Skip to main content
SpringerLink
Log in

A Novel Quasi-oppositional Chaotic Harris Hawk’s Optimization Algorithm for Optimal Siting and Sizing of Distributed Generation in Radial Distribution System

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This article proffers a novel quasi-oppositional chaotic Harris hawk’s optimization (HHO) (QOCHHO) algorithm for interpreting global optimization problems. In the proposed QOCHHO algorithm, quasi-opposition based learning (QOBL) and chaotic local search (CLS) approaches are integrated with the basic HHO for better quality of solution and faster convergence. The idea of QOBL assists to explore new regions of the search space and offers superior exploration. Again, CLS guides the search process nearby the most favorable regions of the search space yielding superior exploitation. Thus, a superior balance between the exploration and the exploitation holds in the case of QOCHHO making this newly projected algorithm more robust as correlated to the HHO algorithm. To demonstrate and validate effectiveness of the suggested QOCHHO algorithm, twenty-nine benchmark test functions of various categories, varied complexities (i.e., unimodal, multimodal, fixed dimension and composite functions) and different dimensions (i.e., 30 and 100) are used for simulation experiments. The simulation results attained by the projected QOCHHO algorithm are compared with the results obtained by recently surfaced HHO and other state-of-the-art algorithms (i.e., particle swarm optimization, moth-flame optimization algorithm, grey wolf optimizer, sine cosine algorithm, salp swarm algorithm, whale optimization algorithm and multi verse optimization algorithm). The outcomes of the benchmark test functions evidence that the anticipated QOCHHO algorithm is able to offers better outcomes in terms of improved exploration, local optima circumvention and faster convergence characteristics. The proposed QOCHHO algorithm is further employed to decipher real world engineering optimization problem (i.e., optimal siting and sizing of distributed generation (DG) in IEEE 33-bus and practical Brazil 136-bus radial distribution system (RDS) considering different types of load models at three load levels) and proffers a real application of the suggested algorithm in the field of electrical engineering. The simulation outcomes evidence that the obtained location and size of DGs in the RDS may be feasible one and the suggested QOCHHO algorithm may be a promising optimization algorithm for the chosen engineering optimization application.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Notes

  1. The used abbreviations are in line with the referred literatures.

  2. The used abbreviations are in line with the referred literatures.

  3. The used abbreviations are in line with the referred literatures.

Abbreviations

3D-GSO:

Three dimensional group search optimization

ABC:

Artificial bee colony

BFOA:

Bacterial foraging optimization algorithm

BSA:

Backtracking search algorithm

BSOA:

Backtracking search optimization algorithm

CC:

Constant current

CEL:

Cost of energy loss

CI:

Constant impedance

CLS:

Chaotic local search

CP:

Constant power

DE:

Differential evolution

DG:

Distributed generation

FPA:

Flower pollination algorithm

GA:

Genetic algorithm

GSA:

Gravitational search algorithm

GWO:

Grey wolf optimizer

HHO:

Harris hawk’s optimization

HAS:

Harmony search algorithm

ISCA:

Improved SCA

KHA:

Krill herd algorithm

LL:

Light load

LSF:

Loss sensitivity factor

MFO:

Moth-flame optimization

ML:

Medium load

MOA:

Metaheuristic optimization algorithm

MOF:

Multiobjective function

MVO:

Multi verse optimization

PABC:

Particle ABC

PL:

Peak load

PSO:

Particle swarm optimization

RDS:

Radial distribution system

SCA:

Sine cosine algorithm

SKHA:

Stud KHA

SOS:

Symbiotic organisms search

SSA:

Salp swarm algorithm

TLBO:

Teaching–learning based optimization

TOC:

Total operating cost

TVD:

Total voltage deviation

WOA:

Whale optimization algorithm

VSI:

Voltage stability index

\(A\) :

Objective wise comparison matrix

\(Ch\) :

Chaotic number

D :

Dimensions

\(E\) :

