Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach
This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operat...
- Autores:
-
Montoya, Oscar Danilo
Cabrera, Alexander Molina
Grisales-Noreña, Luis Fernando
Hincapié-Isaza, Ricardo Alberto
Granada, Mauricio
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10372
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10372
https://doi.org/10.3390/computation9060067
- Palabra clave:
- Three-phase distribution networks
Phase-balancing problem
Improved Chu and Beasley genetic algorithm
Mutation multi-point criteria
Vortex search algorithm
Normal Gaussian distribution
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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| dc.title.spa.fl_str_mv |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| title |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| spellingShingle |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach Three-phase distribution networks Phase-balancing problem Improved Chu and Beasley genetic algorithm Mutation multi-point criteria Vortex search algorithm Normal Gaussian distribution LEMB |
| title_short |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| title_full |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| title_fullStr |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| title_full_unstemmed |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| title_sort |
Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approach |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Cabrera, Alexander Molina Grisales-Noreña, Luis Fernando Hincapié-Isaza, Ricardo Alberto Granada, Mauricio |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Cabrera, Alexander Molina Grisales-Noreña, Luis Fernando Hincapié-Isaza, Ricardo Alberto Granada, Mauricio |
| dc.subject.keywords.spa.fl_str_mv |
Three-phase distribution networks Phase-balancing problem Improved Chu and Beasley genetic algorithm Mutation multi-point criteria Vortex search algorithm Normal Gaussian distribution |
| topic |
Three-phase distribution networks Phase-balancing problem Improved Chu and Beasley genetic algorithm Mutation multi-point criteria Vortex search algorithm Normal Gaussian distribution LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-09-28T14:32:05Z |
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2021-09-28T14:32:05Z |
| dc.date.issued.none.fl_str_mv |
2021-05-14 |
| dc.date.submitted.none.fl_str_mv |
2021-09-27 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/restrictedAccess |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Montoya OD, Molina-Cabrera A, Grisales-Noreña LF, Hincapié RA, Granada M. Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach. Computation. 2021; 9(6):67. https://doi.org/10.3390/computation9060067 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10372 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.3390/computation9060067 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya OD, Molina-Cabrera A, Grisales-Noreña LF, Hincapié RA, Granada M. Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach. Computation. 2021; 9(6):67. https://doi.org/10.3390/computation9060067 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10372 https://doi.org/10.3390/computation9060067 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
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http://purl.org/coar/access_right/c_abf2 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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22 páginas |
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application/pdf |
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Cartagena de Indias |
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Computation 2021, 9, 1–22 |
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Universidad Tecnológica de Bolívar |
