Optimal power flow: a bibliographic survey II

Non-deterministic and hybrid methods

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 provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey (this article) examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

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Abbreviations

AC:

Alternating Current

ACO:

Ant Colony Optimization

AIS:

Artificial Immune Systems

ANN:

Artificial Neural Network

BFA:

Bacterial Foraging Algorithm

COA:

Chaos Optimization Algorithm

DBFA:

Dynamic Bacterial Foraging Algorithm

DC:

Direct Current

DE:

Differential Evolution

EA:

Evolutionary Algorithm

EP:

Evolutionary Programming

FACTS:

Flexible AC Transmission Systems

GA:

Genetic Algorithm

IA:

Immune Algorithm

IPM:

Interior Point Method

KKT:

Karush-Kuhn-Tucker (conditions for optimality)

LP:

Linear Programming

MINLP:

Mixed Integer-Nonlinear Programming

NLP:

Nonlinear Programming

NN:

Neural Network

OPF:

Optimal Power Flow

ORPF:

Optimal Reactive Power Flow

PC:

Predictor-Corrector

PDIPM:

Primal-Dual Interior Point Method

PSO:

Particle Swarm Optimization

SA:

Simulated Annealing

SCED:

Security-Constrained Economic Dispatch

SLP:

Sequential Linear Programming

SQP:

Sequential Quadratic Programming

TS:

Tabu Search

UPFC:

Unified Power Flow Controller

VAR:

Volt-Ampere Reactive

References

  1. 1.

    Aarts, E., Korst, J.: Simulated Annealing and Boltzmann Machines. Wiley, New York (1989)

    Google Scholar 

  2. 2.

    Abbasy, A., Tabatabaii, I., Hosseini, S.: Optimal reactive power dispatch in electricity markets using a multiagent-based differential evolution algorithm. In: International Conference on Power Engineering, Energy and Electrical Drives. POWERENG 2007, pp. 249–254 (2007)

    Google Scholar 

  3. 3.

    Abido, M.: Optimal power flow using tabu search algorithm. Electr. Power Compon. Syst. 30, 469–483 (2002)

    Article  Google Scholar 

  4. 4.

    Abido, M.: Multiobjective optimal power flow using strength Pareto evolutionary algorithm. In: 39th International Universities Power Engineering Conference (uPEC 2004), vol. 1, pp. 457–461 (2004)

    Google Scholar 

  5. 5.

    Abido, M.: Multiobjective particle swarm optimization for optimal power flow problem. In: 12th International Middle-East Power System Conference (MEPCON 2008) (2008)

    Google Scholar 

  6. 6.

    Abou El Ela, A., Abido, M., Spea, S.: Optimal power flow using differential evolution algorithm. Electr. Eng. 91, 69–78 (2009)

    Article  Google Scholar 

  7. 7.

    Abou El Ela, A., Abido, M., Spea, S.: Optimal power flow using differential evolution algorithm. Electr. Power Syst. Res. 80(7), 878–885 (2010). doi:10.1016/j.epsr.2009.12.018

    Article  Google Scholar 

  8. 8.

    Allaoua, B., Laoufi, A.: Collective intelligence for optimal power flow solution using ant colony optimization. Leonardo Electron. J. Pract. Technol. 13, 88–105 (2008)

    Google Scholar 

  9. 9.

    Allaoua, B., Laoufi, A.: Optimal power flow solution using ant manners for electrical network. Adv. Electr. Comput. Eng. 9, 34–40 (2009)

    Article  Google Scholar 

  10. 10.

    Alrashidi, M., El-Hawary, M.: Applications of computational intelligence techniques for solving the revived optimal power flow problem. Electr. Power Syst. Res. 79, 694–702 (2009)

    Article  Google Scholar 

  11. 11.

    Altun, H., Yalcinoz, T.: Implementing soft computing techniques to solve economic dispatch problem in power systems. Expert Syst. Appl. 35, 1668–1678 (2008)

    Article  Google Scholar 

  12. 12.

    Aminudin, N., Rahman, T., Musirin, I.: Optimal power flow for load margin improvement using evolutionary programming. In: The 5th Student Conference on Research and Development (SCOReD 2007), Malaysia (2007)

    Google Scholar 

  13. 13.

    Aoki, K., Fan, M., Nishikori, A.: Optimal VAR planning by approximation method for recursive mixed-integer linear programming. IEEE Trans. Power Appar. Syst. 3(4), 1741–1747 (1988)

    Article  Google Scholar 

  14. 14.

    Bakare, G., Krost, G., Venayagamoorthy, G., Aliyu, U.: Differential evolution approach for reactive power optimization of Nigerian grid system. In: IEEE Power Engineering Society General Meeting, pp. 1–6 (2007)

    Google Scholar 

  15. 15.

    Bakirtzis, A., Biskas, P., Zoumas, C., Petridis, V.: Optimal power flow by enhanced genetic algorithm. IEEE Trans. Power Syst. 17(2), 229–236 (2002)

    Article  Google Scholar 

  16. 16.

    Banu, R., Devaraj, D.: Genetic algorithm approach for optimal power flow with FACTS devices. In: 4th International IEEE Conference Intelligent Systems, vol. 23, pp. 11–16 (2008)

    Google Scholar 

  17. 17.

    Basu, M.: Optimal power flow with FACTS devices using differential evolution. Int. J. Electr. Power Energy Syst. 30(2), 150–156 (2008)

    Article  Google Scholar 

  18. 18.

