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Study of Economic Load Dispatch by Various Hybrid Optimization Techniques

  • Dipankar Santra
  • Arindam Mondal
  • Anirban Mukherjee
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 611)

Abstract

The economic load dispatch (ELD) is one of the most complex optimization problems of electrical power system. Classically, it is to identify the optimal combination of generation level of all power generating units in order to minimize the total fuel cost while satisfying the loads and losses in power transmission system. In view of the sharply increasing nature of cost of fossil fuel, energy management has gained lot of significance nowadays. Herein lies the relevance of continued research on improving the solution of ELD problem. A lot of research work have been carried out on this problem using several optimization techniques including classical, linear, quadratic, and nonlinear programming methods. The objective function of the ELD problem being of highly nonlinear and non-convex nature, the classical optimization methods cannot guarantee convergence to the global optimal solution. Some soft computing techniques like Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), Clonal Selection Algorithm (CSA), Ant Colony Optimization (ACO), Simulated Annealing (SA), Genetic Algorithm (GA), etc. are now being applied to find even better solution to the ELD problem. An interesting trend in this area is application of hybrid approaches like GA-PSO, ABC-PSO, CSA-SA, etc. and the results are found to be highly competitive. In this book chapter, we focus on the hybrid soft computing approaches in solving ELD problem and present a concise and updated technical review of systems and approaches proposed by different research groups. To depict the differences in technique of the hybrid approaches over the basic soft computing methods, the individual methods are introduced first. While the basic working principle and case studies of each hybrid approach are described briefly, the achievements of the approaches are discussed separately. Finally, the challenges in the present problem and some of the most promising approaches are highlighted and the possible future direction of research is hinted.

Keywords

Economic load dispatch Artificial bee colony Particle swarm optimization Clonal selection algorithm Ant colony optimization Simulated annealing Genetic algorithm Firefly algorithm Gravitational search algorithm 

