Modification of Harris hawks optimization algorithm with random distribution functions for optimum power flow problem


Harris hawks optimization (HHO) algorithm, which is inspired from Harris hawks hunting strategy, uses uniform random numbers in the optimization process. This paper proposes modifying HHO with seven types of random distribution function definitions that are chi-square distribution, normal distribution, exponential distribution, Rayleigh distribution, Student’s distribution, F distribution, and lognormal distribution to show effects on stochastic search-based optimization algorithm performance. The modified HHO algorithm is tested via some benchmark test functions. Results are compared with each other and with classical HHO solutions. Then, the HHO and its modified versions are applied to optimum power flow (OPF), which is an important problem for power system engineering for decades. The algorithms are applied to IEEE 30-bus test system to minimize total fuel cost of the power system, active/reactive power losses, and emission, by comparing with recent OPF researches. Considering the applicability of the proposed approach and the results achieved, one can confirm that it might be a different alternative method for solving OPF problems. One of the important results of the paper in the IEEE 30-bus test system is that the cost of fuel is calculated as 798.9105 $/h with classical HHO, while it is calculated as 798.66 $/h with the HHO modified with SD function.

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  1. 1.

    Dommel HW, Tinney WF (1968) Optimal power flow solutions. IEEE Trans Power Appar Syst 10:1866–1876.

    Article  Google Scholar 

  2. 2.

    Singh RP, Mukherjee V, Ghoshal SP (2016) Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem. Appl Soft Comput 40:161–177.

    Article  Google Scholar 

  3. 3.

    Maria GA, Findlay JA (1987) A Newton optimal power flow program for Ontario Hydro EMS. IEEE Trans Power Syst 2(3):576–582.

    Article  Google Scholar 

  4. 4.

    Fortenbacher P, Demiray T (2019) Linear/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations. Int J Electr Power Energy Syst 107:680–689

    Article  Google Scholar 

  5. 5.

    Kirchmayer LK, Stagg GW (1951) Analysis of total and incremental losses in transmission systems. Trans Am Inst Electr Eng 70(2):1197–1205.

    Article  Google Scholar 

  6. 6.

    Mota-Palomino R, Quintana VH (1986) Sparse reactive power scheduling by a penalty function-linear programming technique. IEEE Trans Power Syst 1(3):31–39.

    Article  Google Scholar 

  7. 7.

    Momoh JA, El-Hawary ME, Adapa R (1999) A review of selected optimal power flow literature to 1993: II: Newton, linear programming and interior point methods. IEEE Trans Power Syst 14(1):105–111.

    Article  Google Scholar 

  8. 8.

    Wei H, Sasaki H, Kubokawa J, Yokoyama R (1998) An interior point nonlinear programming for optimal power flow problems with a novel data structure. IEEE Trans Power Syst 13(3):870–877

    Article  Google Scholar 

  9. 9.

    Wu YC, Debs AS, Marsten RE (1994) A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Trans Power Syst 9(2):876–883.

    Article  Google Scholar 

  10. 10.

    Habibollahzadeh H, Luo GX, Semlyen A (1989) Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology. IEEE Trans Power Syst 4(2):530–537.

    Article  Google Scholar 

  11. 11.

    Burchett RC, Happ HH, Vierath DR (1984) Quadratically convergent optimal power flow. IEEE Trans Power Appar Syst 11:3267–3275

    Article  Google Scholar 

  12. 12.

    Momoh JA, Guo SX, Ogbuobiri EC, Adapa R (1994) The quadratic interior point method solving power system optimization problems. IEEE Trans Power Syst 9(3):1327–1336

    Article  Google Scholar 

  13. 13.

    Fan JY, Zhang L (1998) Real-time economic dispatch with line flow and emission constraints using quadratic programming. IEEE Trans Power Syst 13(2):320–325

    MathSciNet  Article  Google Scholar 

  14. 14.

