Abstract
The optimal placement of distributed generation in power distribution systems problem consists of defining the most appropriate sites to install those generators and their optimal sizing, aiming to optimize the system performance. From the mathematical point of view, it is a complex nonlinear optimization problem, containing continuous and discrete variables. The present paper deals with the optimal placement and sizing of distributed generators for real power losses minimization in distribution systems. For this purpose, a new metaheuristic approach called War Optimization is proposed. The best sites to place these generators are defined by the War Optimization method, and the sizing is given by an optimal power flow tool. A set of simulations is run using radial distribution test systems containing 69 and 476 busbars. A detailed comparison between War Optimization and other metaheuristics (including Particle Swarm Optimization) shows that the proposed method is efficient, as it presents better solutions more often.
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Abbreviations
- \(P_\mathrm{A} \) :
-
Active power losses (kW).
- \(P_i \) :
-
Active power injection in busbar i (kW).
- \(Q_i \) :
-
Reactive power injection in busbar i (kV Ar).
- \(P_j \) :
-
Active power injection in busbar j (kW).
- \(Q_j \) :
-
Reactive power injection in busbar j kV Ar.
- n :
-
Number of busbars in the system.
- \(R_{ij} \) :
-
Electrical resistance of line between busbars i and j (\(\Omega )\).
- \(V_i \) :
-
Voltage in busbar i (V).
- \(\delta _i \) :
-
Angle in busbar i (rad).
- \(V_j \) :
-
Voltage in busbar j (V).
- \(\delta _j\) :
-
Angle in busbar j (rad).
- \(V_j \) :
-
Voltage in busbar j (V).
- \(\mathrm{CH}_i \) :
-
Binary variable representing the allocation of DG in busbar i.
- \(P_{\mathrm{GD}i} \) :
-
Active power generated by DG in busbar i(kW).
- \(P_{\mathrm{G}i} \) :
-
Active power generated in busbar i(kW).
- \(P_{\mathrm{D}i} \) :
-
Active load in busbar i(kW).
- \(f_{Pij} \) :
-
Active power flow between busbars i and j (kW).
- \(Q_{\mathrm{GD}i} \) :
-
Reactive power (kV Ar) generated by DG in busbar i(kV Ar).
- \(Q_{\mathrm{G}i} \) :
-
Reactive power generated in busbar i(kV Ar).
- \(Q_{\mathrm{D}i} \) :
-
Reactive load in busbar i (kV Ar).
- \(f_{Qij} \) :
-
Reactive power flow between busbars i and j (kV Ar).
- \(P_{\mathrm{GD}i}^\mathrm{min} ;P_{\mathrm{GD}i}^\mathrm{max} \) :
-
Lower and upper bounds of active power generated by the DG in busbar i.
- \(Q_{\mathrm{GD}i}^\mathrm{min} ;Q_{\mathrm{GD}i}^\mathrm{max} \) :
-
Lower and upper bounds of reactive power generated by the DG in busbar i.
- Z :
-
Represents all other variables of the formulation.
- \(Z^\mathrm{min};Z^\mathrm{max}\) :
-
Z variables lower and upper bounds.
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Acknowledgements
The authors thank the “Foundation for Supporting Research in of Minas Gerais” (FAPEMIG), “Coordination for the Improvement of Higher Education Personnel” (CAPES), “Brazilian National Research Council” (CNPq) and “Electric Power National Institute” (INERGE) for supporting this work. This paper is part of GOHB, Heuristics and Bioinspired Optimization Research Group from the Federal University of Juiz de Fora.
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Coelho, F.C.R., da Silva Junior, I.C., Dias, B.H. et al. Optimal Distributed Generation Allocation Using a New Metaheuristic. J Control Autom Electr Syst 29, 91–98 (2018). https://doi.org/10.1007/s40313-017-0346-7
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DOI: https://doi.org/10.1007/s40313-017-0346-7