References

  1. 1.
    Grigsby LL (2009) Power System Stability and Control. CRC Press, New YorkGoogle Scholar
  2. 2.
    Wood AJ, Woollenberg BF, Sheble GB (1984) Power generation operation and control. Wiley Publishers, New YorkGoogle Scholar
  3. 3.
    Yare Y, Venayagamoorthy GK, Saber AY (2009) Conference: economic dispatch of a differential evolution based generator maintenance scheduling of a power system. In: Power & Energy Society General Meeting, 2009 (PES ‘09), IEEEGoogle Scholar
  4. 4.
    Chowdhury BH, Rahman S (1990) A review of recent advances in economic dispatch. IEEE Trans Power Syst 5(4):1248–1259CrossRefGoogle Scholar
  5. 5.
    Garg M, Kumar S (2012) Int J Electron Commun Technol IJECT 3(1)Google Scholar
  6. 6.
    Lee KY et al (1984) Fuel cost minimize at ion for both real-and reactive power dispatches. Proc Inst Elect Eng Gen Trans Distrib 131(3):85–93Google Scholar
  7. 7.
    Sailaja Kumari M, Sydulu M (2009) A fast computational genetic algorithm for economic load dispatch. Int J Recent Trends Eng 1(1)Google Scholar
  8. 8.
    Naveen Kumar KP, Parmar S, Dahiya S (2012) Optimal solution of combined economic emission load dispatch using genetic algorithm. Int J Comput Appl (0975–8887) 48(15)Google Scholar
  9. 9.
    Chopra L, Kaur R (2012) Economic load dispatch using simple and refined genetic algorithm. Int J Adv Eng Technol 5(1):584–590Google Scholar
  10. 10.
    Biswas SD, Debbarma A (2012) Optimal operation of large power system by GA method. J Emerg Trends Eng Appl Sci (JETEAS) 3(1):1–7Google Scholar
  11. 11.
    Anuj Gargeya1 M, Pabba SP (2013) Economic load dispatch using genetic algorithm and pattern search methods. Int J Adv Res Electr Electron Instrum Eng 2(4) 2013Google Scholar
  12. 12.
    Arora D, Sehgal S, Kumar A, Soni A (2013) Economic load dispatch using genetic algorithm. Int J Techn Res (IJTR), 2(2)Google Scholar
  13. 13.
    Kapadia RK, Patel NK (2013) J Inform Knowl Res Electr Eng 2:219–223Google Scholar
  14. 14.
    Mansour WM, Salama MM, Abdelmaksoud SM, Henry HA (2013) Dynamic economic load dispatch of thermal power system using genetic algorithm. IRACST—Eng Sci Technol: An Int J (ESTIJ) 3(2). ISSN:2250–3498Google Scholar
  15. 15.
    Jain AK, Mandloi T Comparison of classical method and soft computing optimization algorithm applied to economic load dispatch problem. Int J Latest Trends Eng Technol (IJLTET) 3(4)Google Scholar
  16. 16.
    Aliyari H, Effatnejad R, Areyaei A (2014) Economic load dispatch with the proposed GA algorithm for large scale system. J Energy Natural Resour 3(1):1–5CrossRefGoogle Scholar
  17. 17.
    Park J-B, Lee K-S, Shin J-R, Lee K-Y (2005) A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans Power Syst 20(1)Google Scholar
  18. 18.
    Mahadevan K, Kannan PS, Kannan S (2005) Particle swarm optimization for economic dispatch of generating units with valve-point loading. J Energy Environ 4:49–61Google Scholar
  19. 19.
    Sudhakaran M, Ajay P, Vimal Raj D, Palanivelu TG (2007) Application of particle swarm optimization for economic load dispatch problems. In: The 14th international conference on intelligent system applications to power systems, ISAP 2007, Kaohsiung, TaiwanGoogle Scholar
  20. 20.
    dos Santos Coelho L, Lee C-S (2008) Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches. Electrical Power Energy Syst. 30:297–307Google Scholar
  21. 21.
    Baskar G, Mohan MR (2008) Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system. Electric Power Energy Syst 30:609–613Google Scholar
  22. 22.
    Mahor A, Prasad V, Rangnekar S (2009) Economic dispatch using particle swarm optimization: a review. Renew Sustain Energy Rev 13:2134–2141CrossRefGoogle Scholar
  23. 23.
    Vlachogiannis JG, Lee KW (2009) Economic load dispatch-a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO. IEEE Trans Power Syst 24(2)Google Scholar
  24. 24.
    Saber AY, Chakraborty S, Abdur Razzak SM, Senjyu T (2009) Optimization of economic load dispatch of higher order general cost polynomials and its sensitivity using modified particle swarm optimization. Electric Power Syst Res 79:98–106Google Scholar
  25. 25.
    Muthu Vijaya Pandian S, Thanushkodi K (2010) Solving economic load dispatch problem considering transmission losses by a Hybrid EP-EPSO algorithm for solving both smooth and non-smooth cost function. Int J Comput Electr Eng 2(3):1793–8163Google Scholar
  26. 26.