    Abido MA (2002) Optimal power flow using particle swarm optimization. Int J Electr Power Energy Syst 24(7):563–571.

    Article  Google Scholar 

  15. 15.

    Reddy ML, Reddy MR, Reddy VV (2012) Optimal power flow using particle swarm optimization. J Eng Sci Emerg Technol 4(1):116–124

    MATH  Google Scholar 

  16. 16.

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

    Article  Google Scholar 

  17. 17.

    Ganguly S, Samajpati D (2015) Distributed generation allocation on radial distribution networks under uncertainties of load and generation using genetic algorithm. IEEE Trans Sustain Energy 6(3):688–697

    Article  Google Scholar 

  18. 18.

    Abido MA (2002) Optimal power flow using tabu search algorithm. Electric Power Compon Syst 30(5):469–483.

    Article  Google Scholar 

  19. 19.

    Kulworawanichpong T, Sujitjorn S (2002) Optimal power flow using tabu search. IEEE Power Eng Rev 22(6):37–39

    Google Scholar 

  20. 20.

    Awasthi A, Venkitusamy K, Padmanaban S, Selvamuthukumaran R, Blaabjerg F, Singh AK (2017) Optimal planning of electric vehicle charging station at the distribution system using hybrid optimization algorithm. Energy 133:70–78.

    Article  Google Scholar 

  21. 21.

    Baydar B, Gozde H, Taplamacioglu MC, Kucuk AO (2019) Resilient optimal power flow with evolutionary computation methods: short survey. In: Power systems resilience. Springer, Cham, pp 163–189

  22. 22.

    Bouchekara HR, Chaib AE, Abido MA, El-Sehiemy RA (2016) Optimal power flow using an improved colliding bodies optimization algorithm. Appl Soft Comput 42:119–131.

    Article  Google Scholar 

  23. 23.

    Duman S, Güvenç U, Sönmez Y, Yörükeren N (2012) Optimal power flow using gravitational search algorithm. Energy Convers Manag 59:86–95.

    Article  Google Scholar 

  24. 24.

    Naveen S, Kumar KS, Rajalakshmi K (2015) Distribution system reconfiguration for loss minimization using modified bacterial foraging optimization algorithm. Int J Electr Power Energy Syst 69:90–97.

    Article  Google Scholar 

  25. 25.

    Mohamed AAA, Mohamed YS, El-Gaafary AA, Hemeida AM (2017) Optimal power flow using moth swarm algorithm. Electr Power Syst Res 142:190–206.

    Article  Google Scholar 

  26. 26.

    Ayan K, Kılıç U, Baraklı B (2015) Chaotic artificial bee colony algorithm based solution of security and transient stability constrained optimal power flow. Int J Electr Power Energy Syst 64:136–147.

    Article  Google Scholar 

  27. 27.

    Chen G, Liu L, Zhang Z, Huang S (2017) Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints. Appl Soft Comput 50:58–70.

    Article  Google Scholar 

  28. 28.

    Pandiarajan K, Babulal CK (2016) Fuzzy harmony search algorithm based optimal power flow for power system security enhancement. Int J Electr Power Energy Syst 78:72–79.

    Article  Google Scholar 

  29. 29.

    Sulaiman MH, Mustaffa Z, Mohamed MR, Aliman O (2015) Using the gray wolf optimizer for solving optimal reactive power dispatch problem. Appl Soft Comput 32:286–292

    Article  Google Scholar 

  30. 30.

    Mohammadi M, Ghadimi N (2015) Optimal location and optimized parameters for robust power system stabilizer using honeybee mating optimization. Complexity 21(1):242–258

    MathSciNet  Article  Google Scholar 

  31. 31.

    Chaib AE, Bouchekara HREH, Mehasni R, Abido MA (2016) Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm. Int J Electr Power Energy Syst 81:64–77.

    Article  Google Scholar 

  32. 32.

