Energy Systems

, Volume 9, Issue 2, pp 415–438 | Cite as

Economic load dispatch problem: quasi-oppositional self-learning TLBO algorithm

  • Tapan Prakash
  • V. P. Singh
  • Sugandh P. Singh
  • S. R. Mohanty
Original Paper


This paper proposes a meta-heuristic algorithm named as quasi-oppositional self-learning teacher-learner-based-optimization (QOSLTLBO) for solving non-convex economic load dispatch (ELD) problem. The ELD problem is an essential concern of power system and its main objective is to allocate optimal power generation to each generating unit so as to minimize the total cost of generation while satisfying all constraints available in the system. The problem considered in this paper is a non-convex quadratic generation cost of the units (with or without valve-point loading effects) with power balance and generation limits as the system constraints. This model of generation cost is a continuous model of the ELD problem. The proposed algorithm includes a quasi-oppositional approach for better initialization of population. A self-learning phase is added after teacher phase and learner phase of basic teacher-learner-based-optimization (TLBO) algorithm to improve the convergence rate. To prove the efficacy and robustness of proposed algorithm, it is applied to solve ELD problem on different standard IEEE generator systems and the results, thus obtained are compared with other state-of-art algorithms. The minimum total cost of generation in all the cases are obtained from the proposed algorithm which proves its effectiveness over others. The additional advantage of the proposed QOSLTLBO algorithm is that it is kept free from algorithm-specific parameters like basic TLBO.


Constraint handling Economic load dispatch Quasi-opposition Self-learning Valve-point effects 