    Muthu S, Pandian V, Thanushkodi K (2011) An efficient particle swarm optimization technique to solve combined economic emission dispatch problem. Eur J Sci Res 54(2):187–192Google Scholar
  27. 27.
    Batham R, Jain K, Pandit M (2011) Improved particle swarm optimization approach for nonconvex static and dynamic economic power dispatch. Int J Eng Sci Technol 3(4):130–146Google Scholar
  28. 28.
    Sreenivasan G, Dr Saibabu CH, Dr Sivanagaraju S (2011) Solution of dynamic economic load dispatch (DELD) problem with valve point loading effects and ramp rate limits using PSO. Int J Electr Comput Eng 1(1):59–70Google Scholar
  29. 29.
    Khokhar B, Singh Parmar KP (2012) A novel weight-improved particle swarm optimization for combined economic and emission dispatch problems. Int J Eng Sci Technol (IJEST) 4(05) 2012Google Scholar
  30. 30.
    Anurag Gupta KK, Wadhwani SK (2012) Combined economic emission dispatch problem using particle swarm optimization. Int J Comput Appl 49(6):0975–8887Google Scholar
  31. 31.
    Hardiansyah J, Yohannes MS (2012) Application of soft computing methods for economic load dispatch problems. Int J Comput Appl 58(13):0975–8887Google Scholar
  32. 32.
    Chakrabarti R, Chattopadhyay PK, Basu M, Panigrahi CK (2006) Particle swarm optimization technique for dynamic economic dispatch. IE(I) J-EL 87:48–54Google Scholar
  33. 33.
    Agrawal S, Bakshi T, Majumdar D (2012) Economic load dispatch of generating units with multiple fuel options using PSO. Int J Control Autom 5(4)Google Scholar
  34. 34.
    Linga Murthy KS, Subramanyam GVS, SriChandan K (2012) Combined economic and emission dispatch for a wind integrated system using particle swarm optimization. Int Electr Eng J (IEEJ) 3(2):769–775Google Scholar
  35. 35.
    Junaidi H, Yohannes MS (2012) Intell Syst Appl 12:12–18Google Scholar
  36. 36.
    Sharma J, Mahor A (2013) Particle swarm optimization approach for economic load dispatch: a review. Int J Eng Res Appl (IJERA) 3(1):013–022Google Scholar
  37. 37.
    Niknam T (2006) An approach based on particle swarm optimization for optimal operation of distribution network considering distributed generators. In: Proceedings of the 32nd annual conference on IEEE industrial electronics, IECON 2006, pp 633–637 1942–1948Google Scholar
  38. 38.
    Soubache ID, Ajay-D-Vimal Raj P (2013) Unified particle swarm optimization to solving economic dispatch. Int J Innov Technol Explor Eng (IJITEE) 2(4)Google Scholar
  39. 39.
    Tiwari S, Kumar A, Chaurasia GS, Sirohi GS (2013) Economic load dispatch using particle swarm optimization. Int J Appl Innov Eng Manag 2(4)Google Scholar
  40. 40.
    Singh N, Kumar Y (2013) Economic load dispatch with valve point loading effect and generator ramp rate limits constraint using MRPSO. Int J Adv Res Comput Eng Technol (IJARCET) 2(4)Google Scholar
  41. 41.
    Venkatesh B, Subbu Chithira Kala V (2013) A particle swarm optimization for multiobjective combined heat and power economic dispatch problem considering the cost, emission and losses. Int J Scient Eng Res 4(6) 2013Google Scholar
  42. 42.
    Md. Khan J, Mahala H (2013) Applications of particle swarm optimization in economic load dispatch. In: Proceedings of national conference on recent advancements in futuristic technologies (NCRAFT 13), vol 1, Issue 1, PAPER ID 0072, Oct-2013Google Scholar
  43. 43.
    Singh Maan R, Mahela OP, Gupta M (2013) Solution of economic load dispatch problems with improved computational performance using particle swarm optimization. Int J Eng Sci Invent 2(6) 01–06Google Scholar
  44. 44.
    Singh N, Kumar Y (2013) Constrained economic load dispatch using evolutionary technique. Asian J Technol Manage Res 03(02)Google Scholar
  45. 45.
    Sinha P (2013) Particle swarm optimization for solving economic load dispatch problem. Int J Commun Comput Technol 01(63)Google Scholar
  46. 46.
    Singh M, Thareja D (2013) A new approach to solve economic load dispatch using particle swarm optimization. Int J Appl Innov Eng Manage (IJAIEM) 2(11)Google Scholar
  47. 47.
    Niknam T, Amiri B, Olamaie J, Arefi A (2008) An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering. J Zhejiang University Sci A. doi: 10.1631/jzus.A0820196 Google Scholar
  48. 48.
    Tikalkar A, Khare M (2014) Economic load dispatch using linearly decreasing inertia weight particle swarm optimization Int J Emerg Technol Adv Eng 4(1)Google Scholar
  49. 49.
