Modified Shuffled Frog Leaping Optimization Algorithm Based Distributed Generation Rescheduling for Loss Minimization

  • L. D. Arya
  • Atul KoshtiEmail author
Original Contribution


This paper investigates the Distributed Generation (DG) capacity optimization at location based on the incremental voltage sensitivity criteria for sub-transmission network. The Modified Shuffled Frog Leaping optimization Algorithm (MSFLA) has been used to optimize the DG capacity. Induction generator model of DG (wind based generating units) has been considered for study. Standard test system IEEE-30 bus has been considered for the above study. The obtained results are also validated by shuffled frog leaping algorithm and modified version of bare bones particle swarm optimization (BBExp). The performance of MSFLA has been found more efficient than the other two algorithms for real power loss minimization problem.


Distributed generation Modified shuffled frog leaping optimization algorithm Modified version of bare bones particle swarm optimization Voltage sensitivity Sub-transmission network 

List of Symbols

\(J_{P\theta } ,J_{PV} ,J_{Q\theta } ,J_{QV}\)

Sub Jacobian matrices

\(\left[ S \right]\)

Sensitivity matrix

\(\Delta P\), \(\Delta Q\)

Real and reactive power injection change vectors

\(\Delta \theta\), \(\Delta V\)

Increment vectors of angles and voltages


Generated real power of ith induction generator


Reactive power drawn by ith induction generator

\(\Delta V_{n}\)

Incremental voltage of nth bus

\(\Delta P_{dg,i}\)

Change in real power generation of ith DG

\(\Delta Q_{dg,i}\)

Change in reactive power consumed of ith DG


Total real power loss of sub-transmission system


Real power loss of kth line


kth MW line flow


kth MW line flow limit


Maximum DG capacity available at ith bus


Number of transmission lines.


Population size


Number of memeplexes

rand, randj, U[0,1]

Random digits in the range [0,1]


ith Position Vector in MSFLA


jth value of ith position vector

\(x_{j - \hbox{min} } ,x_{j - \hbox{max} }\)

Minimum and maximum value of jth value of ith position vector


Best particle for mth memeplex in population


Worst particle for mth memeplex in population


Global best in population


Search acceleration factor




Maximum number of iterations


Modification in worst frog vector


Number of DG units


Number of run

\(\overline{{P_{L} }}\)

Average value of PL in NR run

\(Max \, [P_{{L\text{ - min,1}}} \text{,}P_{{L - \text{min,2}}} { \ldots }P_{{L - \text{min,}NR}} ]\)

Worst minimum value of PL in NR run

\(Min \, [P_{{L\text{ - min,1}}} \text{,}P_{{L - \text{min,2}}} { \ldots }P_{{L - \text{min,}NR}} ]\)

Best value of PL in NR run


Standard deviation of PL for NR number of run


Standard deviation of mean in NR run


Frequency of convergence in NR run


Number of values of objective function above average value in NR run

\(J( \cdot )\)

Objective function to be optimized


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Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentMedi-Caps UniversityIndoreIndia
  2. 2.Electrical Engineering DepartmentGokhale Education Society’s R.H. Sapat College of Engineering, Management Studies and ResearchNashikIndia

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