Escaping energy of the prey

\(E_{0}\) :

Initial state of the prey

\(iter_{\max }\) :

Maximum number of iterations

\(J\) :

Random jump of the prey

\(j_{r}\) :

Jumping rate

\(K\) :

CLS limit

\(K_{p}\) :

Yearly demand cost ($/kW)

\(K_{e}\) :

Annual price of energy loss ($/kWh)

\(lb\) :

Lower bound

\(Lf\) :

Loss factor

\(N\) :

Total number of hawk’s

\(nb\) :

Number of buses

\(N_{dg}\) :

Number of DG units

\(of_{1}\) :

\(P_{loss}\)(KW)

\(of_{2}\) :

TVD (p.u.)

\(of_{3}\) :

VSI (p.u.)

\(of_{4}\) :

TOC ($)

\(of_{5}\) :

CEL ($)

\(P_{d}^{i}\) :

Real power demand at the ith bus

\(P_{dg}^{i}\) :

Output of real power DG at the ith bus

\(P_{pop}\) :

Number of populations

\(P_{loss}\) :

Active power loss

\(P_{dg,\min }^{i} ,P_{dg,\max }^{i}\) :

Lowest and highest limits of DGs (0 MW and 3.5 MW)

\(R_{ij}\) :

Resistance between the ith and the jth buses

\(ub\) :

Upper bound

\(V_{n}\) :

Nominal voltage (1.0 p.u.)

\(V_{\min }^{i} ,V_{\max }^{i}\) :

Least and peak voltages at the ith bus (0.95 p.u. and 1.05 p.u.)

\(w_{1} {\text{ to }}w_{5}\) :

Weighting factors

\(X\) :

Initial population

\(X_{ij}\) :

Reactance between the ith and the jth buses

\(X^{o}\) :

Opposite of \(X\)

\(X^{qo}\) :

Quasi-opposite of \(X\)

References

  1. Blum C, Puchinger J, Raidl GR, Roli A (2011) Hybrid metaheuristics in combinatorial optimization: a survey. Appl Soft Comput 11(6):4135–4151. https://doi.org/10.1016/j.asoc.2011.02.032

    Article  MATH  Google Scholar 

  2. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Article  Google Scholar 

  3. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  4. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Article  Google Scholar 

  5. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  6. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  7. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95-international conference on neural networks. IEEE. 4:1942–1948. https://doi.org/10.1109/ICNN.1995.488968

  8. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  9. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513. https://doi.org/10.1007/s00521-015-1870-7

    Article  Google Scholar 

  10. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471. https://doi.org/10.1007/s10898-007-9149-x

    Article  MathSciNet  MATH  Google Scholar 

  11. Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845. https://doi.org/10.1016/j.cnsns.2012.05.010

    Article  MathSciNet  MATH  Google Scholar 

  12. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  13. Pan WT (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl-Based Syst 26:69–74. https://doi.org/10.1016/j.knosys.2011.07.001

    Article  Google Scholar 

  14. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010

    Article  Google Scholar 

  15. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimization algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1007/s10489-017-1019-8

    Article  Google Scholar 

  16. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359. https://doi.org/10.1007/978-3-642-30504-7_8

    Article  MathSciNet  MATH  Google Scholar 

  17. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39. https://doi.org/10.1109/MCI.2006.329691

    Article  Google Scholar 

  18. Yang XS (2009) Firefly algorithms for multimodal optimization. International symposium on stochastic algorithms. Springer, Berlin, pp 169–178. https://doi.org/10.1007/978-3-642-04944-6_14

    Chapter  Google Scholar 

  19. Kashan AH (2014) League Championship Algorithm (LCA) An algorithm for global optimization inspired by sport championships. Appl Soft Comput 16:171–200. https://doi.org/10.1016/j.asoc.2013.12.005

    Article  Google Scholar 

  20. Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74. https://doi.org/10.1007/978-3-642-12538-6_6