    Duman S (2017) Symbiotic organisms search algorithm for optimal power flow problem based on valve-point effect and prohibited zones. Neural Comput Appl 28(11):3571–3585

    Article  Google Scholar 

  33. 33.

    Akdag O, Okumus F, Kocamaz AF, Yeroglu C (2018) Fractional order Darwinian PSO with constraint threshold for load flow optimization of energy transmission system. Gazi Univ J Sci 31(3):831–844

    Google Scholar 

  34. 34.

    El-Fergany AA, Hasanien HM (2018) Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons. Appl Soft Comput 64:307–316.

    Article  Google Scholar 

  35. 35.

    Raja MAZ, Shah AA, Mehmood A, Chaudhary NI, Aslam MS (2018) Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system. Neural Comput Appl 29(12):1455–1474

    Article  Google Scholar 

  36. 36.

    Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl-Based Syst 163:283–304

    Article  Google Scholar 

  37. 37.

    Ateş A, Yeroglu C (2016) Optimal fractional order PID design via Tabu Search based algorithm. ISA Trans 60:109–118

    Article  Google Scholar 

  38. 38.

    Alagoz BB, Ates A, Yeroglu C (2013) Auto-tuning of PID controller according to fractional-order reference model approximation for DC rotor control. Mechatronics 23(7):789–797

    Article  Google Scholar 

  39. 39.

    Yeroğlu C, Ateş A (2014) A stochastic multi-parameters divergence method for online auto-tuning of fractional order PID controllers. J Frankl Inst 351(5):2411–2429

    MathSciNet  Article  Google Scholar 

  40. 40.

    Ateş A, Yeroğlu C (2018) Modified artificial physics optimization for multi-parameter functions. Iran J Sci Technol Trans Electr Eng 42(4):465–478

    Article  Google Scholar 

  41. 41.

    Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Fut Gen Comput Syst 97:849–872.

    Article  Google Scholar 

  42. 42.

    Lee HM, Jung D, Sadollah A, Lee EH, Kim JH (2019) Performance comparison of metaheuristic optimization algorithms using water distribution system design benchmarks. In: Advances in intelligent systems and computing, pp 97–104

  43. 43.

    Mirjalili S, Mirjalili SM, Saremi S, Mirjalili S (2020) Whale optimization algorithm: theory, literature review, and application in designing photonic crystal filters. In: Studies in computational intelligence, pp 219–238

  44. 44.

    Matlab (2019) Accessed 26 Sept 2019

  45. 45.

    Viswanathan GM, Afanasyev V, Buldyrev SV, Havlin S, Da Luz MGE, Raposo EP, Stanley HE (2000) Lévy flights in random searches. Physica A 282(1–2):1–12

    Article  Google Scholar 

  46. 46.

    Lévy flight (2020)évy_flight. Accessed 09 April 2020

  47. 47.

    Yang XS, Deb S (2009). Cuckoo search via Lévy flights. In: World congress on nature and biologically inspired computing, pp 210–214.

  48. 48.

    Yang XS (2010) Firefly algorithm, Levy flights and global optimization. Res Dev Intell Syst.

    Article  Google Scholar 

  49. 49.

    Li Z, Zhou Y, Zhang S, Song J (2016) Lévy-flight moth-flame algorithm for function optimization and engineering design problems. Math Prob Eng.

    Article  Google Scholar 

  50. 50.

    Ates A, Alagoz BB, Chen YQ, Yeroglu C, Hassan SH (2019) Optimal fractional order PID controller design for fractional order systems by stochastic multi parameter divergence optimization method with different random distribution functions. In: The 7th international conference on control, mechatronics and automation, November 6–8, Delft, Netherlands

  51. 51.

    Niknam T, Rasoul NM, Jabbari M, Malekpour AR (2011) A modified shuffle frog leaping algorithm for multi-objective optimal power flow. Energy 36(11):6420–6432.

    Article  Google Scholar 

  52. 52.

