Soft Computing

, Volume 23, Issue 21, pp 11227–11245 | Cite as

Application of hybrid heuristic technique for optimal shunt capacitors planning problem in radial distribution network

  • K. MuthukumarEmail author
  • S. Jayalalitha
  • K. Sureshkumar
  • A. Sakthivel
  • K. Balamurugan
  • M. Ramasamy
Methodologies and Application


This paper proposes a hybrid HS–DE algorithm-based optimal node identification and sizing of shunt capacitors with an aim to enhance the performance of the radial distribution network. To enhance the exploitation power of harmony search algorithm (HSA), differential evolution algorithm (DE) is embedded with it. The combination of sensitivity analysis and hybrid HS–DE algorithm is used to trace the optimal solution for the installation of shunt capacitive compensation. A comprehensive objective function is formulated to minimize real power loss, improve the voltage stability and voltage profile of the distribution network. The suitability of the proposed hybrid HS–DE-based approach has been validated using IEEE 69 node radial distribution test network at three discrete load scenarios, and the result outcomes are compared with HSA, DE and other similar methods in the literature. The simulation results reflect the superiority and robustness of the hybrid HS–DE-based approach for solving shunt capacitor planning problem in radial distribution networks.


Radial distribution network (RDN) Harmony search algorithm (HSA) Differential evolution (DE) Loss sensitivity factor (LSF) 


Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abdelaziz AY, Ali ES, Elazim SMA (2016) Flower pollination algorithm and loss sensitivity factors for optimal sizing and placement of capacitors in radial distribution systems. Int J Electr Power Energy Syst 78:207–214CrossRefGoogle Scholar
  2. Abo-Hammour Z, Arqub OA, Alsmadi O, Momani S, Alsaedi A (2014) An optimization algorithm for solving systems of singular boundary value problems. Appl Math Inf Sci 8(6):2809–2821MathSciNetCrossRefGoogle Scholar
  3. Abul Wafa AR (2013) Optimal capacitor allocation in radial distribution systems for loss reduction: a two-stage method. Electr Power Syst Res 95:168–174CrossRefGoogle Scholar
  4. Ackermann T, Andersson G, Soder L (2001) Distributed generation: a definition. J Electric Power Syst Res 57(3):195–204CrossRefGoogle Scholar
  5. Aman MM, Jasmon GB, Bakar AHH, Mokhlis H (2012) Optimum capacitor placement and sizing for distribution system based on an improved voltage stability index. Int Rev Electr Eng 7(3):4622–4630Google Scholar
  6. Arqub OA (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610CrossRefGoogle Scholar
  7. Arqub OA, Abo- Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415MathSciNetCrossRefGoogle Scholar
  8. Arqub OA, Mohammed AS, Momani S, Tasawar H (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302CrossRefGoogle Scholar
  9. Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191–7206CrossRefGoogle Scholar
  10. Balamurugan K, Muthukumar K (2018) Differential evolution algorithm for contingency analysis based optimal location of FACTS controllers in deregulated electricity market. Soft Comput. CrossRefGoogle Scholar
  11. Chakravorty M, Das D (2001) Voltage stability analysis of radial distribution networks. Int J Electr Power Energy Syst 23:129–135CrossRefGoogle Scholar
  12. Das K (2008) Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method. Int J Electr Power Energy Syst 30:361–367CrossRefGoogle Scholar
  13. El-Fergany AA (2013) Optimal capacitor allocations using evolutionary algorithms. IET Gener Transm Distrib 7(6):593–601CrossRefGoogle Scholar
  14. El-Fergany AA, Abdelaziz AY (2013) Capacitor allocations in radial distribution networks using cuckoo search algorithm. IET Gener Transm Distrib 8(2):223–232CrossRefGoogle Scholar
  15. El-Fergany AA, Abdelaziz AY (2014) Artificial Bee Colony Algorithm to Allocate Fixed and Switched Static Shunt Capacitors in Radial Distribution Networks. Elect Power Compon Syst 42(5):427–438CrossRefGoogle Scholar
  16. Eminoglu U, Hocaoglu MH (2009) A network topology based voltage stability index for radial distribution networks. Int J Electr Power Energy Syst 29(2):131–143Google Scholar
  17. Fahmi A, Abdullah S, Amin F, Siddque N (2017a) Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. J Intell Fuzzy Syst 33:3323–3337CrossRefGoogle Scholar
  18. Fahmi A, Abdullah S, Amin F, Ali A (2017b) Precursor selection for sol–gel synthesis of titanium carbide nanopowders by a new cubic fuzzy multi-attribute group decision-making model. J Intell Syst. CrossRefGoogle Scholar
  19. Fahmi A, Abdullah S, Amin F, Ali A (2018a) Weighted average rating (War) method for solving group decision making problem using triangular cubic fuzzy hybrid aggregation (Tcfha). Punjab Univ J Math 50(1):23–34MathSciNetGoogle Scholar
  20. Fahmi A, Abdullah S, Amin F, Ahmed R, Ali A (2018b) Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Intell Fuzzy Syst 34:2401–2416CrossRefGoogle Scholar
  21. Fahmi A, Abdullah S, Amin F, Khan MSA (2018c) Trapezoidal cubic fuzzy number Einstein hybrid weighted averaging operators and its application to decision making. Soft Comput 1–31.
  22. Fahmi A, Abdullah S, Amin F, Ali A, Ahmad Khan W (2018d) Some geometric operators with triangular cubic linguistic hesitant fuzzy number and their application in group decision-making. J Intell Fuzzy Syst 35:1–15.
  23. Fesanghary M, Mahdavi M, Minary-Jolandan M, Alizadeh Y (2008) Hybridizing sequential quadratic programming with HS algorithm for engineering optimization. Comput Methods Appl Mech Eng 197:3080–3091CrossRefGoogle Scholar
  24. Geem ZW (2009) Particle-swarm harmony search for water network design. Eng Optim 49:297–311CrossRefGoogle Scholar
  25. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm harmony Search. Simulation 76(2):60–68CrossRefGoogle Scholar
  26. Hamouda A, Lakehal N, Zehar K (2010) Heuristic method for reactive energy management in distribution feeders. Int J Energy Convers Manag 51:518–523CrossRefGoogle Scholar
  27. Lee K, Geem Z (2005) A new meta heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933CrossRefGoogle Scholar
  28. Li Q, Yang S, Ruan Y (2006) A hybrid algorithm for optimizing multi-modal functions. Wuhan Univ J Nat Sci 11:551–554CrossRefGoogle Scholar
  29. Marler RT, Arora JS (2010) The weighted sum method for multiobjective optimization: new sights. Struct Multidiscip Optim 41:853–862MathSciNetCrossRefGoogle Scholar
  30. Mohandas N, Balamurugan R, Lakshminarasimman L (2015) Optimal location and sizing of real power DG units to improve the voltage stability in the distribution system using ABC algorithm united with chaos. Int J Electr Power Energy Syst 66:41–52CrossRefGoogle Scholar
  31. Muthukumar K, Jayalalitha S (2013) Optimal reactive power compensation by shunt capacitor sizing using harmony search algorithm in the unbalanced radial distribution system for power loss minimization. Int J Electr Eng Inform 5(4):474–491CrossRefGoogle Scholar