  1. 1.
    Saadat, H.: Power System Analysis. WCB/McGraw-Hill, New York (1999)Google Scholar
  2. 2.
    El-Keib, A., Ma, H., Hart, J.: Environmentally constrained economic dispatch using the Lagrangian relaxation method. IEEE Trans. Power Syst. 9(4), 1723–1729 (1994)CrossRefGoogle Scholar
  3. 3.
    Lee, F.N., Breipohl, A.M.: Reserve constrained economic dispatch with prohibited operating zones. IEEE Trans. Power Syst. 8(1), 246–254 (1993)CrossRefGoogle Scholar
  4. 4.
    Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey II. Energy Syst. 3(3), 259–289 (2012)CrossRefGoogle Scholar
  5. 5.
    Chen, P.-H., Chang, H.-C.: Large-scale economic dispatch by genetic algorithm. IEEE Trans. Power Syst. 10(4), 1919–1926 (1995)CrossRefGoogle Scholar
  6. 6.
    Orero, S., Irving, M.R.: Economic dispatch of generators with prohibited operating zones: a genetic algorithm approach. In: IEE Proceedings of the Generation, Transmission and Distribution, pp. 529–534. IET (1996)Google Scholar
  7. 7.
    Park, J.-B., Lee, K.-S., Shin, J.-R.: A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans. Power Syst. 20(1), 34–42 (2005)CrossRefGoogle Scholar
  8. 8.
    Gaing, Z.-L.: Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans. Power Syst. 18(3), 1187–1195 (2003)CrossRefGoogle Scholar
  9. 9.
    Sinha, N., Chakrabarti, R., Chattopadhyay, P.: Evolutionary programming techniques for economic load dispatch. IEEE Trans. Evol. Comput. 7(1), 83–94 (2003)CrossRefGoogle Scholar
  10. 10.
    Yang, H.-T., Yang, P.-C., Huang, C.-L.: Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions. IEEE Trans. Power Syst. 11(1), 112–118 (1996)CrossRefGoogle Scholar
  11. 11.
    Noman, N., Iba, H.: Differential evolution for economic load dispatch problems. Electric Power Syst. Res. 78(8), 1322–1331 (2008)CrossRefGoogle Scholar
  12. 12.
    dos Santos Coelho, L., Mariani, V.C.: Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints. Energy Convers. Manag. 48(5), 1631–1639 (2007)CrossRefGoogle Scholar
  13. 13.
    Wong, K., Fung, C.: Simulated annealing based economic dispatch algorithm. In: IEE Proceedings C (Generation, Transmission and Distribution), pp. 509–515. IET (1993)Google Scholar
  14. 14.
    Vo, D.N., Schegner, P., Ongsakul, W.: Cuckoo search algorithm for non-convex economic dispatch. Gener. Transmiss. Distrib. IET 7(6), 645–654 (2013)CrossRefGoogle Scholar
  15. 15.
    Biswal, S., Barisal, A., Behera, A., Prakash, T.: Optimal power dispatch using BAT algorithm. In: 2013 International Conference on Energy Efficient Technologies for Sustainability (ICEETS), pp. 1018–1023. IEEE (2013)Google Scholar
  16. 16.
    Vijay, R.: Intelligent bacterial foraging optimization technique to economic load dispatch problem. Int. J. Soft Comput. Eng. (IJSCE), 2231–2307 (2012)Google Scholar
  17. 17.
    Niknam, T., Golestaneh, F., Sadeghi, M.S.: Multiobjective teaching-learning-based optimization for dynamic economic emission dispatch. IEEE Syst. J. 6(2), 341–352 (2012)CrossRefGoogle Scholar
  18. 18.
    Yang, X.-S., Hosseini, S.S.S., Gandomi, A.H.: Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl. Soft Comput. 12(3), 1180–1186 (2012)CrossRefGoogle Scholar
  19. 19.
    Pothiya, S., Ngamroo, I., Kongprawechnon, W.: Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints. Energy Convers. Manag. 49(4), 506–516 (2008)CrossRefGoogle Scholar
  20. 20.
    dos Santos Coelho, L., Mariani, V.C.: An improved harmony search algorithm for power economic load dispatch. Energy Convers. Manag. 50(10), 2522–2526 (2009)CrossRefGoogle Scholar
  21. 21.
    Özyön, S., Aydin, D.: Incremental artificial bee colony with local search to economic dispatch problem with ramp rate limits and prohibited operating zones. Energy Convers. Manag. 65, 397–407 (2013)CrossRefGoogle Scholar
  22. 22.
    Mandal, B., Roy, P.K., Mandal, S.: Economic load dispatch using Krill Herd algorithm. Int. J. Electr. Power Energy Syst. 57, 1–10 (2014)CrossRefGoogle Scholar
  23. 23.
    Bhattacharya, A., Chattopadhyay, P.K.: Biogeography-based optimization for different economic load dispatch problems. IEEE Trans. Power Syst. 25(2), 1064–1077 (2010)CrossRefGoogle Scholar
  24. 24.
    Boroojeni, K.G., Amini, M.H., Iyengar, S.S., Rahmani, M., Pardalos, P.M.: An economic dispatch algorithm for congestion management of smart power networks. Energy Syst., 1–25 (2016). doi: 10.1007/s12667-016-0224-6