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Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Cabrera, Alexander Molina53d521e7-fd37-4eb5-9362-7b39719c6427Grisales-Noreña, Luis Fernando7c27cda4-5fe4-4686-8f72-b0442c58a5d1Hincapié-Isaza, Ricardo Alberto8e1bb164-f59a-4597-a637-69dbde1bf0a8Granada, Mauriciof3e182e8-3f60-48ee-a1df-cd42695b37922021-09-28T14:32:05Z2021-09-28T14:32:05Z2021-05-142021-09-27Montoya OD, Molina-Cabrera A, Grisales-Noreña LF, Hincapié RA, Granada M. Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach. Computation. 2021; 9(6):67. https://doi.org/10.3390/computation9060067https://hdl.handle.net/20.500.12585/10372https://doi.org/10.3390/computation9060067Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values22 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Computation 2021, 9, 1–22Improved genetic algorithm for phase-balancing in three-phase distribution networks: A master-slave optimization approachinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Three-phase distribution networksPhase-balancing problemImproved Chu and Beasley genetic algorithmMutation multi-point criteriaVortex search algorithmNormal Gaussian distributionLEMBCartagena de IndiasInvestigadoresTemiz, A.; Almalki, A.M.; Kahraman, Ö; Alshahrani, S.S.; Sönmez, E.B.; Almutairi, S.S.; Nadar, A.; Smiai, M.S.; Alabduljabbar, A.A. Investigation of MV Distribution Networks with High-Penetration Distributed PVs: Study for an Urban Area. Energy Procedia 2017, 141, 517–524. doi:10.1016/j.egypro.2017.11.069.Cortés-Caicedo, B.; Avellaneda-Gómez, L.S.; Montoya, O.D.; Alvarado-Barrios, L.; Chamorro, H.R. Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems. Energies 2021, 14, 1282. doi:10.3390/en14051282Aboshady, F.M.; Thomas, D.W.P.; Sumner, M. A Wideband Single End Fault Location Scheme for Active Untransposed Distribution Systems. IEEE Trans. Smart Grid 2020, 11, 2115–2124. doi:10.1109/tsg.2019.2947870.Arias, J.; Calle, M.; Turizo, D.; Guerrero, J.; Candelo-Becerra, J. Historical Load Balance in Distribution Systems Using the Branch and Bound Algorithm. Energies 2019, 12, 1219. doi:10.3390/en12071219Montoya, O.D.; Gil-González, W.; Hernández, J.C. Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA. Appl. Sci. 2021, 11, 2175. doi:10.3390/app11052175Cabrera, J.B.; Veiga, M.F.; Morales, D.X.; Medina, R. Reducing Power Losses in Smart Grids with Cooperative Game Theory. In Advanced Communication and Control Methods for Future Smartgrids; IntechOpen: London, UK, 2019. doi:10.5772/intechopen.88568Ogunsina, A.A.; Petinrin, M.O.; Petinrin, O.O.; Offornedo, E.N.; Petinrin, J.O.; Asaolu, G.O. Optimal distributed generation location and sizing for loss minimization and voltage profile optimization using ant colony algorithm. SN Appl. Sci. 2021, 3. Doi: 10.1007/s42452-021-04226-y.Hooshmand, R.; Soltani, S. Simultaneous optimization of phase balancing and reconfiguration in distribution networks using BF-NM algorithm. Int. J. Electr. Power Energy Syst. 2012, 41, 76–86. doi:10.1016/j.ijepes.2012.03.010.Al-Sumaiti, A.S.; Kavousi-Fard, A.; Salama, M.; Pourbehzadi, M.; Reddy, S.; Rasheed, M.B. Economic Assessment of Distributed Generation Technologies: A Feasibility Study and Comparison with the Literature. Energies 2020, 13, 2764. doi:10.3390/en13112764.Rajaram, R.; Kumar, K.S.; Rajasekar, N. Power system reconfiguration in a radial distribution network for reducing losses and to improve voltage profile using modified plant growth simulation algorithm with Distributed Generation (DG). Energy Rep. 2015, 1, 116–122. doi:10.1016/j.egyr.2015.03.002Grigoras, , G.; Neagu, B.C.; Gavrilas, , M.; Tris,tiu, I.; Bulac, C. Optimal Phase Load Balancing in Low Voltage Distribution Networks Using a Smart Meter Data-Based Algorithm. Mathematics 2020, 8, 549. doi:10.3390/math8040549Boroujeni, S.T.; Mardaneh, M.; Hashemi, Z. A Dynamic and Heuristic Phase Balancing Method for LV Feeders. Appl. Comput. Intell. Soft Comput. 2016, 2016, 1–8. doi:10.1155/2016/6928080Granada-Echeverri, M.; Gallego-Rendón, R.A.; López-Lezama, J.M. Optimal Phase Balancing Planning for Loss Reduction in Distribution Systems using a Specialized Genetic Algorithm. Ing. Cienc. 2012, 8, 121–140. doi:10.17230/ingciencia.8.15.6Montoya, O.D.; Grajales, A.; Hincapié, R.A.; Granada, M. A new approach to solve the distribution system planning problem considering automatic reclosers. Ingeniare. Rev. Chil. Ing. 2017, 25, 415–429. doi:10.4067/s0718-33052017000300415Garcés, A.; Castaño, J.C.; Rios, M.A. Phase Balancing in Power Distribution Grids: A Genetic Algorithm with a Group-Based Codification. In Energy Systems; Springer International Publishing: Cham, Switzerland, 2020; pp. 325–342. doi:10.1007/978-3-030- 36115-0_11.. Darmawan, I.; Kuspriyanto, Y.; Priyan, M.I.J. Integration of Genetic and Tabu Search algorithm based load balancing for heterogenous grid computing. In Proceedings of the 2013 International Conference on Computer, Control, Informatics and Its Applications (IC3INA), Jakarta, Indonesia, 19–21 November 2013. doi:10.1109/ic3ina.2013.6819195. Li, D.; Qiang, R.; Yoon, S.W. Balanced Adaptive Tabu Search Algorithm to Optimize Dual-gantry Pick-and-place Assembly. Procedia Manuf. 