    Abdullah MN, Bakar AHA, Rahim NA, Mokhlis H, Illias HA, Jamian JJ (2014) Modified particle swarm optimization with time varying acceleration coefficients for economic load dispatch with generator constraints. J. Electr Eng Technol 9(1):15–26CrossRefGoogle Scholar
  50. 50.
    Sarath Babu G, Anupama S, Suresh Babu P (2014) Int J Eng Res Develop 9(11):15–23Google Scholar
  51. 51.
    Chaturvedi N et al (2014) A novel approach for economic load dispatch problem based on GA and PSO. Int J Eng Res Appl 4(3):24–31Google Scholar
  52. 52.
    Sivaraman P, Manimaran S, Parthiban K, Gunapriya D (2014) PSO approach for dynamic economic load dispatch problem. Int J Innov Res Sci Eng Technol 3(4)Google Scholar
  53. 53.
    Mistry P, Vyas S (2014) A study on: optimisation of economic load dispatch problem by PSO. Indian J Appl Res 4(6)Google Scholar
  54. 54.
    Khan S, Gupta C (2014) An optimization techniques used for economic load dispatch. Int J Adv Technol Eng Res (IJATER) 4(4)Google Scholar
  55. 55.
    Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1)Google Scholar
  56. 56.
    Nomana N, Iba H (2008) Differential evolution for economic load dispatch problems. Electr Power Syst Res 78:1322–1331CrossRefGoogle Scholar
  57. 57.
    Surekha P, Sumathi S (2012) Solving economic load dispatch problems using differential evolution with opposition based learning. WSEAS Trans Inf Sci Appl 9(1)Google Scholar
  58. 58.
    Soni SK, Bhuria V (2012) Multi-objective emission constrained economic power dispatch using differential evolution algorithm. Int J Eng Innov Technol (IJEIT) 2(1)Google Scholar
  59. 59.
    Kumar C, Alwarsamy T Solution of economic dispatch problem using differential evolution algorithm. Int J Soft Comput Eng (IJSCE) 1(6)Google Scholar
  60. 60.
    Balamurugan K, Krishnan SR (2013) Differential evolution based economic load dispatch problem. In: Proceedings of 1st national conference on advances in electrical energy applications, 3–4 Jan 2013Google Scholar
  61. 61.
    Pramod Kumar Gouda, PK, Raguraman H (2013) Economic load dispatch optimization in power system with renewable energy using differential evolution algorithm. In: Proceedings of national conference on advances in electrical energy applications, Jan 3–4 2013Google Scholar
  62. 62.
    Baijal A, Chauhan VS, Jayabarathi T (2011) IJCSI Int J Comput Sci 8(4):1Google Scholar
  63. 63.
    Tankasala GR Artificial bee colony optimisation for economic load dispatch of a modern power system. Int J Sci Eng Res 3(1)Google Scholar
  64. 64.
    Bommirani B, Thenmalar K (2013) Optimization technique for the economic dispatch in power system operation. Proceedings of national conference on advances in electrical energy applications, Jan 3–4 2013Google Scholar
  65. 65.
    Musirin I et al (2008) Ant colony optimization (ACO) technique in economic power dispatch problems. In: Proceedings of the international multi-conference of engineers and computer scientists (IMECS), vol 2I, Hong Kong 19–21 March 2008Google Scholar
  66. 66.
    Rahmat NA, Musirin I, Abidin AF (2013) Differential evolution immunized ant colony optimization (DEIANT) technique in solving weighted economic load dispatch problem. Asian Bull Eng Sci Technol (ABEST) 1(1):17–26Google Scholar
  67. 67.
    Effatnejad R, Aliyari H, Tadayyoni, Abdollahshirazi A (2013) Int J Techn Phys Probl Eng (IJTPE) 5(15):2Google Scholar
  68. 68.
    Rahmat NA, Musirin I (2013) Differential evolution immunized ant colony optimization technique in solving economic load dispatch problem. Sci Res 5(1B)Google Scholar
  69. 69.
    Vasovala PJ, Jani CY, Ghanchi VH, Bhavsar PHK (2014) Application of ant colony optimization technique in economic load dispatch problem for IEEE-14 Bus System. IJSRD—Int J Sci Res Dev 2(2)Google Scholar
  70. 70.
    Mishra NK et al (2011) Economic dispatch of electric power using clone optimization technique. Elixir Electr Eng 40:5155–5158Google Scholar
  71. 71.
    Padmini S, Sekhar Dash S, Vijayalakshmi, Chandrasekar S (2013) Comparison of simulated annealing over differential evolutionary technique for 38 unit generator for economic load dispatch problem. In: Proceedings of national conference on advances in electrical energy applications, 3–4 Jan 2013Google Scholar
  72. 72.
    Swain RK, Sahu NC, Hota PK (2012) Gravitational search algorithm for optimal economic dispatch. In: 2nd international conference on communication, computing and amp; security, vol 6, pp 411–419Google Scholar
  73. 73.
    Serapião ABS (2013) Cuckoo search for solving economic dispatch load problem. Intell Control Autom 4(4):385–390CrossRefGoogle Scholar