  25. 25.
    Duman, S., Güvenç, U., Yörükeren, N.: Gravitational search algorithm for economic dispatch with valve-point effects. Int. Rev. Electr. Eng. 5(6), 2890–2895 (2010)Google Scholar
  26. 26.
    Pandi, V.R., Panigrahi, B.K.: Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm. Expert Syst. Appl. 38(7), 8509–8514 (2011)CrossRefGoogle Scholar
  27. 27.
    Victoire, T.A.A., Jeyakumar, A.E.: Hybrid PSO-SQP for economic dispatch with valve-point effect. Electric Power Syst. Res. 71(1), 51–59 (2004)CrossRefGoogle Scholar
  28. 28.
    Chakraborty, S., Senjyu, T., Yona, A., Saber, A.Y., Funabashi, T.: Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation. Gener. Transmiss. Distrib. IET 5(10), 1042–1052 (2011)CrossRefGoogle Scholar
  29. 29.
    Niknam, T.: A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem. Appl. Energy 87(1), 327–339 (2010)CrossRefGoogle Scholar
  30. 30.
    He, D., Wang, F., Mao, Z.: A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect. Int. J. Electr. Power Energy Syst. 30(1), 31–38 (2008)CrossRefGoogle Scholar
  31. 31.
    Sinha, N., Purkayastha, B.: PSO embedded evolutionary programming technique for nonconvex economic load dispatch. In: Power Systems Conference and Exposition, 2004. IEEE PES 2004, pp. 66–71. IEEE (2004)Google Scholar
  32. 32.
    Bayat, M., Rahimpour, M.R.: Dynamic optimal analysis of a novel cascade membrane methanol reactor by using genetic algorithm (GA) method. Energy Syst. 4(2), 137–164 (2013). doi: 10.1007/s12667-012-0070-0 CrossRefGoogle Scholar
  33. 33.
    Samal, P., Ganguly, S., Mohanty, S.: Planning of unbalanced radial distribution systems using differential evolution algorithm. Energy Syst., 1–22 (2016). doi: 10.1007/s12667-016-0202-z
  34. 34.
    Gürbüz, F., Öztürk, C., Pardalos, P.: Prediction of electricity energy consumption of Turkey via artificial bee colony: a case study. Energy Syst. 4(3), 289–300 (2013). doi: 10.1007/s12667-013-0079-z CrossRefGoogle Scholar
  35. 35.
    Rao, R.V., Savsani, V.J., Vakharia, D.: Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011)CrossRefGoogle Scholar
  36. 36.
    Rao, R.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016)MathSciNetGoogle Scholar
  37. 37.
    Yan, J., Li, K., Bai, E., Yang, Z., Foley, A.: Time series wind power forecasting based on variant Gaussian Process and TLBO. Neurocomputing (2016)Google Scholar
  38. 38.
    Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evolut. Comput. 4(1), 1–32 (1996)CrossRefGoogle Scholar
  39. 39.
    Tizhoosh, H.R.: Opposition-based learning: a new scheme for machine intelligence. In: CIMCA/IAWTIC 2005, pp. 695–701 (2005)Google Scholar
  40. 40.
    Peng, L., Wang, Y.: Differential evolution using uniform-quasi-opposition for initializing the population. Inf. Technol. J. 9(8), 1629–1634 (2010)CrossRefGoogle Scholar
  41. 41.
    Zhile, Y., Kang, L., Qun, N., Yusheng, X., Foley, A.: A self-learning TLBO based dynamic economic/environmental dispatch considering multiple plug-in electric vehicle loads. J. Mod. Power Syst. Clean Energy 2(4), 298–307 (2014)CrossRefGoogle Scholar
  42. 42.
    Aragón, V., Esquivel, S., Coello, C.C.: An immune algorithm with power redistribution for solving economic dispatch problems. Inf. Sci. 295, 609–632 (2015)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, New York, pp. 39–43 (1995)Google Scholar
  44. 44.
    Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Price, K., Storn, R.: Differential Evolution—A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Space. Intenational Computer Science Institute, Berkeley (1995)zbMATHGoogle Scholar
  46. 46.
    Mohamed, A.W.: An improved differential evolution algorithm with triangular mutation for global numerical optimization. Comput. Ind. Eng. 85, 359–375 (2015)CrossRefGoogle Scholar
  47. 47.
    Brest, J., Greiner, S., Bošković, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evolut. Comput. 10(6), 646–657 (2006)CrossRefGoogle Scholar
  48. 48.
    Huang, J., Li, X., Gao, L.: A new hybrid algorithm for unconstrained optimisation problems. Int. J. Comput. Appl. Technol. 46(3), 187–194 (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Electrical EngineeringNational Institute of TechnologyRaipurIndia
  2. 2.Department of Electrical EngineeringMotilal Nehru National Institute of TechnologyAllahabadIndia

Personalised recommendations