Soft Computing

, Volume 23, Issue 23, pp 12317–12330 | Cite as

A fuzzy pragmatic DE–CSA hybrid approach for unbalanced radial distribution system planning with distributed generation

  • Padarbinda SamalEmail author
  • Sanjib Ganguly
  • Sanjeeb Mohanty
Methodologies and Application


This paper presents a multi-objective planning approach for the optimal placement of distributed generation (DG) units in unbalanced radial distribution systems using a hybrid differential evolution (DE) and cuckoo search algorithm (CSA). In this planning optimization, the objective functions formulated are the minimization of: (i) total real power loss, (ii) maximum average voltage deviation index, (iii) total neutral current, and (iv) total cost. The total cost includes the cost of energy purchased from the grid and the capital investment and operational cost of DG units. These objective functions are aggregated using max–max and max–min analogies. Fuzzy set theory is used to model the uncertainties in load and generation of renewable DG units. Hence, these objective functions are found to be fuzzy sets. An appropriate defuzzification approach is used so as to compare and rank different solutions. A modified three-phase forward–backward sweep-based load flow algorithm including the DG model is used as the support subroutine of the proposed solution algorithm using the hybrid DE–CSA. The simulation results show that significant improvements in power loss, maximum average voltage deviation, system unbalance, and total annual energy cost are obtained due to the DG integration in unbalanced distribution networks. The results obtained with fuzzy-based modeling of load and generation are found to be superior as compared to the deterministic load and generation.


Unbalanced radial distribution system planning Fuzzy set Distributed generation Differential evolution algorithm Cuckoo search algorithm 

List of symbols


Total number of branches/lines/feeder segments


Total number of buses


Total number of DG units


Removal function

Superscript (woDG)

Without DG

Superscript (wDG)

With DG

Superscript ~

Fuzzy quantity

Superscript −

Phasor quantity

Superscript a, b, c

Phases a, b, c

\( IL(I) \)

Load (branch) current


Bus voltage

\( P\left( Q \right) \)

Active (reactive) power demand by the load


Compliance with ethical standards

Conflict of interest

The 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.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Padarbinda Samal
    • 1
    Email author
  • Sanjib Ganguly
    • 2
  • Sanjeeb Mohanty
    • 3
  1. 1.Department of Electrical EngineeringKIIT Deemed to be UniversityBhubaneswarIndia
  2. 2.Department of Electronics and Electrical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia
  3. 3.Department of Electrical EngineeringNational Institute of TechnologyRourkelaIndia

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