Multiobjective Economic Load Dispatch Studies in 2-D and 3-D Space by Particle Swarm Optimization Technique

  • N. K. JainEmail author
  • Uma Nangia
  • Jyoti Jain
Original Contribution


In this paper, three important objectives of power systems—cost of generation (FC), system transmission losses (FL) and environmental emissions (FE)—have been considered. The multiobjective economic load dispatch problem has been formulated using weighting method. The noninferior set for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems has been generated using particle swarm optimization technique. The noninferior set obtained has been displayed in 3-D space considering all the three objectives and in 2-D space all the combinations of two objectives, viz. for FC & FL, FC & FE and FL & FE for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems. The target point or best compromise solution has been obtained by maximizing the minimum relative attainments of all the objectives.


Optimization Maximization of minimum relative attainment Noninferior set Ideal point Target point 



Objective function to be optimized


Cost of generation, measured in $/h


Transmission losses, measured in MW


Cost of environmental emission, measured in kg/h

ai, bi, ci

Cost coefficients of ith generator

di, ei, fi

Emission coefficients of ith generator


Active power generation of the ith generator


Maximum power generation limit of ith generator


Minimum power generation limit of ith generator


Total power demand


Penalty factor


Total number of generators in the system

Bij, Boi, Boo

Loss coefficients


Number of particles in the swarm


Velocity of jth particle of ith generator at kth iteration


Inertia weight factor

Cp, Cg

Acceleration coefficients

rp, rg

Random numbers between 0 and 1

\(\it \it x_{ij}^{k}\)