    Chapter  Google Scholar 

  21. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to tackle structural optimization problems. Eng Comput 29(1):17–35. https://doi.org/10.1007/s00366-011-0241-y

    Article  Google Scholar 

  22. Rao RV, Savsani VJ, Balic J (2012) Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems. Eng Optim 44(12):1447–1462. https://doi.org/10.1080/0305215X.2011.652103

    Article  Google Scholar 

  23. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102:49–63. https://doi.org/10.1016/j.asoc.2012.11.026

    Article  Google Scholar 

  24. Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112. https://doi.org/10.1016/j.compstruc.2014.03.007

    Article  Google Scholar 

  25. Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Oper Res 55:1–11. https://doi.org/10.1016/j.cor.2014.10.008

    Article  MathSciNet  MATH  Google Scholar 

  26. Ebrahimi A, Khamehchi E (2016) Sperm whale algorithm: an effective metaheuristic algorithm for production optimization problems. J Nat Gas Sci Eng 29:211–222. https://doi.org/10.1016/j.jngse.2016.01.001

    Article  Google Scholar 

  27. Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12. https://doi.org/10.1016/j.compstruc.2016.03.001

    Article  Google Scholar 

  28. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713. https://doi.org/10.1109/TEVC.2008.919004

    Article  Google Scholar 

  29. Yang XS (2012) Flower pollination algorithm for global optimization. International conference on unconventional computing and natural computation. Springer, Berlin, pp 240–249. https://doi.org/10.1007/978-3-642-32894-7_27

    Chapter  Google Scholar 

  30. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  31. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

    Article  Google Scholar 

  32. Abbasi A, Firouzi B, Sendur P (2019) On the application of Harris hawks optimization (HHO) algorithm to the design of microchannel heat sinks. Eng Comput. https://doi.org/10.1007/s00366-019-00892-0

    Article  Google Scholar 

  33. Yu J, Kim CH, Rhee SB (2020) The comparison of lately proposed Harris hawks optimization and Jaya optimization in solving directional overcurrent relays coordination problem. Complexity. https://doi.org/10.1155/2020/3807653

    Article  Google Scholar 

  34. Shehabeldeen TA, Abd Elaziz M, Elsheikh AH, Zhou J (2019) Modeling of friction stir welding process using adaptive neuro-fuzzy inference system integrated with Harris hawks optimizer. J Mark Res 8(6):5882–5892. https://doi.org/10.1016/j.jmrt.2019.09.060

    Article  Google Scholar 

  35. Houssein EH, Saad MR, Hussain K, Zhu W, Shaban H, Hassaballah M (2020) Optimal sink node placement in large scale wireless sensor networks based on Harris’ hawk optimization algorithm. IEEE Access. 8:19381–19397. https://doi.org/10.1109/ACCESS.2020.2968981

    Article  Google Scholar 

  36. Yıldız BS, Yıldız AR (2019) The Harris hawks optimization algorithm, salp swarm algorithm, grasshopper optimization algorithm and dragonfly algorithm for structural design optimization of vehicle components. Mater Test 61(8):744–748. https://doi.org/10.3139/120.111379

    Article  Google Scholar 

  37. Yıldız AR, Yıldız BS, Sait SM, Li X (2019) The Harris hawks, grasshopper and multi-verse optimization algorithms for the selection of optimal machining parameters in manufacturing operations. Mater Test 61(8):725–733. https://doi.org/10.3139/120.111377

    Article  Google Scholar 

  38. Islam MZ, Wahab NIA, Veerasamy V, Hizam H, Mailah NF, Guerrero JM, Mohd Nasir MN (2020) A Harris Hawks optimization based single-and multi-objective optimal power flow considering environmental emission. Sustainability 12(13):5248. https://doi.org/10.3390/su12135248

