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

- 43 Downloads

## 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

## References

- 1.J.A. Pecas Lopes, N. Hatziargyriou, J. Mutale, P. Djapic, N. Jenkins, Integrating distributed generation into electric power systems: a review of drivers, challenges and opportunities. Electr. Power Syst. Res.
**77**(9), 1189–1203 (2007)CrossRefGoogle Scholar - 2.M. Kolenc, I. Papič, B. Blažič, Assessment of maximum distributed generation penetration levels in low voltage networks using a probabilistic approach. Int. J. Electr. Power Energy Syst.
**64**, 505–515 (2015)CrossRefGoogle Scholar - 3.A. El-Fergany, Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm. Int. J. Electr. Power Energy Syst.
**64**, 1197–1205 (2015)CrossRefGoogle Scholar - 4.N. Mohandas, R. Balamurugan, L. Lakshminarasimman, 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**, 41–52 (2015)CrossRefGoogle Scholar - 5.A. Shahmohammadi, M.T. Ameli, Proper sizing and placement of distributed power generation aids the intentional islanding process. Electr. Power Syst. Res.
**106**, 73–85 (2014)CrossRefGoogle Scholar - 6.A. Kechroud, P.F. Ribeiro, W.L. Kling, Distributed generation support for voltage regulation: an adaptive approach’. Electr. Power Syst. Res.
**107**, 213–220 (2014)CrossRefGoogle Scholar - 7.L.D. Arya, A. Koshti, S.C. Choube, Distributed generation planning using differential evolution accounting voltage stability consideration. Int. J. Electr. Power Energy Syst.
**42**(1), 196–207 (2012)CrossRefGoogle Scholar - 8.A. Koshti, L.D. Arya, S.C. Choube, Voltage stability constrained distributed generation planning using modified bare bones particle swarm optimization. J. Inst. Eng. (India) Ser. B
**94**(2), 123–133 (2013)CrossRefGoogle Scholar - 9.E.S. Ali, S.M.A. Elazim, A.Y. Abdelaziz, Ant lion optimization algorithm for optimal location and sizing of renewable distributed generations. Renew. Energy
**101**, 1311–1324 (2017)CrossRefGoogle Scholar - 10.L.W. Oliveira, T.C.J. Maria, Planning of renewable generation in distribution systems considering daily operating periods. IEEE Latin America Transactions
**15**(5), 901–907 (2017)CrossRefGoogle Scholar - 11.H.A. Mahmoud Pesaran, P.D. Huy, V.K. Ramachandaramurthy, A review of the optimal allocation of distributed generation: objectives, constraints, methods, and algorithms. Renewable Sustainable Energy Rev
**75**, 293–312 (2017)CrossRefGoogle Scholar - 12.M.A. Akbari, J. Aghaei, M. Barani, Multiobjective capacity planning of photovoltaics in smart electrical energy networks: improved normal boundary intersection method. IET Renew. Power Gener.
**11**(13), 1679–1687 (2017)CrossRefGoogle Scholar - 13.Z. Abdmouleh, A. Gastli, L.B. Brahim, M. Haouari, N.A. Al-Emadi, Review of optimization techniques applied for the integration of distributed generation from renewable energy sources. Renew. Energy
**113**, 266–280 (2017)CrossRefGoogle Scholar - 14.H.H. Fard, A. Jalilian, A novel objective function for optimal DG allocation in distribution systems using meta-heuristic algorithms. Int. J. Green Energy
**13**(15), 1615–1625 (2016)Google Scholar - 15.A.E. Fergany, Multi-objective allocation of multi-type distributed generators along distribution networks using backtracking search algorithm and fuzzy expert rules. Electr. Power Compon. Syst.
**44**(3), 252–267 (2016)CrossRefGoogle Scholar - 16.S. Dahal, H. Salehfar, Impact of distributed generators in the power loss and voltage profile of three phase unbalanced distribution network. Int. J. Electr. Power Energy Syst.
**77**, 256–262 (2016)CrossRefGoogle Scholar - 17.A.M. Dalavi, P.J. Pawar, T.P. Singh, Tool path planning of hole-making operations in ejector plate of injection mould using modified shuffled frog leaping algorithm. J. Comput. Des. Eng.
**3**(3), 266–273 (2016)Google Scholar - 18.M.M. Rasid, M. Junichi, T. Hirotaka, Simultaneous determination of optimal sizes and locations of distributed generation units by differential evolution, in
*Intelligent System Application to Power Systems (ISAP), 18th International IEEE Conference*, Porto, Portugal, 11–16 Sept 2015Google Scholar - 19.C.W. Taylor,
*Power System Voltage Stability*(Tata McGraw-Hill, New York, 1994)Google Scholar - 20.W. Prommee, W. Ongsakul, Optimal multiple distributed generation placement in microgrid system by improved reinitialized social structures particle swarm optimization. Eur. Trans. Electr. Power
**21**(1), 489–504 (2011)CrossRefGoogle Scholar - 21.T. Venkatesan, M.Y. Sana Vullah, SFLA approach to solve PBUC problem with emission limitation. Int. J. Electr. Power Energy Syst.
**46**, 1–4 (2013)CrossRefGoogle Scholar - 22.E. Elbeltagi, T. Hegazy, D. Grierson, A modified shuffled frog-leaping optimization algorithm: applications to project management. Struct. Infrastruct. Eng.
**3**(1), 53–60 (2007)CrossRefGoogle Scholar - 23.L.D. Arya, A. Koshti, Anticipatory load shedding for line overload alleviation using Teaching learning based optimization (TLBO). Int. J. Electr. Power Energy Syst.
**63**, 862–877 (2014)CrossRefGoogle Scholar - 24.J. Kennedy, Bare bones particle swarms, in
*Proceeding of the IEEE Swarm Intelligence Symposium*, 2003, pp. 80–87Google Scholar - 25.H. Zhang, D.D. Kennedy, G.P. Rangaiah, A. Bonilla-Petriciolet, Novel bare-bones particle swarm optimization and its performance for modeling vapor–liquid equilibrium data. Fluid Phase Equilib.
**301**(1), 33–45 (2011)CrossRefGoogle Scholar