    Biskas, P., Ziogos, N., Tellidou, A., Zoumas, C., Bakirtzis, A., Petridis, V.: Comparison of two metaheuristics with mathematical programming methods for the solution of OPF. IEE Proc., Gener. Transm. Distrib. 153(1), 16–24 (2006). doi:10.1049/ip-gtd:20050047

    Article  Google Scholar 

  19. 19.

    Bland, J., Dawson, G.: Tabu search and design optimization. Comput. Aided Des. 23(3), 195–201 (1991)

    MATH  Article  Google Scholar 

  20. 20.

    Borges, C., Alves, J.: Power system real time operation based on security constrained optimal power flow and distributed processing. In: IEEE Power Tech, Lausanne, pp. 960–965 (2007)

    Google Scholar 

  21. 21.

    Bouktir, T., Slimani, L., Belkacemi, M.: A genetic algorithm for solving the optimal power flow problem. Leonardo J. Sci. 4, 44–58 (2004)

    Google Scholar 

  22. 22.

    Cai, H., Chung, C., Wong, K.: Application of differential evolution algorithm for transient stability constrained optimal power flow. IEEE Trans. Power Syst. 23(2), 719–728 (2008)

    Article  Google Scholar 

  23. 23.

    Carpaneto, E., Cavallero, C., Freschi, F., Repetto, M.. In: Immune Procedure for Optimal Scheduling of Complex Energy Systems ICARIS 2006. LNCS, pp. 309–320. Springer, Heidelberg (2006)

    Google Scholar 

  24. 24.

    Castro, L., Zubben, F.: Artificial immune systems: part I—basic theory and applications. Tech. rep., FEEC/UNICAMP, Campinas, Brazil (2000)

  25. 25.

    Chakraborty, U. (ed.): Advances in Differential Evolution. Springer, Berlin (2008)

    Google Scholar 

  26. 26.

    Changa, C.F., Wong, J.J., Chiou, J.P., Sua, C.T.: Robust searching hybrid differential evolution method for optimal reactive power planning in large-scale distribution systems. Electr. Power Syst. Res. 77, 430–437 (2007)

    Article  Google Scholar 

  27. 27.

    Chayakulkheeree, K., Ongsakul, W.: Optimal power flow considering non-linear fuzzy network and generator ramprate constrained. Int. Energy J. 8(2), 131–138 (2007)

    Google Scholar 

  28. 28.

    Chen, G.: Differential evolution based optimal reactive power flow with simulated annealing updating method. In: International Symposium on Computational Intelligence and Design (2008)

    Google Scholar 

  29. 29.

    Chen, L., Suzuki, H., Katou, K.: Mean field theory for optimal power flow. IEEE Trans. Power Syst. 12(4), 1481–1486 (1997)

    Article  Google Scholar 

  30. 30.

    Chibante, R. (ed.): Simulated Annealing Theory with Applications. Sciyo, Rijeka (2010)

    Google Scholar 

  31. 31.

    Chiou, J., Wang, F.: A hybrid method of differential evolution with application to optimal control problems of a bioprocess system. In: Proceeding 1998 IEEE on Evolutionary Computation Conference, vol. 1, pp. 627–632 (1998)

    Google Scholar 

  32. 32.

    Chuanwena, J., Bomp, E.: A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation. Math. Comput. Simul. 68, 57–65 (2005)

    Article  Google Scholar 

  33. 33.

    Clerc, M.: Particle Swarm Optimization. Wiley-ISTE, New York (2006)

    Google Scholar 

  34. 34.

    Coath, G., Al-Dabbagh, M., Halgamuge, S.K.: Particle swarm optimisation for reactive power and voltage control with grid-integrated wind farms. In: IEEE Power Engineering Society General Meeting, vol. 1, pp. 303–308 (2004)

    Google Scholar 

  35. 35.

    Coelho, L., Mariani, V.: Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints. Energy Convers. Manag. 48, 1631–1639 (2007)

    Article  Google Scholar 

  36. 36.

    Colorni, A., Dorigo, M., Maniezzo, V.: Distributed optimization by ant colonies. In: Actes de la Première Conférence Européenne sur la Vie Artificielle, pp. 134–142. Elsevier, Amsterdam (1991)

    Google Scholar 

  37. 37.

    Das, D., Patvardhan, C.: Useful multi-objective hybrid evolutionary approach to optimal power flow. In: IEE Proceedings—Generation, Transmission and Distribution, vol. 150, pp. 275–282 (2003)

    Google Scholar 

  38. 38.

    Das, B., Verma, P.: Artificial neural network-based optimal capacitor switching in a distribution system. Electr. Power Syst. Res. 60, 55–62 (2001)

    Article  Google Scholar 

  39. 39.

    de Castro, L., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Berlin (2002)

    Google Scholar 

  40. 40.

    de Mello Honório, L., da Silva, A.M.L., Barbosa, D.A.: A gradient-based artificial immune system applied to optimal power flow problems. In: De Castro, L.N., Von Zuben, F.J., Knidel, H. (eds.) Proceedings of Artificial Immune Systems: 6th International Conference (ICARIS 2007), Santos, Brazil, August 2007 (2007)

    Google Scholar 

  41. 41.

    Dorigo, M.: Optimization, learning and natural algorithms. PhD thesis, Politecnico di Milano, Italy (1992)

  42. 42.