    A data for IEEE-30 bus test system (2019) Accessed 28 Sept 2019

  53. 53.

    Reddy SS, Rathnam CS (2016) Optimal power flow using glowworm swarm optimization. Int J Electr Power Energy Syst 80:128–139.

    Article  Google Scholar 

  54. 54.

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

    Article  Google Scholar 

  55. 55.

    Pulluri H, Naresh R, Sharma V (2017) An enhanced self-adaptive differential evolution based solution methodology for multiobjective optimal power flow. Appl Soft Comput 54:229–245.

    Article  Google Scholar 

  56. 56.

    Bouchekara HREH (2014) Optimal power flow using black-hole-based optimization approach. Appl Soft Comput 24:879–888.

    Article  Google Scholar 

  57. 57.

    Liang RH, Tsai SR, Chen YT, Tseng WT (2011) Optimal power flow by a fuzzy based hybrid particle swarm optimization approach. Electr Power Syst Res 81(7):1466–1474.

    Article  Google Scholar 

  58. 58.

    Mojtaba G, Sahand G, Ebrahim AA, Azizi V (2014) Solving non-linear, non-smoothand non-convex optimal power flow problems using chaotic invasive weedoptimization algorithms based on chaos. Energy 73:340–353

    Article  Google Scholar 

  59. 59.

    Kumar AR, Premalatha L (2015) Optimal power flow for a deregulated power system using adaptive real coded biogeography-based optimization. Int J Electr Power Energy Syst 73:393–399.

    Article  Google Scholar 

  60. 60.

    El-Fergany AA, Hasanien HM (2015) Single and multi-objective optimal power flow using grey wolf optimizer and differential evolution algorithms. Electr Power Compon Syst 43(13):1548–1559.

    Article  Google Scholar 

  61. 61.

    Adaryani MR, Karami A (2013) Artificial bee colony algorithm for solving multi-objective optimal power flow problem. Int J Electr Power Energy Syst 5:219–230

    Article  Google Scholar 

  62. 62.

    Bouchekara HREH, Abido MA, Boucherma M (2014) Optimal power flow using teaching-learning-based optimization technique. Electr Power Syst Res 114:49–59.

    Article  Google Scholar 

  63. 63.

    Trivedi IN, Bhoye M, Jangir P, Parmar SA, Jangir N, Kumar A (2016) Voltage stability enhancement and voltage deviation minimization using BAT optimization algorithm. In: 3rd International conference on electrical energy systems (ICEES), pp 112–116

  64. 64.

    Raviprabakaran V, Subramanian, RC (2018) Enhanced ant colony optimization to solve the optimal power flow with ecological emission. Int J Syst Assur Eng Manag 9(1):58–65

  65. 65.

    Ongsakul W, Tantimaporn T (2006) Optimal power flow by improved evolutionary programming. Electric Power Compon Syst 34(1):79–95.

    Article  Google Scholar 

  66. 66.

    Kılıç U (2015) Backtracking search algorithm-based optimal power flow with valve point effect and prohibited zones. Electr Eng 97(2):101–110

    Article  Google Scholar 

  67. 67.

    Ozyon S, Yasar C, Ozcan G, Temurtas H (2011) An artificial bee colony algorithm (ABC) approach to nonconvex economic power dispatch problems with valve point effect. In: National conference on electrical, electronics and computer, pp 294–299

  68. 68.

    Malik TN, 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):1128–1136.

    Article  Google Scholar 

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Appendix 1

See Table 15.

Table 15 F1–F13 Benchmark test function

Appendix 2

See Table 16.

Table 16 Standard distribution functions

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Akdag, O., Ates, A. & Yeroglu, C. Modification of Harris hawks optimization algorithm with random distribution functions for optimum power flow problem. Neural Comput & Applic (2020).

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  • Stochastic optimization
  • Random distribution function
  • OPF problem
  • Harris hawks