  74. 74.
    Tomassini M (1999) Parallel and distributed evolutionary algorithms: a review. In: Miettinen K, M¨akel¨a M, Neittaanm¨aki P, Periaux J (eds) Evolutionary algorithms in engineering and computer science, pp 113–133. Wiley, ChichesterGoogle Scholar
  75. 75.
    Nada MA, AL-Salami N (2009) System evolving using ant colony optimization algorithm. J Comput Sci 5(5):380–387Google Scholar
  76. 76.
    Dorigo M, Ganbardella L (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66CrossRefGoogle Scholar
  77. 77.
    Younes M, Hadjeri S, Zidi S, Laarioua S (2009) Economic power dispatch using an ant colony optimization method. In: The 10th international conference on sciences and techniques of automatic control & computer engineering ~ STA, Hammamet, Tunisia, pp 20–22, Dec 2009Google Scholar
  78. 78.
    Dorigo M (1992) Optimization, learning and natural algorithms. PhD Thesis, Dipartimento di Elettronica, Politecnico di Milano, ItalyGoogle Scholar
  79. 79.
    Sonmez Y (2011) Multi-objective environmental/ economic dispatch solution with penalty factor using Artificial Bee Colony algorithm. Sci Res Essays 6(13):2824–2831Google Scholar
  80. 80.
    Sudhakara Reddy K, Damodar Reddy M (2012) Economic load dispatch using firefly algorithm. Int J Eng Res Appl (IJERA) 2:2325–2330Google Scholar
  81. 81.
    Apostolopoulos T, Vlachos A (2011) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Comb 1(3):1–23MathSciNetGoogle Scholar
  82. 82.
    Wood, AJ, Wollenberg BF (1984) Example problem 4e. Power Generation, Operation and Control, pp 85–88. WileyGoogle Scholar
  83. 83.
    Bhattacharya A, Chattopadhyay PK (2010) Biogeography-based optimization for different economic load dispatch problems. IEEE Trans Power Syst 25:1064–1073. http://ieeexplore.ieee.org/xpl/tocpreprint.jsp
  84. 84.
    Rashedi E, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248Google Scholar
  85. 85.
    Farhat IA, Hawary E (2012) Multi-objective economic-emission optimal load dispatch using bacterial foraging algorithm. In: 25th IEEE Canadian conference on electrical and computer engineering (CCECE)Google Scholar
  86. 86.
    Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Magaz 22(3):52–67CrossRefMathSciNetGoogle Scholar
  87. 87.
    Aruldoss Albert Victoire T, Ebenezer Jeyakumar A (2003) Hybrid PSO-DS for non-convex economic dispatch problems. In: Digest of the proceedings of the WSEAS conferences, Nov 2003Google Scholar
  88. 88.
    Lee SC, Kim YH (2002) An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints. Electr Power Syst Res 60:167–177CrossRefGoogle Scholar
  89. 89.
    Won J-R, Park Y-M (2012) Economic dispatch solutions with piece-wise quadratic cost functions using improve genetic algorithm. Electr Power Energy Syst 25:355–361Google Scholar
  90. 90.
    Park JH, Yang SO, Lee HS, Park M (1996) Economic load dispatch using evolutionary algorithms. IEEE Proc 441–445Google Scholar
  91. 91.
    dos Santos Coelho L, Mariani VC (2007) Economic dispatch optimization using hybrid chaotic particle swarm optimizer. In: IEEE international conference systems, man and Cybernetics, ISIC 2007Google Scholar
  92. 92.
    Bertsekas DB (1976) On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans Autom Control 21(2):74–184CrossRefMathSciNetGoogle Scholar
  93. 93.
    Hénon MA (1976) A two-dimensional mapping with a strange attractor. Commun Math Phys 50:69–77CrossRefMATHGoogle Scholar
  94. 94.
    Reynolds RG (1994) An introduction to cultural algorithms. In: Proceedings of the third annual conference on evolutionary programming, SanDiego, CA, USA, pp 131–139Google Scholar
  95. 95.
    Muthu Vijaya Pandian S, Thanushkodi K (2010) Int J Comput Electr Eng 2(3):1793–8163Google Scholar
  96. 96.
    Younes M, Benhamida F (2011) PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN:0033-2097, R. 87 NR 10/2011Google Scholar
  97. 97.
    Younes M, Hadjeri S, Zidi S, Houari S, Laarioua M (2009) Economic power dispatch using an ant colony optimization method. In: 10th International conference on sciences and techniques of automatic control & computer engineering, Hammamet, Tunisia, pp 785–794 Dec 20–22Google Scholar
  98. 98.
    Bouzeboudja H, Chaker A, Allali A, Naama B (2005) Economic dispatch solution using a real-coded genetic algorithm. Acta Electrotechnica et Informatica 5(4)Google Scholar
  99. 99.