    Dorigo, M., Stützle, T.: Ant Colony Optimization. Bradford Books. MIT Press, Cambridge (2004)

    Google Scholar 

  43. 43.

    Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A. (eds.): Ant Colony Optimization and Swarm Intelligence. Proceedings of 6th International Conference, ANTS 2008, Brussels, Belgium, September 22–24, 2008. Springer, Berlin (2008)

    Google Scholar 

  44. 44.

    Dreyfus, G.: Neural Networks: Methodology and Applications. Springer, Berlin (2005)

    Google Scholar 

  45. 45.

    Esmin, A., Lambert-Torres, G.: Loss power minimization using particle swarm optimization. In: International Joint Conference on Neural Networks (IJCNN ’06), pp. 1988–1992 (2006)

    Google Scholar 

  46. 46.

    Esmin, A., Lambert-Torres, G., de Souza, A.Z.: A hybrid particle swarm optimization applied to loss power minimization. IEEE Trans. Power Syst. 20(2), 859–866 (2005)

    Article  Google Scholar 

  47. 47.

    Faigle, U., Kern, W.: Some convergence results for probabilistic tabu search. ORSA J. Comput. 4(1), 32–37 (1992)

    MATH  Article  Google Scholar 

  48. 48.

    Feoktistov, V.: Differential evolution. In: Search of Solutions, 1st edn. Springer Optimization and Its Applications, vol. 5. Springer, Berlin (2006)

    Google Scholar 

  49. 49.

    Floudas, C., Gounaris, C.: A review of recent advances in global optimization. J. Glob. Optim. 45, 3–38 (2009)

    MathSciNet  MATH  Article  Google Scholar 

  50. 50.

    Fogel, D. (ed.): Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, 3rd edn. Wiley, New York (2006)

    Google Scholar 

  51. 51.

    Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey I, formulations and deterministic methods. Energy Syst. (2012). doi:10.1007/s12667-012-0056-y

    Google Scholar 

  52. 52.

    Gaing, Z.L.: Constrained optimal power flow by mixed-integer particle swarm optimization. In: Proceedings of 2005 IEEE Power Engineering Society General Meeting, vol. 1, pp. 243–250 (2005)

    Google Scholar 

  53. 53.

    Gaing, Z.L., Chang, R.F.: Security-Constrained optimal power flow by mixed-integer genetic algorithm with arithmetic operators. In: IEEE Power Engineering Society General Meeting (2006)

    Google Scholar 

  54. 54.

    Gaing, Z.L., Liu, X.H.: New constriction particle swarm optimization for Security-Constrained optimal power flow solution. In: International Conference on Intelligent Systems Applications to Power Systems (ISAP 2007), pp. 1–6 (2007)

    Google Scholar 

  55. 55.

    Gasbaoui, B., Allaoua, B.: Ant colony optimization applied on combinatorial problem for optimal power flow solution. Leonardo J. Sci. 14, 1–17 (2009)

    Google Scholar 

  56. 56.

    Glover, F.: Tabu search-part I. ORSA J. Comput. 1, 190–206 (1989)

    MathSciNet  MATH  Article  Google Scholar 

  57. 57.

    Glover, F.: Tabu search: a tutorial. Interfaces 20(4), 74–94 (1990)

    Article  Google Scholar 

  58. 58.

    Glover, F.: Tabu search—part II. ORSA J. Comput. 1(2), 4–32 (1990)

    Article  Google Scholar 

  59. 59.

    Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Dordrecht (1997)

    Google Scholar 

  60. 60.

    Gomes, B., Saraiva, J., Neves, L.: Impact of load and generation price uncertainties in spot prices. In: IEEE Bucharest Power Tech Conference, Bucharest, Romania (2009)

    Google Scholar 

  61. 61.

    Gopalakrishnan, V., Thirunavukkarasu, P., Prasanna, R.: Reactive power planning using hybrid evolutionary programming method. In: IEE Proceedings—Generation, Transmission and Distribution, vol. 150, pp. 275–282 (2003)

    Google Scholar 

  62. 62.

    Guan, X., Liu, W., Papalexopoulos, A.: Application of a fuzzy set method in an optimal power flow. Electr. Power Syst. Res. 34, 11–18 (1995)

    Article  Google Scholar 

  63. 63.

    Hahn, T., Kim, M.K., Hur, D., Park, J.K., Yoon, Y.: Evaluation of available transfer capability using fuzzy multi-objective contingency-constrained optimal power flow. Electr. Power Syst. Res. 78, 873–882 (2008)

    Article  Google Scholar 

  64. 64.

    Hajian-Hoseinabadi, H., Hosseini, S., Hajian, M.: Optimal power flow solution by a modified particle swarm optimization algorithm. In: 43rd International Universities Power Engineering Conference (UPEC 2008), pp. 1–4 (2008)

    Google Scholar 

  65. 65.

    Han, F., Lu, Q.S.: An improved chaos optimization algorithm and its application in the economic load dispatch problem. Int. J. Comput. Math. 85(6), 969–982 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  66. 66.

    Han, Z., Jiang, Q., Cao, Y.: Sequential feasible optimal power flow in power systems. Sci. China Ser. E 52(2), 429–435 (2009)

    MATH  Article  Google Scholar 

  67. 67.

    Haque, M., Kashtiban, A.: Application of neural networks in power systems; a review. In: World Academy of Science, Engineering and Technology, vol. 6, pp. 53–57 (2005)

    Google Scholar 

  68. 68.

