Skip to main content

Multi-objective optimal power flow using a new heuristic optimization algorithm with the incorporation of renewable energy sources


The current research study proposes a multi-objective optimal power flow (OPF) solution using a modified Interior Search Algorithm in which Levy Flight feature with two different strategies is incorporated to accelerate the convergence speed and to enhance solution quality. In traditional OPF problems, the thermal generation units alone are accounted, whereas the security challenges faced by the network are mostly ignored. In other terms, the emission needs to be significantly reduced in terms of environmental sustainability aspects. So, the electrical grid must be infused with power generated from different renewable energy sources. Consequently, the current research article proposes an approach in order to accomplish OPF through a combination of stochastic wind and solar power coupled with traditional thermal power generators in the system. The authors leveraged modified IEEE 30-bus system, IEEE 118-bus system and real-time electrical network 62-bus Indian Utility System in order to validate the Levy Interior Search Algorithm proposed in the study by incorporating renewable energy sources. During implementation, the researchers considered different factors such as network security limitations, for instance transmission line capacity, bus voltage limits and restricted operation zones for thermal units. The simulation results obtained using the proposed LISA Strategy-II algorithm are compared with the results obtained using LISA Strategy-I, ISA and other optimization algorithms reported in the literature. The results achieved from the implementation infer that the proposed method has inherently good convergence characteristic and affords better exploration of the Pareto front.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41
Fig. 42


h :


t :



Economic load dispatch


Optimal power flow


Modified honey bee mating optimization


Particle swarm optimization


Differential evolution


Shuffled frog leaping algorithm


Modified SFLA


Sequential quadratic programming


Evolutionary programming


Modified evolutionary programming


Teaching learning-based optimization


Quasi-oppositional-based TLBO


Innovative tribe-modified differential evolution


Interior search algorithm


Levy ISA


Hybrid EP, PSO and SQP


Biogeography-based optimization


Hybrid DE and BBO


Glowworm swarm optimization


Weighted sum method incorporated GSO


Glowworm swarm optimization with TOPSIS


Technique for order preference by similarity to the ideal solution


Genetic algorithm


Flower pollination algorithm


Mine blast algorithm


Parallel synchronous PSO


Cuckoo search


Improved cuckoo search


Power search algorithm


Forward search approach


Hybrid PSA and FSA


Artificial bee colony


Hybrid ABC and PSO


Success history-based parameter adaptation technique of differential evolution


Superiority of feasibility solutions


Summation-based multi-objective differential evolution


Multi-objective evolutionary algorithm based on decomposition


Evolutionary multi-objective crowding algorithm


Pareto differential evolution


Gravitational search algorithm


Strength Pareto evolutionary algorithm 2


Hopfield modeling framework


Opposition-based harmony search


Modified bacterial foraging algorithm


Non-dominated sorting genetic algorithm II


Evolutionary PSO


Differential evolutionary PSO


Independent system operator


Moth swarm algorithm


Backtracking search algorithm


Differential search algorithm


Thermal generator


Probability density function


Prohibited operating zone




Distributed generation


Wind turbine


Not available


  1. 1.

    Mojica-Nava, E., Rivera, S., Quijano, N.: Game-theoretic dispatch control in microgrids considering network losses and renewable distributed energy resources integration. IET Gener. Transm. Distrib. 11(6), 1583–1590 (2017)

    Article  Google Scholar 

  2. 2.

    Lu, X., Liu, N., Chen, Q., Zhang, J.: Multi-objective optimal scheduling of a DC micro-grid consisted of PV system and EV charging station. In: 2014 IEEE Innovative Smart Grid Technologies—Asia (ISGT ASIA), Kuala Lumpur, Malaysia, 20–23 May, (2014)

  3. 3.

    Frank, S., Rebennack, S.: An introduction to optimal power flow: theory formulation, and examples. IIE Trans. 48(12), 1172–1197 (2016)

    Article  Google Scholar 

  4. 4.

    Abdi, H.: Soheil Derafshi Beigvand, Massimo La Scala, A review of optimal power flow studies applied to smart grids and microgrids. Renew. Sustain. Energy Rev. 71(1), 742–766 (2017)

    Article  Google Scholar 

  5. 5.

    Samakpong, T., Ongsakul, W., Manjiparambil, N.M.: Optimal power flow incorporating renewable uncertainty related opportunity costs. Comput. Intell. 1, 26 (2020).

    Article  Google Scholar 

  6. 6.

    Abbasi, M., Abbasi, E., Mohammadi-Ivatloo, B.: Single and multi-objective optimal power flow using a new differential-based harmony search algorithm. J. Ambient Intell. Human Comput. (2020).

    Article  Google Scholar 

  7. 7.