    Soni N, Dr Pandit M (2012) A fuzzy adaptive hybrid particle swarm optimization algorithmt to solve non-convex economic dispatch problem. Int J Engineering Innov Technol (IJEIT) 1(4)Google Scholar
  100. 100.
    Manteaw ED, Abungu Odero N (2012) Multi-objective environmental/economic dispatch solution using ABC_PSO hybrid algorithm. Int J Sci Res Publ 2(12)Google Scholar
  101. 101.
    Bharathkumar S, Arul Vineeth AD, Ashokkumar K, Vijay Anand K (2013) Multi objective economic load dispatch using hybrid fuzzy, bacterial Foraging-Nelder–Mead algorithm. Int J Electr EngTechnol 4(3):43–52Google Scholar
  102. 102.
    Ashouri M, Hosseini SM (2013) Application of new hybrid particle swarm optimization and gravitational search algorithm for non convex economic load dispatch problem. J Adv Comput Res Quart 4(2):41–51Google Scholar
  103. 103.
    Dubey HM, Pandit M, Panigrahi BK, Udgir M (2013) Economic load dispatch by hybrid swarm intelligence based gravitational search algorithm. Int J Intell Syst Appl 5(08):21–32Google Scholar
  104. 104.
    Amjadi N, Sharifzadeh H (2010) Solution of nonconvex economic dispatch problem considering valve loading effect by a new modified differential evolution algorithm. Electr Power Energy SystGoogle Scholar
  105. 105.
    Biswas A (2009) Hybrid artificial intelligence systems lecture notes in computer science 5572:252–260Google Scholar
  106. 106.
    Lampinen J, Zelinka I (2000) On stagnation of the differential evolution algorithm. In: Proceedings of MENDEL, 6th International Mendel Conference on Soft Computing, Brno, Czech RepublicGoogle Scholar
  107. 107.
    Nadeem Malik T, ul Asar A, Wyne MF, Akhtar S (2010) A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects. Electr Power Syst Res 80(9):1128–1136Google Scholar
  108. 108.
    Malik TN, Abbasi AQ, Ahmad A (2006) Computational framework for power economic dispatch using genetic algorithm. In: Proceeding of the third international conference on informatics in control, automation and robotics (ICINCO), pp 191–194. Stubal, Portugal, Aug 1–5Google Scholar
  109. 109.
    Wood AJ, Wollenberg BF (1996) Power Generation Operation and Control. John Wiley, New YorkGoogle Scholar
  110. 110.
    Pai MA (2006) Computer techniques in power system analysis. Tata McGraw-Hill, New DelhiGoogle Scholar
  111. 111.
    Narayana PP, Latha K (2004) Evolutionary programming based economic power dispatch solutions with independent power producers. In: IEEE international conference on electric utility deregulation, restructuring and power technologies (DRPT), pp 172–177Google Scholar
  112. 112.
    Bhattacharya A, Chattopadhyay PK (2010) Hybrid differential evolution with biogeography based optimization for solution of economic load dispatch. IEEE Trans Power Syst 25(4)Google Scholar
  113. 113.
    Selvakumar I, Thanushkodi K (2007) A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst 22(1):42–51CrossRefGoogle Scholar
  114. 114.
    Chiang CL (2005) Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels. IEEE Trans Power Syst 20(4):1690–1699CrossRefGoogle Scholar
  115. 115.
    Hosseini MM, Ghorbani H, Rabii A, Anvari Sh (2012) A novel heuristic algorithm for solving non-convex economic load dispatch problem with non-smooth cost function. J Basic Appl Sci Res 2(2):1130–1135Google Scholar
  116. 116.
    Soroudi A, Ehsan M, Zareipour H (2011) A practical eco-environmental distribution network planning model including fuel cells and non-renewable distributed energy resources. Renew Energy 36:179–188CrossRefGoogle Scholar
  117. 117.
    Jain LC, Palade V, Srinivasan D (2007) Advances in evolutionary computing for system design. In: Studies in computational intelligence, vol 66. SpringerGoogle Scholar
  118. 118.
    Koodalsamy C, Simon SP (2013) Fuzzied artificial bee colony algorithm for nonsmooth and nonconvex multiobjective economic dispatch problem. Turkish J Electr Eng Comput Sci 21:1995–2014CrossRefGoogle Scholar
  119. 119.
    Younes M (2013) A novel hybrid FFA-ACO algorithm for economic power dispatch. Control Eng Appl Inf 15(2):67–77Google Scholar
  120. 120.
    Sayah S, Zehar K (2008) Modified differential evolution algorithm for optimal power flow with non-smooth cost functions. Energy Convers Manag 49:3036–3042CrossRefGoogle Scholar

Copyright information

© Springer India 2016

Authors and Affiliations

  • Dipankar Santra
    • 1
  • Arindam Mondal
    • 1
  • Anirban Mukherjee
    • 1
  1. 1.RCC Institute of Information TechnologyKolkataIndia

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