    Hartati, R., El-Hawary, M.: Optimal active power flow solutions using a modified Hopfield neural network. In: Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 189–194 (2001)

    Google Scholar 

  69. 69.

    Haupt, R.: Practical Genetic Algorithms. Wiley/IEEE Press, New York (2004)

    Google Scholar 

  70. 70.

    He, S., Wen, J.Y., Prempaint, E., Wu, Q., Fitch, J., Mann, S.: An improved particle swarm optimization for optimal power flow. In: Proceedings of 2004 International Conference on Power System Technology, vol. 2, pp. 1633–1637 (2004)

    Google Scholar 

  71. 71.

    Hsiao, Y.T., Liu, C.C., Chiang, H., Chen, Y.L.: A new approach for optimal VAR sources planning in large scale electric power systems. IEEE Trans. Power Syst. 8(3), 988–996 (1993)

    Article  Google Scholar 

  72. 72.

    Hugang, X., Haozhong, C., Haiyu, L.: Optimal reactive power flow incorporating static voltage stability based on multi-objective adaptive immune algorithm. Energy Convers. Manag. 49, 1175–1181 (2008)

    Article  Google Scholar 

  73. 73.

    Ingber, A.L.: Simulated annealing: practice versus theory. Math. Comput. Model. 18(11), 29–57 (1993)

    MathSciNet  MATH  Article  Google Scholar 

  74. 74.

    Jiang, C., Quan, X., Zhang, Y.: A chaotic optimization method for economical operation of hydro power plants. J. Huazhong Univ. Sci. Technol. 27, 39–40 (1999)

    Google Scholar 

  75. 75.

    Jurada, J.: Introduction to Artificial Neural Systems. Jaico Publishing House, Mumbai (1997)

    Google Scholar 

  76. 76.

    Kalil, M., Musirin, I., Othman, M.: Ant colony based optimization technique for voltage stability control. In: Proceedings of the 6th WSEAS International Conference on Power Systems (2006)

    Google Scholar 

  77. 77.

    Kallrath, J.: Combined strategic design and operative planning in the process industry. Comput. Chem. Eng. 33, 1983–1993 (2009)

    Google Scholar 

  78. 78.

    Kallrath, J.: Polylithic modeling and solution approaches using algebraic modeling systems. Optim. Lett. 5(3), 453–466 (2011)

    MathSciNet  Article  Google Scholar 

  79. 79.

    Kamal, M., Rahman, T., Musirin, I.: Application of improved genetic algorithms for loss minimisation in power system. In: Proceedings National Power and Energy Conference, pp. 258–262 (2004)

    Google Scholar 

  80. 80.

    Karthikeyan, S., Palanisamyl, K., Varghese, L., Raglend, I., Kothari, D.: Comparison of intelligent techniques to solve economic load dispatch problem with line flow constraints. In: IEEE International Advance Computing Conference (IACC) (2009)

    Google Scholar 

  81. 81.

    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks IV, pp. 1942–1948 (1995)

    Google Scholar 

  82. 82.

    Kephart, J.: A biologically inspired immune system for computers. In: Proceedings of Artificial Life IV: The Fourth International Workshop on the Synthesis and Simulation of Living Systems, pp. 130–139. MIT Press, Cambridge (1994)

    Google Scholar 

  83. 83.

    Kim, J.Y., Jeong, H.M., Lee, H.S., Park, J.H.: PC cluster based parallel PSO algorithm for optimal power flow. In: International Conference on Intelligent Systems Applications to Power Systems (ISAP 2007), pp. 1–6 (2007)

    Google Scholar 

  84. 84.

    Kirpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    MathSciNet  Article  Google Scholar 

  85. 85.

    Kulworawanichpong, T., Sujitjorn, S.: Optimal power flow using tabu search. IEEE Power Eng. Rev. 6, 37–40 (2002)

    Google Scholar 

  86. 86.

    Kumar, V., Mohan, M.: Solution to security constrained unit commitment problem using genetic algorithm. Int. J. Electr. Power Energy Syst. 32, 117–125 (2010)

    Article  Google Scholar 

  87. 87.

    Kumar, S., Renuga, P.: Reactive power planning using real GA comparison with evolutionary programming. Int. J. Recent Trends Eng. 1(3), 124–148 (2009)

    Google Scholar 

  88. 88.

    Kumari, M., Maheswarapu, S.: Enhanced genetic algorithm based computation technique for multi-objective optimal power flow solution. Int. J. Electr. Power Energy Syst. 32, 736–742 (2010)

    Article  Google Scholar 

  89. 89.

    Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. Mathematics and Its Applications, vol. 37. Springer, Berlin (1987)

    Google Scholar 

  90. 90.

    Lage, G., de Sousa, V., da Costa, G.: Power flow solution using the penalty/modified barrier method. In: IEEE Bucharest Power Tech Conference, Bucharest, Romania (2009)

    Google Scholar 

  91. 91.

    Lai, L., Sinha, N.: Modern heuristic optimization techniques: theory and applications to power systems. In: Genetic Algorithms for Solving Optimal Power Flow Problems, pp. 471–508. Wiley, New York (2008)

    Google Scholar 

  92. 92.

    Lai, L., Ma, J., Yokoyama, R., Zhao, M.: Improved genetic algorithms for optimal power flow under both normal and contingent operation states. Int. J. Electr. Power Energy Syst. 19(5), 287–292 (1997)

    Article  Google Scholar 

  93. 93.