    Article  Google Scholar 

  39. Jia H, Lang C, Oliva D, Song W, Peng X (2019) Dynamic Harris hawks optimization with mutation mechanism for satellite image segmentation. Remote Sensing 11(12):1421. https://doi.org/10.3390/rs11121421

    Article  Google Scholar 

  40. Kamboj VK, Nandi A, Bhadoria A, Sehgal S (2020) An intensify Harris Hawks optimizer for numerical and engineering optimization problems. Appl Soft Comput 89:106018. https://doi.org/10.1016/j.asoc.2019.106018

    Article  Google Scholar 

  41. Yousri D, Allam D, Eteiba MB (2020) Optimal photovoltaic array reconfiguration for alleviating the partial shading influence based on a modified Harris hawks optimizer. Energy Convers Manag 206:112470. https://doi.org/10.1016/j.enconman.2020.112470

    Article  Google Scholar 

  42. Too J, Abdullah AR, Mohd Saad N (2019) A new quadratic binary Harris hawk optimization for feature selection. Electronics 8(10):1130. https://doi.org/10.3390/electronics8101130

    Article  Google Scholar 

  43. Kurtuluş E, Yıldız AR, Sait SM, Bureerat S (2020) A novel hybrid Harris hawks-simulated annealing algorithm and RBF-based meta-model for design optimization of highway guardrails. Mater Test 62(3):251–260. https://doi.org/10.3139/120.111478

    Article  Google Scholar 

  44. Moradi MH, Abedini M (2012) A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems. Int J Electr Power Energy Syst 34(1):66–74. https://doi.org/10.1016/j.ijepes.2011.08.023

    Article  Google Scholar 

  45. El-Fergany A (2015) Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm. Int J Electr Power Energy Syst 64:1197–1205. https://doi.org/10.1016/j.ijepes.2014.09.020

    Article  Google Scholar 

  46. Muthukumar K, Jayalalitha S (2016) Optimal placement and sizing of distributed generators and shunt capacitors for power loss minimization in radial distribution networks using hybrid heuristic search optimization technique. Int J Electr Power Energy Syst 78:299–319. https://doi.org/10.1016/j.ijepes.2015.11.019

    Article  Google Scholar 

  47. Imran AM, Kowsalya M (2014) Optimal size and siting of multiple distributed generators in distribution system using bacterial foraging optimization. Swarm Evol Comput 15:58–65. https://doi.org/10.1016/j.swevo.2013.12.001

    Article  Google Scholar 

  48. Raut U, Mishra S (2020) An improved sine-cosine algorithm for simultaneous network reconfiguration and DG allocation in power distribution systems. Appl Soft Comput 92:106–293. https://doi.org/10.1016/j.asoc.2020.106293

    Article  Google Scholar 

  49. Hamid T, Behnam MI (2020) A three-dimensional group search optimization approach for simultaneous planning of distributed generation units and distribution network reconfiguration. Appl Soft Comput 88:106–112. https://doi.org/10.1016/j.asoc.2019.106012

    Article  Google Scholar 

  50. El-Fergany A (2015) Study impact of various load models on DG placement and sizing using backtracking search algorithm. Appl Soft Comput 30:803–811. https://doi.org/10.1016/j.asoc.2015.02.028

    Article  Google Scholar 

  51. Yuvaraj T, Ravi K (2018) Multi-objective simultaneous DG and DSTATCOM allocation in radial distribution networks using cuckoo searching algorithm. Alex Eng J 57(4):2729–2742. https://doi.org/10.1016/j.aej.2018.01.001

    Article  Google Scholar 

  52. Chithra Devi SA, Lakshminarasimman L, Balamurugan R (2017) Stud Krill herd Algorithm for multiple DG placement and sizing in a radial distribution system. Eng Sci Technol Int J 20(2):748–759. https://doi.org/10.1016/j.jestch.2016.11.009