    Surender Reddy, S., Bijwe, P.R.: Multi-objective optimal power flow using efficient evolutionary algorithm. Int. J. Emerg. Electr. Power Syst. 18(2), 0233 (2016).

    Article  Google Scholar 

  8. 8.

    Arul, R., Ravi, G., Velusami, S.: Solving optimal power flow problems using chaotic self-adaptive differential harmony search algorithm. Electr. Power Compon. Syst. 48, 782–805 (2013)

    Article  Google Scholar 

  9. 9.

    Biswas, P.P., Suganthan, P.N., Mallipeddi, R., Amaratunga, G.A.J.: Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms. Soft Comput 24, 2999–3023 (2020)

    Article  Google Scholar 

  10. 10.

    Bai, W., Ekeb, I., Lee, K.Y.: An improved artificial bee colony optimization algorithm based on orthogonal learning for optimal power flow problem. Control. Eng. Pract. 61, 163–172 (2017)

    Article  Google Scholar 

  11. 11.

    Hmida, J.B., Chambers, T., Lee, J.: Solving constrained optimal power flow with renewables using hybrid modified imperialist competitive algorithm and sequential quadratic programming. Electr. Power Syst. Res. 177, 105989 (2019)

    Article  Google Scholar 

  12. 12.

    Hmida, J.B., Morshed, M.J., Lee, J., Chambers, T.: Hybrid imperialist competitive and grey wolf algorithm to solve multi-objective optimal power flow with wind and solar units. Energies 11(11), 2891 (2018).

    Article  Google Scholar 

  13. 13.

    Chen, G., Qian, J., Zhang, Z., Li, S.: Application of modified pigeon-inspired optimization algorithm and constraint-objective sorting rule on multi-objective optimal power flow problem. Appl. Soft Comput. J. 92, 106321 (2020)

    Article  Google Scholar 

  14. 14.

    Panda, A., Mishra, U., Tseng, M.-L., Ali, M.H.: Hybrid power systems with emission minimization: multi-objective optimal operation. J. Clean. Prod. 268, 121418 (2020)

    Article  Google Scholar 

  15. 15.

    Hu, F., Hughes, K.J., Ma, L., Pourkashanian, M.: Combined economic and emission dispatch considering conventional and wind power generating units. Int. Trans. Electr. Energy Syst. 27(12), etep.2424 (2017)

    Article  Google Scholar 

  16. 16.

    Naidji, M., Boudour, M.: Stochastic multi-objective optimal reactive power dispatch considering load and renewable energy sources uncertainties: a case study of the Adrar isolated power system. Int. Trans. Electr. Energy Syst. 30(6), e12374 (2020)

    Article  Google Scholar 

  17. 17.

    Sharifzadeh, H., Amjady, N.: Stochastic security-constrained optimal power flow incorporating preventive and corrective actions. Int. Trans. Electr. Energy Syst. 26(11), 2207 (2016)

    Article  Google Scholar 

  18. 18.

    Taher, M.A., Kamel, S., Jurado, F., Ebeed, M.: An improved moth‐flame optimization algorithm for solving optimal power flow problem. Int. Trans. Electr. Energy Syst. 29(3), e2743 (2018)

  19. 19.

    Li, S., Gong, W., Wang, L., Yan, X., Hu, C.: Optimal power flow by means of improved adaptive differential evolution. Energy 198(1), 117314 (2020)

  20. 20.

    Kahourzade, S., Mahmoudi, A., Mokhlis, H.B.: A comparative study of multi-objective optimal power flow based on particle swarm, evolutionary programming, and genetic algorithm. Electr. Eng. 97, 1–12 (2015)

    Article  Google Scholar 

  21. 21.

    Ye, C.-J., Huang, M.-X.: Multi-objective optimal power flow considering transient stability based on parallel NSGA-II. IEEE Trans. Power Syst. 30(2), 857–866 (2015)

    Article  Google Scholar 

  22. 22.

    Gandomi, A.H.: Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans. 53(4), 1168–1183 (2014)

  23. 23.

    Karthik, N., Parvathy, A.K., Arul, R.: Multi-objective economic emission dispatch using interior search algorithm. Int. Trans. Electr. Energy Syst. 29, e2683 (2019)

    Article  Google Scholar 

  24. 24.

    Karthik, N., Parvathy, A.K., Arul, R., Padmanathan, K.: Economic load dispatch in a microgrid using interior search algorithm. In: International Conference on Power and advanced computing, i-PACT 2019 (2019)

  25. 25.

    Biswas, P.P., Suganthan, P.N., Amaratunga, G.A.J.: Optimal power flow solutions incorporating stochastic wind and solar power. Energy Convers. Manag. 148(1), 1194–1207 (2017)

    Article  Google Scholar 

  26. 26.