    Lampinen, J., Zelinka, I.: Mixed integer-discrete-continuous optimization by differential evolution. In: 5th International Mendel Conference on Soft Computing, Brno, Czech Republic, pp. 77–81 (1999)

    Google Scholar 

  94. 94.

    Lee, K., Vlachogiannis, J.: Optimization of power systems based on ant colony system algorithms: an overview. In: Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems, pp. 22–35 (2005)

    Google Scholar 

  95. 95.

    Leung, H., Chung, T.: Optimal power flow with a versatile FACTS controller by genetic algorithm approach. International Conference on Advances in Power System Control, Operation and Management, vol. 1, pp. 178–183 (2000)

    Google Scholar 

  96. 96.

    Li, B., Jiang, W.: Optimizing complex function by chaos search. Cybern. Syst. 29(4), 409–419 (1998)

    MathSciNet  MATH  Article  Google Scholar 

  97. 97.

    Li, D., Gao, L., Lu, S., Ma, J., Li, Y.: Adaptive particle swarm optimization algorithm for power system reactive power optimization. In: American Control Conference (ACC ’07), pp. 4733–4737 (2007)

    Google Scholar 

  98. 98.

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

    Google Scholar 

  99. 99.

    Liang, C., Chung, C., Wong, K., Duan, X.: Parallel optimal reactive power flow based on cooperative co-evolutionary differential evolution and power system decomposition. IEEE Trans. Power Syst. 22(1), 249–257 (2007)

    Article  Google Scholar 

  100. 100.

    Liang, C., Chung, C., Wong, K., Duan, X., Tse, C.: Study of differential evolution for optimal reactive power flow. IET Gener. Transm. Distrib. 1(2), 253–260 (2007)

    Article  Google Scholar 

  101. 101.

    Liao, G.C.: Application of an immune algorithm to the short term unit commitment problem in power system operation. IEE Proc., Gener. Transm. Distrib. 153(3), 309–320 (2006)

    Article  Google Scholar 

  102. 102.

    Lin, S.Y., Ho, Y.H., Lin, C.H.: An ordinal optimization theory-based algorithm for solving the optimal power flow problem with discrete control variables. IEEE Trans. Power Syst. 19(1), 276–286 (2004)

    MathSciNet  Article  Google Scholar 

  103. 103.

    Liu, Y., Passino, K.: Biomimicry of social foraging bacteria for distributed optimization: models, principles, and emergent behaviors. J. Optim. Theory Appl. 115(3), 603–628 (2002)

    MathSciNet  MATH  Article  Google Scholar 

  104. 104.

    Liu, Y., Ma, L., Zhang, J.: GA/SA/TS hybrid algorithms for reactive power optimization. In: Power Engineering Society Summer Meeting, vol. 1, pp. 245–249. IEEE Press, New York (2000)

    Google Scholar 

  105. 105.

    Liu, F., Chung, C., Wong, K., Yan, W., Xu, G.: Hybrid immune genetic method for dynamic reactive power optimization. In: International Conference on Power System Technology (PowerCon 2006), pp. 1–6 (2006)

    Google Scholar 

  106. 106.

    Mahdad, B., Bouktir, T., Srairi, K.: Optimal power flow of the Algerian network using genetic algorithm/fuzzy rules. In: IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8 (2008)

    Google Scholar 

  107. 107.

    Mahdad, B., Srairi, K., Bouktir, T., Benbouzid, M.: Optimal power flow for large-scale power system with shunt FACTS using efficient parallel GA. In: 34th Annual Conference of IEEE Industrial Electronics (IECON 2008) (2008)

    Google Scholar 

  108. 108.

    Mahdad, B., Srairi, K., Bouktir, T.: Dynamic strategy based parallel GA coordinated with FACTS devices to enhance the power system security. In: Power & Energy Society General Meeting (PES ’09), pp. 1–8. IEEE Press, New York (2009)

    Google Scholar 

  109. 109.

    Mahdad, B., Srairi, K., Bouktir, T.: Optimal power flow with environmental constraints of the algerian network using decomposed parallel GA. In: IEEE Bucharest Power Tech Conference, Bucharest, Romania (2009)

    Google Scholar 

  110. 110.

    Mahdad, B., Bouktir, T., Srairi, K., Benbouzid, M.E.: Dynamic strategy based fast decomposed GA coordinated with FACTS devices to enhance the optimal power flow. Energy Convers. Manag. 51, 1370–1380 (2010)

    Article  Google Scholar 

  111. 111.

    Miranda, V., Saraiva, J.: Fuzzy modelling of power system optimal local flow. IEEE Trans. Power Syst. 7(2), 843–849 (1992)

    Article  Google Scholar 

  112. 112.

    Mishra, S.: Bacteria foraging based solution to optimize both real power loss and voltage stability limit. In: IEEE Power Engineering Society General Meeting (2007)

    Google Scholar 

  113. 113.

    Mo, N., Zou, Z., Chan, K., Pong, T.: Transient stability constrained optimal power flow using particle swarm optimisation. IET Gener. Transm. Distrib. 1(3), 476–483 (2007)

    Article  Google Scholar 

  114. 114.

    Mori, H., Hayashi, T.: New parallel tabu search for voltage and reactive power control in power systems. In: IEEE International Symposium on Circuit and Systems (ISACAS’98), pp. 431–434 (1998)

    Google Scholar 

  115. 115.