    Article  Google Scholar 

  53. Yuvaraj T, Devabalaji KR, Sudhakar BT (2020) Simultaneous allocation of DG and DSTATCOM using whale optimization algorithm. Iran J Sci Technol Trans Electr Eng 44(2):879–896. https://doi.org/10.1007/s40998-019-00272-w

    Article  Google Scholar 

  54. Abdelsalam AA (2020) Optimal distributed energy resources allocation for enriching reliability and economic benefits using sine-cosine algorithm. Technol Econ Smart Grids Sustain Energy 5(1):1–18. https://doi.org/10.1007/s40866-020-00082-8

    Article  Google Scholar 

  55. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06). IEEE 1:695–701. https://doi.org/10.1109/CIMCA.2005.1631345

    Article  Google Scholar 

  56. Da Silveira A, Soncco-Álvarez J, de Lima TA, Ayala-Rincón M (2016) Memetic and opposition-based learning genetic algorithms for sorting unsigned genomes by translocations. Advances in Nature and Biologically Inspired Computing. Springer, Cham, pp 73–85. https://doi.org/10.1007/978-3-319-27400-3_7

    Chapter  Google Scholar 

  57. Rahnamayan S, Tizhoosh HR, Salama MM (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79. https://doi.org/10.1109/TEVC.2007.894200

    Article  Google Scholar 

  58. Abd Elaziz M, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500. https://doi.org/10.1016/j.eswa.2017.07.043

    Article  Google Scholar 

  59. Abd Elaziz M, Oliva D (2018) Parameter estimation of solar cells diode models by an improved opposition-based whale optimization algorithm. Energy Convers Manag 171:1843–1859. https://doi.org/10.1016/j.enconman.2018.05.062

    Article  Google Scholar 

  60. Dinkar SK, Deep K (2018) An efficient opposition based Lévy Flight Antlion optimizer for optimization problems. J Comput Sci 29:119–141. https://doi.org/10.1016/j.jocs.2018.10.002

    Article  Google Scholar 

  61. Rahnamayan S, Tizhoosh HR, Salama MM (2007) Quasi-oppositional differential evolution. In: 2007 IEEE congress on evolutionary computation. IEEE, pp 2229–2236. https://doi.org/10.1109/CEC.2007.4424748

  62. Guha D, Roy PK, Banerjee S (2016) Load frequency control of large-scale power system using quasi-oppositional grey wolf optimization algorithm. Eng Sci Technol Int J 19(4):1693–1713. https://doi.org/10.1016/j.jestch.2016.07.004

    Article  Google Scholar 

  63. Sharma S, Bhattacharjee S, Bhattacharya A (2016) Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network. Int J Electr Power Energy Syst 74:48–373. https://doi.org/10.1016/j.ijepes.2015.07.034

    Article  Google Scholar 

  64. Shiva CK, Mukherjee V (2015) A novel quasi-oppositional harmony search algorithm for automatic generation control of power system. Appl Soft Comput 35:749–765. https://doi.org/10.1016/j.asoc.2015.05.054

    Article  Google Scholar 

  65. Truong KH, Nallagownden P, Baharudin Z, Vo DN (2019) A quasi-oppositional-chaotic symbiotic organisms search algorithm for global optimization problems. Appl Soft Comput 77:567–583. https://doi.org/10.1016/j.asoc.2019.01.043

    Article  Google Scholar 

  66. Sultana S, Roy PK (2014) Multi-objective quasi-oppositional teaching learning based optimization for optimal location of distributed generator in radial distribution systems. Int J Electr Power Energy Syst 63:534–545. https://doi.org/10.1016/j.ijepes.2014.06.031

    Article  Google Scholar 

  67. Basu M (2016) Quasi-oppositional group search optimization for multi-area dynamic economic dispatch. Int J Electr Power Energy Syst 78:356–367. https://doi.org/10.1016/j.ijepes.2015.11.120

    Article  Google Scholar 

  68. Liu B, Wang L, Jin YH, Tang F, Huang DX (2005) Improved particle swarm optimization combined with chaos. Chaos Solitons Fractals 25(5):1261–1271. https://doi.org/10.1016/j.chaos.2004.11.095

