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

## Abstract

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.

## Keywords

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

- \(P_{dg,i}\)
Generated real power of

*ith*induction generator- \(Q_{dg,i}\)
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- \(P_{L}\)
Total real power loss of sub-transmission system

- \(P_{Loss,k}\)
Real power loss of

*kth*line- \(f_{k}\)
*kth*MW line flow- \(\overline{f}_{k}\)
*kth*MW line flow limit- \(\bar{P}_{dg,i}\)
Maximum DG capacity available at

*ith*bus*NL*Number of transmission lines.

*p*Population size

*M*Number of memeplexes

*rand, rand*_{j}, U[0,1]Random digits in the range [0,1]

*X*_{i}*ith*Position Vector in MSFLA- \(x_{ij}\)
*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- \(X_{b}\)
Best particle for

*mth*memeplex in population- \(X_{w}\)
Worst particle for

*mth*memeplex in population- \(X_{g}\)
Global best in population

*c*Search acceleration factor

*it*Iteration

*it*_{max}Maximum number of iterations

- \(\rho\)
Modification in worst frog vector

- NDG
Number of DG units

- NR
Number of run

- \(\overline{{P_{L} }}\)
Average value of

*P*_{L}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

*P*_{L}in NR run- \(Min \, [P_{{L\text{ - min,1}}} \text{,}P_{{L - \text{min,2}}} { \ldots }P_{{L - \text{min,}NR}} ]\)
Best value of

*P*_{L}in NR run- \(\sigma\)
Standard deviation of

*P*_{L}for NR number of run- \(s\)
Standard deviation of mean in NR run

- \(F\)
Frequency of convergence in NR run

- \(n_{b}\)
Number of values of objective function above average value in NR run

- \(J( \cdot )\)
Objective function to be optimized

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