    Muthuselvan, N., Somasundaram, P.: Application of tabu search algorithm to security constrained economic dispatch. J. Theor. Appl. Inf. Technol. 5, 602–608 (2009)

    Google Scholar 

  116. 116.

    Nakawiro, W., Erlich, I.: A combined GA-ANN strategy for solving optimal power flow with voltage security constraint. In: Asia-Pacific Power and Energy Engineering Conference (APPEEC) (2009)

    Google Scholar 

  117. 117.

    Nguyen, T.: Neural network load-flow. IEE Proc., Gener. Transm. Distrib. 142, 51–58 (1995)

    Article  Google Scholar 

  118. 118.

    Nguyen, T.: Neural network optimal-power-flow. In: Proceedings of the 4th International Conference on Advances in Power System Control, Operation and Management, Hong Kong, pp. 266–271 (1997)

    Google Scholar 

  119. 119.

    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)

    Google Scholar 

  120. 120.

    Numnonda, T., Annakkage, U.: Optimal power dispatch in multinode electricity market using genetic algorithm. Electr. Power Syst. Res. 49, 211–220 (1999)

    Article  Google Scholar 

  121. 121.

    Onate, P., Ramirez, J.: Optimal power flow solution with security constraints by a modified PSO. In: IEEE Power Engineering Society General Meeting, pp. 1–6 (2007)

    Google Scholar 

  122. 122.

    Ongsakul, W., Jirapong, P.: Optimal allocation of facts devices to enhance total transfer capability using evolutionary programming. In: IEEE International Symposium (2005)

    Google Scholar 

  123. 123.

    Onwubolu, G., Davendra, D. (eds.): Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization. Studies in Computational Intelligence. Springer, Berlin (2009)

    Google Scholar 

  124. 124.

    Panigrahi, B., Pandi, V.: Congestion management using adaptive bacterial foraging algorithm. Energy Convers. Manag. 50, 1202–1209 (2009)

    Article  Google Scholar 

  125. 125.

    Passino, K.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst. Mag. 22(3), 52–67 (2002)

    MathSciNet  Article  Google Scholar 

  126. 126.

    Passino, K.: Biomimicry for Optimization, Control, and Automation. Springer, Berlin (2005)

    Google Scholar 

  127. 127.

    Poli, R., Kennedy, J., Blackwell, T., Freitas, A. (eds.): Particle Swarms: The Second Decade. Hindawi Publishing Corporation, New York (2008)

    Google Scholar 

  128. 128.

    Pouya, K., Lesani, H.: An angle-based PSO approach for reactive power management problem. In: Power Systems Conference and Exposition (PSCE ’09), pp. 1–6. IEEE/PES, Piscataway (2009)

    Google Scholar 

  129. 129.

    Prasanna, T., Somasundaram, P.: OPF with FACTS devices in interconnected power systems using fuzzy stochastic algorithms. Int. J. Power Energy Convers. 1, 279–299 (2009)

    Article  Google Scholar 

  130. 130.

    Prasanna, T., Muthuselvan, N., Somasundaram, P.: Security constrained OPF by fuzzy stochastic algorithms in interconnected power systems. J. Electr. Syst. 5(1), P7 (2009)

    Google Scholar 

  131. 131.

    Price, K., Storn, R., Lampinen, J.: Differential Evolution: a Practical Approach to Global Optimization. Birkhäuser, Berlin (2005)

    Google Scholar 

  132. 132.

    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, pp. 1–6 (2009)

    Google Scholar 

  133. 133.

    Raju, C., Vaisakh, K., Raju, S.: An IPM-EPSO based hybrid method for security enhancement using SSSC. Int. J. Recent Trends Eng. 2(5), 208–212 (2009)

    Google Scholar 

  134. 134.

    Ramech, V., Li, X.: A fuzzy multiobjective approach to contingency constrained OPF. IEEE Trans. Power Syst. 12(3), 1348–1354 (1997)

    Article  Google Scholar 

  135. 135.

    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 

  136. 136.

    Reeves, C., Rowe, J.: Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory, 2nd edn. Springer, Berlin (2003)

    Google Scholar 

  137. 137.

    Ripley, B.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  138. 138.

    Roa-Sepulveda, C., Pavez-Lazo, B.: A solution to the optimal power flow using simulated annealing. In: IEEE Porto Power Tech Conference, Porto, Portugal (2001)

    Google Scholar 

  139. 139.

    Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Netw. 5, 96–101 (1994)

    Article  Google Scholar 

  140. 140.

    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 

  141. 141.

    Santoso, N., Tan, O.: Neural-net based real-time control of capacitors installed on distribution systems. IEEE Trans. Power Deliv. 5(1), 266–272 (1990)

    Article  Google Scholar 

  142. 142.

    Saraiva, J., Miranda, V.: Evaluation of the performance of a fuzzy optimal power flow algorithm. In: Proceedings of 7th Mediterranean Electrotechnical Conference, vol. 3, pp. 897–900 (1994)

    Google Scholar 

  143. 143.

    Sayah, S., Zehar, K.: Modified differential evolution algorithm for optimal power flow with non-smooth cost functions. Energy Convers. Manag. 49, 3036–3042 (2008)

    Article  Google Scholar 

  144. 144.

    Shengsong, L., Min, W., Zhijian, H.: A hybrid algorithm for optimal power flow using the chaos optimization and the linear interior point algorithm. In: Proceedings International Conference on Power System Technology, vol. 2, pp. 793–797 (2002)

    Google Scholar 

  145. 145.

