wang, H., Thomas, R.: Towards reliable computation of large-scale market-based optimal power flow. In: Proceedings of the 40th Hawaii International Conference on System Sciences, pp. 1–10 (2007)

    Google Scholar 

  160. Wang, H., Murillo-Sanchez, C., Zimmerman, R., Thomas, R.: On computational issues of market-based optimal power flow. IEEE Trans. Power Syst. 22(3), 1185–1193 (2007)

    Article  Google Scholar 

  161. Wang, L., Xiang, N., Wang, S., Huang, M.: Parallel reduced gradient optimal power flow solution. Electr. Power Syst. Res. 17, 229–237 (1989)

    Article  Google Scholar 

  162. Wei, H., Sasaki, H., Yokoyama, R.: An interior point nonlinear programming for optimal power flow problems within a novel data structure. IEEE Trans. Power Syst. 13(3), 870–877 (1998)

    Article  Google Scholar 

  163. Wolf, P.: Methods of nonlinear programming. In: Nonlinear Programming. Wiley, New York (1967)

    Google Scholar 

  164. Wood, A., Wollenberg, B.: Power Generation Operation and Control. Wiley, New York (1996)

    Google Scholar 

  165. Wright, S.: Primal-dual Interior-point Methods. SIAM, Philadelphia (1997)

    Book  MATH  Google Scholar 

  166. Wu, Y.C., Debs, A., Marsten, R.: A direct nonlinear predictor-corrector primaldual interior point algorithm for optimal power flows. IEEE Trans. Power Syst. 9(2), 876–883 (1994)

    Article  Google Scholar 

  167. Xia, X., Elaiw, A.: Optimal dynamic economic dispatch of generation: a review. Electr. Power Syst. Res. 80(8), 975–986 (2010)

    Article  Google Scholar 

  168. Xia, Y., Chan, K.: Dynamic constrained optimal power flow using semi-infinite programming. IEEE Trans. Power Syst. 21(3), 1455–1458 (2006)

    Article  Google Scholar 

  169. Xiao, Y., Song, Y., Liu, C., Sun, Y.: Available transfer capability enhancement using FACTS devices. IEEE Trans. Power Syst. 18(1), 305–312 (2003)

    Article  Google Scholar 

  170. Xie, K., Song, Y.: Optimal spinning reserve allocation with full AC network constraints via a nonlinear interior point method. Electr. Power Compon. Syst. 28(11), 1071–1090 (2000)

    Google Scholar 

  171. Yamin, H.Y., Al-Tallaq, K., Shahidehpour, S.M.: New approach for dynamic optimal power flow using Benders decomposition in a deregulated power market. Electr. Power Syst. Res. 65, 101–107 (2003)

    Article  Google Scholar 

  172. 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 Trans. Power Syst. 21(1), 61–67 (2006)

    Article  Google Scholar 

  173. Yan, X., Quintana, V.: Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Trans. Power Syst. 14(2), 709–717 (1999)

    Article  Google Scholar 

  174. Yehia, M., Ramadan, R., El-Tawail, Z., Tarhini, K.: An integrated technico-economical methodology for solving reactive power compensation problem. IEEE Trans. Power Appar. Syst. 13(1), 54–59 (1998)

    Article  Google Scholar 

  175. Yu, D., Fagan, J., Foote, B., Aly, A.: An optimal load flow study by the generalized reduced gradient approach. Electr. Power Syst. Res. 10, 47–53 (1986). doi:10.1016/0378-7796(86)90048-9

    Article  Google Scholar 

  176. Yuan, Y.: A review of trust region algorithms for optimization. In: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, pp. 271–282 (1999)

    Google Scholar 

  177. Yuan, Y., Kubokawa, J., Sasaki, H.: A solution of optimal power flow with multicontingency transient stability constraints. IEEE Trans. Power Syst. 18(3), 1094–1102 (2003)

    Article  Google Scholar 

  178. Zehar, K., Sayah, S.: Optimal power flow with environmental constraint using a fast successive linear programming algorithm: application to the Algerian power system. Energy Convers. Manag. 49, 3361–3365 (2008)

    Article  Google Scholar 

  179. Zhang, J.: A successive linear programming method and its convergence on nonlinear problems. Defense Technical Information Center (1983)

  180. Zhang, W., Tolbert, L.: Survey of reactive power planning methods. In: IEEE Power Engineering Society General Meeting, vol. 2, pp. 1430–1440 (2005)

    Google Scholar 

  181. Zhang, W., Li, F., Tolbert, L.: Review of reactive power planning: objectives, constraints, and algorithms. IEEE Trans. Power Syst. 22(4), 2177–2186 (2007)

    Article  Google Scholar 

  182. Zhang, X., Handschin, E.: Advanced implementation of UPFC in a nonlinear interior-point OPF. IEE Proc., Gener. Transm. Distrib. 148(5), 489–496 (2001)

    Article  Google Scholar 

  183. Zhang, X., Petoussis, S., Godfrey, K.: Nonlinear interior-point optimal power flow method based on a current mismatch formulation. IEE Proc., Gener. Transm. Distrib. 152, 795–805 (2005)

    Article  Google Scholar 

  184. Zhang, X.P.: In: Fundamentals of Electric Power Systems, pp. 1–52. Wiley, New York (2010). doi:10.1002/9780470608555.ch1

    Google Scholar 

  185. Zhang, X.P., Handschin, E., Yao, M.: Modeling of the generalized unified power flow controller (GUPFC) in a nonlinear interior point OPF. IEEE Trans. Power Syst. 16(3), 367–373 (2001)

    Article  Google Scholar 

  186. Zhang, X.P., Rehtanz, C., Pal, B.: Flexible AC Transmission Systems—Modelling and Control. Springer, Berlin (2006)

    Google Scholar 

  187. Zhang, X.P., Rehtanz, C., Pal, B.: Power Systems Flexible AC Transmission Systems: Modelling and Control. Springer, Berlin (2006)

    Google Scholar 

  188. Zhang, Y., Ren, Z.: Optimal reactive power dispatch considering costs of adjusting the control devices. IEEE Trans. Power Syst. 20(3), 1349–1356 (2005)

    Article  MathSciNet  Google Scholar 

  189. Zhu, J.: Optimization of Power System Operation. Wiley, New York (2009)

    Book  Google Scholar 

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Frank, S., Steponavice, I. & Rebennack, S. Optimal power flow: a bibliographic survey I. Energy Syst 3, 221–258 (2012). https://doi.org/10.1007/s12667-012-0056-y

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