  32. 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 78:299–319CrossRefGoogle Scholar
  33. Muthukumar K, Jayalalitha S (2017a) Multiobjective hybrid evolutionary approach for optimal planning of shunt capacitors in radial distribution systems with load models. Ain Shams Eng J. CrossRefGoogle Scholar
  34. Muthukumar K, Jayalalitha S (2017b) Integrated approach of network reconfiguration with distributed generation and shunt capacitors placement for power loss minimization in radial distribution networks. Appl Soft Comput 52:1262–1284CrossRefGoogle Scholar
  35. Muthukumar K, Jayalalitha S, Karthika R (2013) Unbalanced radial distribution system power loss reduction by optimal distributed generator sizing and location using differential evolution technique. Int Rev Model Simul 6(4):1176–1412Google Scholar
  36. Neelimarakesh S, Subramanyam PS (2011) Efficient optimal sizing and allocation of capacitors in radial distribution systems using drdlf and differential evolution. Int J Electr Power Eng 2(3):56–61Google Scholar
  37. Pan QK, Suganthan PN, Tasgetiren MF (2010) A self-adaptive global best harmony search algorithm for continuous optimization problems. Appl Math Comput 216:830–848MathSciNetzbMATHGoogle Scholar
  38. Prakash K, Sydulu M (2007) Particle swam optimization based capacitor placement on radial distribution systems. In: IEEE PES general meeting, pp 1–5Google Scholar
  39. Raju MR, Ramachandra Murthy KVS, Ravindra K (2012) Direct search algorithm for capacitive compensation in radial distribution systems. Int J Electr Power Energy Syst 42:24–30CrossRefGoogle Scholar
  40. Ramadan HA, Wahab MA, EI-Sayed AH, Hamada MM (2014) A Fuzzy-based approach for optimal allocation and sizing of capacitor banks. Electric Power Syst Res 106:232–240CrossRefGoogle Scholar
  41. Reddy MD, Kumar NV (2012) Optimal capacitor placement for loss reduction in distribution systems using fuzzy and harmony search algorithm. ARPN J Eng Appl Sci 7:15–19Google Scholar
  42. Saha S, Mukherjee V (2016) Optimal placement and sizing of DGs in RDS using chaos embedded SOS algorithm. IET Gener Transm Distrib 10(14):3671–3680CrossRefGoogle Scholar
  43. Sarma AK, Rafi KM (2011) Optimal selection of capacitors for radial distribution systems using plant growth simulation algorithm. Int J Adv Sci Technol 30:43–54Google Scholar
  44. Sedighizadeh M, Kalimdast MA (2012) Honey bee foraging approach to optimal capacitor placement with harmonic distortion consideration. Int Rev Electr Eng 7(1):3592–3599Google Scholar
  45. Shayeghi H, Karimi M, Farhadi P (2012) Solving optimal capacitor placement problem using improved bi-strategy differential evolutionary algorithm considering varying load conditions. Int Rev Electr Eng 7(2):4092–4104Google Scholar
  46. Singh D, Singh D, Verma KS (2009) Multiobjective optimization for DG planning with load models. IEEE Trans Power Syst 24(1):427–436CrossRefGoogle Scholar
  47. Sirjani R, Mohamed A, Shareef H (2010) Optimal capacitor placement in a radial distribution systems using harmony search algorithm. J Appl Sci 10(23):2998–3006CrossRefGoogle Scholar
  48. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetCrossRefGoogle Scholar
  49. Su X, Masoum MA, Wolfs PJ (2016) PSO and improved BSFS based sequential comprehensive placement and real-time multi-objective control of delta-connected switched capacitors in unbalanced radial MV distribution networks. IEEE Trans Power Syst 31(1):612–622CrossRefGoogle Scholar
  50. Sudharani D, Subrahmanyan N, Syudulu M (2013) Self adaptive harmony search Algorithm for optimal capacitor placement on radial distribution systems. In: International conference on energy-efficient technologies for sustainability, pp 1330–1335Google Scholar
  51. Sultana S, Roy PK (2014) Optimal capacitor placement in radial distribution systems using teaching learning-based optimization. Int J Electr Power Energy Syst 54(5):387–398CrossRefGoogle Scholar
  52. Sydulu M, Reddy VVK (2007) Index and GA based optimal location and sizing of distribution system capacitor. In: IEEE PES general meeting, pp 1–4Google Scholar
  53. Tan WS, Hassan MY, Rahman HA, Abdullah MP, Hussin F (2013) Multi-distributed generation planning using hybrid particle swarm optimization—gravitational search algorithm including voltage rise issue. IET Gener Transm Distrib 7(9):929–942CrossRefGoogle Scholar
  54. Wu B, Cunhua Q, Ni W, Fan S (2012) Hybrid harmony search and artificial bee colony algorithm for global optimization problems. Comput Math Appl 64:2621–2634MathSciNetCrossRefGoogle Scholar
  55. Yang XS (2009) Harmony search as a metaheuristic algorithm. In: Music-inspired harmony search algorithm: theory and applications. Studies in computational intelligence, vol 191. Springer, Berlin, pp 1–14Google Scholar
  56. Zhao X, Yao Y, Yan L (2009) Learning algorithm for multimodal optimization. Comput Math Appl 57:2016–2021CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • K. Muthukumar
    • 1
    Email author
  • S. Jayalalitha
    • 1
  • K. Sureshkumar
    • 2
  • A. Sakthivel
    • 3
  • K. Balamurugan
    • 3
  • M. Ramasamy
    • 4
  1. 1.SASTRA Deemed UniversityTirumalaisamudram, ThanjavurIndia
  2. 2.Velammal Engineering CollegeChennaiIndia
  3. 3.Dr. Mahalingam College of Engineering and TechnologyPollachiIndia
  4. 4.Annamalai UniversityChidambaramIndia

Personalised recommendations