    Shengsong, L., Min, W., Zhijian, H.: Hybrid algorithm of chaos optimisation and SLP for optimal power flow problems with multimodal characteristic. In: IEE Proceedings—Generation, Transmission and Distribution, vol. 150, pp. 543–547 (2003)

    Google Scholar 

  146. 146.

    Simon, S., Padhy, N., Anand, R.: An ant colony system approach for unit commitment problem. Int. J. Electr. Power Energy Syst. 28, 315–323 (2006)

    Article  Google Scholar 

  147. 147.

    Song, Y., Wang, G., Wang, P., Johns, A.: Environmental/economic dispatch using fuzzy logic controlled genetic algorithms. IEE Proc., Gener. Transm. Distrib. 144(4), 377–382 (1997)

    Article  Google Scholar 

  148. 148.

    Sood, Y., Padhy, N., Gupta, H.: Discussion of optimal power flow by enhanced genetic algorithm. IEEE Trans. Power Syst. 18(3), 1219 (2003)

    Article  Google Scholar 

  149. 149.

    Spall, J.: Introduction to Stochastic Search and Optimization. Wiley-Interscience, New York (2003)

    Google Scholar 

  150. 150.

    Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech. Rep. TR-95-012, ICSI (1995)

  151. 151.

    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 

  152. 152.

    Swapur, K.: Swarm intelligence approach to the solution of optimal power flow. J. Indian Inst. Sci. 86, 439–455 (2006)

    Google Scholar 

  153. 153.

    Swarup, K.: Ant colony optimization for economic generator scheduling and load dispatch. In: Proceedings of the 6th WSEAS International Conference on Evolutionary Computing, Portugal, pp. 167–175 (2005)

    Google Scholar 

  154. 154.

    Tang, K., Kwong, S.: Genetic Algorithms: Concepts and Designs, 2nd edn. Springer, Berlin (1999)

    Google Scholar 

  155. 155.

    Tang, W., Li, M., He, S., Wu, Q., Saunders, J.: Optimal power flow with dynamic loads using bacterial foraging algorithm. In: International Conference on Power System Technology (2006)

    Google Scholar 

  156. 156.

    Tang, W., Li, M., Wu, Q., Saunders, J.: Bacterial foraging algorithm for optimal power flow in dynamic environments. IEEE Trans. Circuits Syst. I, Regul. Pap. 55(8), 2433–2443 (2008)

    MathSciNet  Article  Google Scholar 

  157. 157.

    Tangpatiphan, K., Yokoyama, A.: Optimal power flow with steady-state voltage stability consideration using improved evolutionary programming. In: 2009 IEEE Bucharest Power Tech Conference, Bucharest, Romania (2009)

    Google Scholar 

  158. 158.

    Teng, J.H., Liu, Y.H.: A novel ACS-based optimum switch relocation method. IEEE Trans. Power Syst. 18(1), 113–120 (2003)

    Article  Google Scholar 

  159. 159.

    Todorovski, M., Rajicic, D.: An initialization procedure in solving optimal power flow by genetic algorithm. IEEE Trans. Power Syst. 21(2), 480–487 (2006)

    Article  Google Scholar 

  160. 160.

    Tripathy, M., Mishra, S.: Bacteria foraging-based solution to optimize both real power loss and voltage stability limit. IEEE Trans. Power Syst. 22(1), 240–248 (2007)

    Article  Google Scholar 

  161. 161.

    Vaisakh, K., Srinivas, L.R.: Differential evolution based OPF with conventional and non-conventional cost characteristics. In: Joint International Conference on Power System Technology and IEEE Power India Conference (POWERCON), pp. 1–9 (2008)

    Google Scholar 

  162. 162.

    Varadarajan, M., Swarup, K.: Solving multi-objective optimal power flow using differential evolution. IET Gener. Transm. Distrib. 2(5), 720–730 (2008)

    Article  Google Scholar 

  163. 163.

    Venayagamoorthy, G., Harley, R.: Swarm intelligence for transmission system control. In: IEEE Power Engineering Society General Meeting, pp. 1–4 (2007)

    Google Scholar 

  164. 164.

    Venkatesh, B., Sadasivam, G., Khan, M.: Optimal reactive power planning against voltage collapse using the successive multiobjective fuzzy LP technique. In: IEE Proceedings on Generation, Transmission and Distribution, vol. 146, pp. 343–348 (1999)

    Google Scholar 

  165. 165.

    Vlachogiannis, J., Lee, K.: Reactive power control based on particle swarm multi-objective optimization. In: Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems, vol. 1, pp. 303–308 (2005)

    Google Scholar 

  166. 166.

    Vlachogiannis, J., Lee, K.: A comparative study on particle swarm optimization for optimal steady-state performance of power systems. IEEE Trans. Power Syst. 21(4), 1718–1728 (2006)

    Article  Google Scholar 

  167. 167.

    Vlachogiannis, J., Hatziargyriou, N., Lee, K.: Ant colony system-based algorithm for constrained load flow problem. IEEE Trans. Power Syst. 20(3), 1241–1249 (2005)

    Article  Google Scholar 

  168. 168.

    Wang, C.R., Yuan, H.J., Huang, Z.Q., Zhang, J.W., Sun, C.J.: A modified particle swarm optimization algorithm and its application in optimal power flow problem. In: Proceedings of 2005 International Conference on Machine Learning and Cybernetics, vol. 5, pp. 2885–2889 (2005)

    Google Scholar 

  169. 169.

