Application of NSGA-II in Solving Multiobjective Optimal Power Flow


T. Malakar
N. Sinha
S. K. Goswami
A. K. Sinha


This paper is an application of NSGA-II for solving multiobjective optimal power flow problems in power systems. Objective functions considered in this work are conventional quadratic cost and emission along with highly non-linear features like cost curve with valve point loading and cubic emission function etc. In addition, more than two objectives are optimized simultaneously. The problem is formulated as mixed integer one with both continuous and discrete control variables. The performance of the proposed algorithm has been tested on three different IEEE test systems. Results for the test system-1 have been validated with the reported works. The comparison is done with the classical weighted sum method for IEEE-30 bus system and further experimentation is done on two other test cases such as IEEE-57 bus and IEEE-118 bus systems. The results demonstrate the effectiveness of the proposed approach for finding the Power System optimal solutions even when more than two confl icting objectives are considered simultaneously.


How to Cite
Malakar, T., Sinha, N., Goswami, S. K., & Sinha, A. K. (2011). Application of NSGA-II in Solving Multiobjective Optimal Power Flow. Power Research - A Journal of CPRI, 171–186. Retrieved from


  1. . Dommel H W, Tinney W F. “Optimal power fl ow solutions”, IEEE, Trans. Power Apparatus Syst., Vol. PAS–87, pp. 1866–1876, 1968.
  2. Bjelogrlic M, Calovic M S, Babic B S and Ristanovic P. “Application of newton’s optimal power fl ow in voltage/reactive power Control”, IEEE, 1989.
  3. Pai M A. “Computer techniques in power system analysis”, Second Edition Tata McGraw-Hill.
  4. Wood A J and Wallenberg B F. “Power generation operation and control”, John Wiley & Sons, Inc.
  5. AlRashidi M R and El-Hawary M E. “Hybrid particle swarm optimization approach for solving the discrete OPF problem considering the valve loading effects”, IEEE, Trans. Power Syst., Vol. 22, No. 4, 2007.
  6. Todorovski M and Rajicic D. “An initialization procedure in solving optimal power fl ow by genetic algorithm”, IEEE, Trans Power Syst., Vol. 21, No. 2, 2006.
  7. AlRashidi M R and El-Hawary M E. “Applications of computational intelligent techniques for solving the revived optimal power fl ow problem”, Electric Power Sys. Res., Vol. 79, No. 4, 2009.
  8. Jason Y and Wong Kit Po. “Evolutionary programming based optimal power fl ow algorithm”, IEEE, Trans. Power Syst., Vol. 14, No. 4, 1999.
  9. Bakirtzis G, Pandel N Bikas, Zoumas C E and Petridis V. “Optimal power fl ow by enhenced genetic algorithm”, IEEE, Trans. Power System, Vol. 17, No. 2, 2002.
  10. Venkatesh P, Gnanadass R and Padhy N P. “Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line fl ow constraints”, IEEE, Trans. Power Syst., Vol. 18, No. 2, 2003.
  11. Venkatesh P, and Lee K Y. “Multiobjective evolutionary programming economic emission dispatch problem”, IEEE, 2008.
  12. Zahavi J and Eisenberg L. “Economicenvironmental power dispatch”, IEEE, Trans. Syst. Man, Cybern., SMC-5, No. 5, 1985.
  13. Chang C S, Wong K P, and Fan B. “Securityconstrained multiobjective generation dispatch using bicriterion global optimization”. IEE Proc.-Gener. Transm. Distrib., Vol. 142, No. 4, 1995.
  14. Osman M S, Abo-Sinna M A and Mousa A A. “An ∈-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem”, Electrical Power Syst. Res., Vol. 79, No. 11, 2009.
  15. Varadarajan M and Swarup K S. “Solving multi-objective optimal power fl ow using differential evolution”, IET, Gener. Transm. Distrib., Vol. 2, No. 4, 2008.
  16. Fonseca C M and Fleming P J. “An overview of evolutionary algorithms in multiobjective optimization”, IEEE, Trans. Evol. Comput, Vol. 3, No. 1, 1999.
  17. Coello C A C. “A comprehensive servey of evolutionary-based multiobjective optimization techniques”, Knowledge Inf. Syst., Vol. 1, No. 3, 1999.
  18. Raghuwanshi M M and Kakde O G. “Survey on multiobjective evolutionary and real coded genetic algorithms”, In proceedings of the 8th Asia Pacifi c Symposium on Intelligent and Evolutionary Systems, pp. 150–161, 2004.
  19. Srinivas N and Kalyanmoy Deb. “Multiobjective function optimization using nondominated sorting in genetic algorithms”, Evol. Comp. Vol. 2, No. 3, pp. 221–248, 1995.
  20. Deb K, Pratap A, Agarwal S and Meyarivan T. “A Fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans”, Evol. Comput. Vol. 6, No. 2, pp. 182–197, 2002.
  21. Deb K and Agarwal R B. “Simulated Binary Crossover for continuous search space”, Complex Syst., Vol. 9, pp. 115–148, April 1995.
  22. Abido M A. “Multiobjective evolutionary algorithms for electric power dispatch problem”, IEEE Trans., Evol. Compu., Vol. 10, No. 3, pp. 315–329, 2006.
  23. Abido M A. “Multiobjective particle swarm optimization for environmental/economic dispatch problem elsevier”, Electrical Power Syst. Research, Vol. 79, No. 7, 2009.
  24. Qui Z, Deconinck G and Belmans R. A “Literature survey of optimal power fl ow problems in the electricity market context”, IEEE, 2009.
  25. Murugan P, Kannan S and Baskar S. “NSGA-II algorithm for multi-objective generation expansion planning problem”, Electrical Power System Research, Vol. 79, No.4, 2009.
  26. Jeyadevi S, Baskar S, Babulal C K, Iruthayarajan Willjuice M. “Solving multiobjective optimal reactive power dispatch using modifi ed NSGA-II”, International Journal of Electric Power Energy Syst., Vol. 33, No. 2, 2011.