    Article  MATH  Google Scholar 

  69. Li P, Xu D, Zhou Z, Lee WJ, Zhao B (2015) Stochastic optimal operation of micro grid based on chaotic binary particle swarm optimization. IEEE Trans Smart Grid 7(1):66–73. https://doi.org/10.1109/TSG.2015.2431072

    Article  Google Scholar 

  70. Jia D, Zheng G, Khan MK (2011) An effective memetic differential evolution algorithm based on chaotic local search. Inf Sci 181(15):3175–3187. https://doi.org/10.1016/j.ins.2011.03.018

    Article  Google Scholar 

  71. Lu P, Zhou J, Zhang H, Zhang R, Wang C (2014) Chaotic differential bee colony optimization algorithm for dynamic economic dispatch problem with valve-point effects. Int J Electr Power Energy Syst 62:130–143. https://doi.org/10.1016/j.ijepes.2014.04.028

    Article  Google Scholar 

  72. Pan QK, Wang L, Gao L (2011) A chaotic harmony search algorithm for the flow shop scheduling problem with limited buffers. Appl Soft Comput 11(8):5270–5280. https://doi.org/10.1016/j.asoc.2011.05.033

    Article  Google Scholar 

  73. He X, Rao Y, Huang J (2016) A novel algorithm for economic load dispatch of power systems. Neurocomputing 171:1454–1461. https://doi.org/10.1016/j.neucom.2015.07.107

    Article  Google Scholar 

  74. Saha S, Mukherjee V (2016) Optimal placement and sizing of DGs in RDS using chaos embedded SOS algorithm. IET Gener Transm Distrib 10(14):3671–3680. https://doi.org/10.1049/iet-gtd.2016.0151

    Article  Google Scholar 

  75. Truong KH, Nallagownden P, Elamvazuthi I, Vo DN (2020) A quasi-oppositional-chaotic symbiotic organisms search algorithm for optimal allocation of DG in radial distribution networks. Appl Soft Comput 88:106067. https://doi.org/10.1016/j.asoc.2020.106067

    Article  Google Scholar 

  76. Kim IY, De Weck OL (2006) Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation. Struct Multidiscip Optim 31(2):105–116. https://doi.org/10.1007/s00158-005-0557-6

    Article  MathSciNet  MATH  Google Scholar 

  77. Chakravorty M, Das D (2001) Voltage stability analysis of radial distribution networks. Int J Electr Power Energy Syst 23(2):129–135. https://doi.org/10.1016/S0142-0615(00)00040-5

    Article  Google Scholar 

  78. Pehlivan NY, Pakso T, Çalik A (2017) Comparison of methods in FAHP with application in supplier selection. Ali Emrouznejad and William Ho, pp 45–76

  79. Baran ME, Wu FF (1989) Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Deliv 4(2):1401–1407. https://doi.org/10.1109/61.25627

    Article  Google Scholar 

  80. Mantovani JRS, Casari F, Romero RA (2000) Reconfiguration of radial distribution systems using the voltage drop criterion. Control Autom SBA 11(3):150–159

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    Korra Balu & V. Mukherjee

Authors
  1. Korra Balu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. KB and VM performed material preparation, data collection and analysis. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Korra Balu.

Ethics declarations

Conflict of interest

All the authors declare that they have no conflict of interest. We have also not received any funding support for this work.

Human and Animal Rights

This research does not involve any harmful impact to human participants and/or animals.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Balu, K., Mukherjee, V. A Novel Quasi-oppositional Chaotic Harris Hawk’s Optimization Algorithm for Optimal Siting and Sizing of Distributed Generation in Radial Distribution System. Neural Process Lett 54, 4051–4121 (2022). https://doi.org/10.1007/s11063-022-10800-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10800-1

Keywords

Search

Navigation