Current position of jth particle of ith generator at kth iteration


Personal best position of jth particle of ith generator at kth iteration


Global best position of swarm for ith generator till kth iteration


Maximum number of iterations


Current iteration


Weight attached to cost of generation


Weight attached to transmission losses


Weight attached to environmental emissions


Maximum value of cost of generation


Minimum value of cost of generation


Maximum value of transmission losses


Minimum value of transmission losses


Maximum value of environmental emission


Minimum value of environmental emission


Function evaluation


Minimum relative attainment for cost of generation


Minimum relative attainment for transmission losses


Minimum relative attainment for environmental emission



  1. 1.
    C.L. Wadhwa, N.K. Jain, Multiple objective optimal load flow: a new perspective. IEE Proc. C 137(1), 59–64 (1990)Google Scholar
  2. 2.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Investigations of multiobjective optimal load flow study by sequential goal programming. J. IE 77, 99–103 (1996)Google Scholar
  3. 3.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Multiobjective load flow studies through maximization of minimum relative attainments. J. IE 77, 154–159 (1996)Google Scholar
  4. 4.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Surrogate worth tradeoff technique for multiobjective optimal power flows. IEE Proc. Gener. Transm. Distrib. 144(6), 547–553 (1997)CrossRefGoogle Scholar
  5. 5.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Noninferior set estimation for multiobjective optimal load flow study. J. IE 78, 229–235 (1998)Google Scholar
  6. 6.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Optimal weight assessment based on range of objectives in multiobjective optimal load flow study. IEE Proc. C 145(1), 65–69 (1998)Google Scholar
  7. 7.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Multiobjective optimal load flow based on ideal distance minimization in 3D space. Electr. Power Energy Syst. 23, 847–855 (2001)CrossRefGoogle Scholar
  8. 8.
    U. Nangia, N.K. Jain, C.L. Wadhwa, Comprehensive comparison of various multiobjective techniques. Eng. Intell. Syst. J. 11(3), 123–132 (2003)Google Scholar
  9. 9.
    N.K. Jain, U. Nangia, J. Jain, Effect of population and bit size on optimization of function by genetic algorithm, in International Conference on Computing for Sustainable Global Development, Delhi (16–18 Mar 2016), pp. 189–194Google Scholar
  10. 10.
    N.K. Jain, U. Nangia, J. Jain, GA based Multi-objective economic load dispatch by maximization of minimum relative attainments, in IEEE 5th India International Conference on Power Electronics (IICPE 2012), Delhi (Dec 2012)Google Scholar
  11. 11.
    N.K. Jain, U. Nangia, I. Singh, Multiobjective economic load dispatch in 3-D space by genetic algorithm. J. Inst. Eng. India Ser. B 98(5), 495–501 (2017)CrossRefGoogle Scholar
  12. 12.
    N.K. Jain, U. Nangia, J. Jain, An improved PSO based on initial selection of particles (ISBPSO) for economic load dispatch, in IEEE First International Conference on Power Electronics, Intelligent Control and Energy, Delhi (4–6 July 2016), pp. 1–5Google Scholar
  13. 13.
    N.K. Jain, U. Nangia, A. Jain, PSO for multiobjective economic load dispatch (MELD) for minimizing generation cost and transmission losses. J. Inst. Eng. India Ser. B 97(2), 185–191 (2015)CrossRefGoogle Scholar
  14. 14.
    N. Singh, Y. Kumar, Multiobjective economic load dispatch problem solved by new PSO. Adv. Electr. Eng. 2015, 1–6 (2015)CrossRefGoogle Scholar
  15. 15.
    M.A. Abido, Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans. Power Syst. 18(4), 1529–1537 (2003)CrossRefGoogle Scholar
  16. 16.
    M.A. Abido, Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Trans. Comput. 10(3), 315–329 (2006)Google Scholar
  17. 17.
    M.A. Abido, Multiobjective particle swarm optimization for environmental/economic dispatch problem. Electr. Power Syst. Res. 79, 1105–1113 (2009)CrossRefGoogle Scholar
  18. 18.
    A. Rey, R. Zmeureanu, Micro-time variant multi-objective particle swarm optimization (micro-TVMOPSO) of solar thermal combisystem. Swarm Evolut. Comput. 36, 76–90 (2017)CrossRefGoogle Scholar
  19. 19.
    R. Shankar, H. Mahala, Multi objective economic load dispatch using new PSO. Int. J. Eng. Sci. Comput. 6, 2250–2255 (2016)Google Scholar
  20. 20.
    B. Hadji, K. Srairi, N. Mancer, Multi-objective PSO-TVAC for environmental/economic dispatch problem. Sci. Direct Energy Procedia 74, 102–111 (2015)CrossRefGoogle Scholar
  21. 21.
    B. Taheri, G. Aghajani, M. Sedaghat, Economic dispatch in a power system considering environmental pollution using a multi-objective particle swarm optimization algorithm based on the Pareto criterion and fuzzy logic. Int. J. Energy Environ Eng. 8(2), 99–107 (2017)CrossRefGoogle Scholar
  22. 22.
    A. Man-Im, W. Ongsakul, J. GovindSingh, C. Boonchuay, Multi-objective economic dispatch considering wind power penetration using stochastic weight trade-off chaotic NSPSO. J. Electr. Power Compon. Syst. 45(14), 1525–1542 (2017)CrossRefGoogle Scholar
  23. 23.
    X. Yu, X. Yu, Y. Lu, J. Sheng, Economic and emission dispatch using ensemble multiobjective differential evolution algorithm. Sustainability 10(2), 418 (2018)CrossRefGoogle Scholar
  24. 24.
    D. Poornima, S.P. Simon, B. Sonia, T. Sunita, Multiobjective economic load dispatch problem using A-loss coefficients. Int. J. Pure Appl. Math. 114(8), 143–153 (2017)Google Scholar
  25. 25.
    M. Mohammadian, A. Lorestani, M.M. Ardehali, Optimization of single and multi-areas economic dispatch problems based on evolutionary particle swarm optimization algorithm. Sci. Direct 161, 710–724 (2018)Google Scholar
  26. 26.
    J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceedings of IEEE International Conference on Neural Networks (1995), pp. 1942–1948Google Scholar
  27. 27.
    Y. Shi, R. Eberhart, A modified particle swarm optimizer, in Proceedings of IEEE International Conference on Evolutionary Computation (1998), pp. 69–73Google Scholar

Copyright information

© The Institution of Engineers (India) 2019

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentDelhi Technological UniversityDelhiIndia

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