    Wong, K., Fung, C.: Simulated annealing based economic dispatch algorithm. In: IEE Proceedings, vol. 140, pp. 509–515 (1993)

    Google Scholar 

  170. 170.

    Wong, K., Yuryevich, J.: Optimal power flow method using evolutionary programming. In: Simulated Evolution and Learning, pp. 405–412. Springer, Berlin (1999)

    Google Scholar 

  171. 171.

    Wu, Q., Ma, J.: Power system optimal reactive power dispatch using evolutionary programming. IEEE Trans. Power Syst. 10(3), 1243–1249 (1995)

    MathSciNet  Article  Google Scholar 

  172. 172.

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

    Article  Google Scholar 

  173. 173.

    Xiangzheng, X.: Research on reactive power optimizing control based on immune algorithms. In: The Eighth International Conference on Electronic Measurement and Instruments, vol. 3, pp. 898–901 (2007)

    Google Scholar 

  174. 174.

    Xu, H., Zhu, Y., Zhang, T.: Application of mutative scale chaos optimization algorithm in power plant units economic dispatch. J. Harbin Inst. Technol. 32, 55–58 (2000)

    Google Scholar 

  175. 175.

    Yang, B., Chen, Y., Zhao, Z.: Survey on applications of particle swarm optimization in electric power systems. In: IEEE International Conference on Control and Automation (ICCA), pp. 481–486 (2007)

    Google Scholar 

  176. 176.

    Yang, D., Li, G., Cheng, G.: On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34, 1366–1375 (2007)

    Article  Google Scholar 

  177. 177.

    Yoshida, H., Kawata, K., Fukuyama, Y., Takayama, S., Nakanishi, Y.: A particle swarm optimization for reactive power and voltage control considering voltage security assessment. IEEE Trans. Power Syst. 15(4), 1232–1239 (2001)

    Article  Google Scholar 

  178. 178.

    Younes, M., Rahli, M., Abdelhakem-Koridak, L.: Optimal power flow based on hybrid genetic algorithm. J. Inf. Sci. Eng. 23, 1801–1816 (2007)

    Google Scholar 

  179. 179.

    Yu, X., Gen, M.: Introduction to Evolutionary Algorithms. Springer, Berlin (2010)

    Google Scholar 

  180. 180.

    Yumbla, P., Ramirez, J., Coello, C.: Optimal power flow subject to security constraints solved with a particle swarm optimizer. IEEE Trans. Power Syst. 23(1), 33–40 (2008)

    Article  Google Scholar 

  181. 181.

    Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    MathSciNet  MATH  Article  Google Scholar 

  182. 182.

    Zadeh, L.: Fuzzy Sets, Fuzzy Logic, Fuzzy Systems. Advances in Fuzzy Systems—Applications and Theory, vol. 6. World Scientific, Berlin (1996)

    Google Scholar 

  183. 183.

    Zhang, W., Liu, Y.: Reactive power optimization based on PSO in a practical power system. In: IEEE Power Engineering Society General Meeting, vol. 1, pp. 239–243 (2004)

    Google Scholar 

  184. 184.

    Zhang, W., Liu, Y.: Fuzzy logic controlled particle swarm for reactive power optimization considering voltage stability. In: The 7th International Power Engineering Conference (IPEC) (2005)

    Google Scholar 

  185. 185.

    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 

  186. 186.

    Zhang, H., Zhang, L., Meng, F.: Reactive power optimization based on genetic algorithm. In: International Conference on Power System Technology, vol. 2, pp. 1448–1453 (1998)

    Google Scholar 

  187. 187.

    Zhao, B., Guo, C., Cao, Y.: Improved particle swam optimization algorithm for OPF problems. In: IEEE PES Power Systems Conference and Exposition, vol. 1, pp. 233–238 (2004)

    Google Scholar 

  188. 188.

    Zhao, B., Guo, C., Cao, Y.: An improved particle swarm optimization algorithm for optimal reactive power dispatch. In: IEEE Power Engineering Society General Meeting, vol. 1, pp. 272–279 (2005)

    Google Scholar 

  189. 189.

    Zhihuan, L., Yinhong, L., Xianzhong, D.: Improved strength Pareto evolutionary algorithm with local search strategies for optimal reactive power flow. Inf. Technol. J. 9, 749–757 (2010)

    Article  Google Scholar 

  190. 190.

    Zhijiang, Y., Zhijian, H., Chuanwen, J.: Economic dispatch and optimal power flow based on chaotic optimization. In: Proceedings of International Conference on Power System Technology (PowerCon), vol. 4, pp. 2313–2317 (2002)

    Google Scholar 

  191. 191.

    Zimmerman, R.D., Murillo-Sánchez, C.E., Thomas, R.J.: MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26(1), 12–19 (2011). doi:10.1109/TPWRS.2010.2051168

    Article  Google Scholar 

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Correspondence to Steffen Rebennack.

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Frank, S., Steponavice, I. & Rebennack, S. Optimal power flow: a bibliographic survey II. Energy Syst 3, 259–289 (2012). https://doi.org/10.1007/s12667-012-0057-x

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Keywords

  • Electric power systems
  • Optimal power flow
  • Non-deterministic optimization
  • Stochastic search
  • Hybrid methods
  • Heuristics
  • Global optimization
  • Survey