    Abdullah, M., Javaid, N., Khan, I.U., Khan, Z.A., Chand, A., Ahmad, N.: Optimal power flow with uncertain renewable energy sources using flower pollination algorithm. In: Advances in Intelligent Systems and Computing, pp. 95–107 (2020)

  27. 27.

    Abdullah, M., Javaid, N., Chand, A., Khan, Z.A., Waqas, M., Abbas, Z.: Multi-objective optimal power flow using improved multi-objective multi-verse algorithm. In: Advances in Intelligent Systems and Computing, pp. 1071–1093 (2019)

  28. 28.

    Biswas, P.P., Suganthan, P.N., Qu, B.Y., Amaratunga, G.A.J.: Multiobjective economic-environmental power dispatch with stochastic wind-solar small hydro power. Energy 150(1), 1039–1057 (2018)

    Article  Google Scholar 

  29. 29.

    Chang, T.P.: Investigation on frequency distribution of global radiation using dierent probability density functions. Int. J. Appl. Sci. Eng. 8(2), 99–107 (2010)

    Google Scholar 

  30. 30.

    Surender, R.S., Bijwe, P.R., Abhyankar, A.R.: Real-time economic dispatch considering renewable power generation variability and uncertainty over scheduling period. IEEE Syst. J. 9(4), 1440–1451 (2014)

    Article  Google Scholar 

  31. 31.

    Never, M.: Flood frequency analysis using the Gumbel distribution. Int. J. Comput. Sci. Eng. 3(7), 2774e8 (2011)

    Google Scholar 

  32. 32.

    Pieter, C.: River flow prediction through rainfall runoff modelling with a probability-distributed model (PDM) in Flanders, Belgium. Agric. Water Manag. 95(7), 859e68 (2008)

    Google Scholar 

  33. 33.

    Gnanadass, R., Padhy, N.P., Manivannan, K.: Assessment of available transfer capability for practical power systems with combined economic emission dispatch. Electr. Power Syst. Res. 69, 267–276 (2004)

    Article  Google Scholar 

  34. 34.

    Yang, X.-S.: Engineering optimization an introduction with metaheuristic applications, 1st edn. Wiley, New Jersey (2010)

    Book  Google Scholar 

  35. 35.

    Mandal, B., Kumar Roy, P.: Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization. Appl. Soft Comput. J. (2014).

    Article  Google Scholar 

  36. 36.

    Duman, S., Rivera, S., Li, J., Wu, L.: Optimal power flow of power systems with controllable wind-photovoltaic energy systems via differential evolutionary particle swarm optimization. Int. Trans. Electr. Energy Syst. 30, e12270 (2019)

    Google Scholar 

  37. 37.

    Yao, F., Dong, Z.Y., Meng, K., Xu, Z., Iu, H.H.C., Wong, K.P.: Quantum-inspired particle swarm optimization for power system operations considering wind power uncertainty and carbon tax in Australia. IEEE Trans. Ind. Inf. 8(4), 880–888 (2012)

    Article  Google Scholar 

  38. 38.

    Man-Im, A., Ongsakul, W., Singh, J.G., Nimal Madhu, M.: Multi-objective optimal power flow considering wind power cost functions using enhanced PSO with chaotic mutation and stochastic weights. Electr. Eng. 101(1), 699–718 (2019)

    Article  Google Scholar 

  39. 39.

    Yang, X.-S., Deb, S.: Multi-objective cuckoo search for design optimization. Comput. Oper. Res. 40(6), 1616–1624 (2013)

    MathSciNet  Article  Google Scholar 

  40. 40.

    IEEE 118-bus test system data

  41. 41.

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

    Article  Google Scholar 

  42. 42.


  43. 43.

    Gnanadass, R., Venkatesh, P., Padhy, N.P.: evolutionary programming based optimal power flow for units with non-smooth fuel cost functions. Electr. Power Compon. Syst. 33(3), 349–361 (2004).

    Article  Google Scholar 

  44. 44.

    Hakli, H., Uguz, H.: A novel particle swarm optimization algorithm with Levy flight. Appl. Soft Comput. 23(1), 333–345 (2014)

    Article  Google Scholar 

  45. 45.

    Chechkin, A.V., Metzler, R., Klafter, J., Gonchar, V.Y.: Introduction to the theory of levy flights. In: Klages, R., Radons, G., Sokolov, I.M. (eds.) Anomalous Transport: Foundations and Applications, pp. 129–162. Wiley, London (2008)

    Chapter  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Nagarajan Karthik.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Karthik, N., Parvathy, A.K., Arul, R. et al. Multi-objective optimal power flow using a new heuristic optimization algorithm with the incorporation of renewable energy sources. Int J Energy Environ Eng (2021).

Download citation


  • Levy interior search algorithm
  • Optimal power flow
  • Multi-objective optimization
  • Emission
  • Renewable energy sources
  • Probability density function