2017, 11, 1892–1899. doi:10.1016/j.promfg.2017.07.331Sim, K.M.; Sun, W.H. Ant colony optimization for routing and load-balancing: Survey and new directions. IEEE Trans. Syst. Man, Cybern. Part A Syst. Humans 2003, 33, 560–572. doi:10.1109/tsmca.2003.817391Keskinturk, T.; Yildirim, M.B.; Barut, M. An ant colony optimization algorithm for load balancing in parallel machines with sequence-dependent setup times. Comput. Oper. Res. 2012, 39, 1225–1235. doi:10.1016/j.cor.2010.12.003.Huang, M.Y.; Chen, C.S.; Lin, C.H.; Kang, M.S.; Chuang, H.J.; Huang, C.W. Three-phase balancing of distribution feeders using immune algorithm. IET Gener. Transm. Distrib. 2008, 2, 383. doi:10.1049/iet-gtd:20070206. Garces, A.; Gil-González, W.; Montoya, O.D.; Chamorro, H.R.; Alvarado-Barrios, L. A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids. Appl. Sci. 2021, 11, 1972. doi:10.3390/app11051972Amon, D.A. A Modified Bat Algorithm for Power Loss Reduction in Electrical Distribution System. Telkomnika Indones. J. Electr. Eng. 2015, 14. doi:10.11591/telkomnika.v14i1.7629.Toma, N.; Ivanov, O.; Neagu, B.; Gavrila, M. A PSO Algorithm for Phase Load Balancing in Low Voltage Distribution Networks. In Proceedings of the 2018 International Conference and Exposition on Electrical Furthermore, Power Engineering (EPE), Iasi, Romania, 18–19 October 2018. doi:10.1109/icepe.2018.8559805.Schweickardt, G.; Alvarez, J.M.G.; Casanova, C. Metaheuristics approaches to solve combinatorial optimization problems in distribution power systems. An application to Phase Balancing in low voltage three-phase networks. Int. J. Electr. Power Energy Syst. 2016, 76, 1–10. doi:10.1016/j.ijepes.2015.09.023.Sathiskumar, M.; kumar, A.N.; Lakshminarasimman, L.; Thiruvenkadam, S. A self adaptive hybrid differential evolution algorithm for phase balancing of unbalanced distribution system. Int. J. Electr. Power Energy Syst. 2012, 42, 91–97. doi:10.1016/j.ijepes.2012.03.029Zhu, J.; Bilbro, G.; Chow, M.Y. Phase balancing using simulated annealing. IEEE Trans. Power Syst. 1999, 14, 1508–1513. doi:10.1109/59.801943.Montoya, O.D.; Gil-González, W.; Orozco-Henao, C. Vortex search and Chu-Beasley genetic algorithms for optimal location and sizing of distributed generators in distribution networks: A novel hybrid approach. Eng. Sci. Technol. Int. J. 2020, 23, 1351–1363. doi:10.1016/j.jestch.2020.08.002Montoya, O.D.; Gil-González, W. On the numerical analysis based on successive approximations for power flow problems in AC distribution systems. Electr. Power Syst. Res. 2020, 187, 106454. doi:10.1016/j.epsr.2020.106454Montoya, O.D.; Giraldo, J.S.; Grisales-Noreña, L.F.; Chamorro, H.R.; Alvarado-Barrios, L. Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation 2021, 9, 61. doi:10.3390/computation9060061Da Cunha, A.S.; Peixoto, F.C.; Prata, D.M. Robust data reconciliation in chemical reactors. Comput. Chem. Eng. 2021, 145, 107170. doi:10.1016/j.compchemeng.2020.107170.Sereeter, B.; Vuik, K.; Witteveen, C. Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks. Energies 2017, 10, 1658. doi:10.3390/en10101658Shen, T.; Li, Y.; Xiang, J. A Graph-Based Power Flow Method for Balanced Distribution Systems. Energies 2018, 11, 511. doi:10.3390/en11030511.. Oliveira-De-Jesus, P.M.D.; Rojas, A.A.; Gonzalez-Longatt, F.M. Unbalanced Power Flow Analysis in Distribution Systems Using TRX Matrix: Implementation Using DIgSILENT Programming Language. In PowerFactory Applications for Power System Analysis; Springer International Publishing: Cham, Switzerland, 2014; pp. 85–110. doi:10.1007/978-3-319-12958-7_4.Do ˘gan, B.; Ölmez, T. Vortex search algorithm for the analog active filter component selection problem. AEU Int. J. Electron. Commun. 2015, 69, 1243–1253. doi:10.1016/j.aeue.2015.05.005Li, P.; Zhao, Y. A quantum-inspired vortex search algorithm with application to function optimization. Nat. Comput. 2018, 18, 647–674. doi:10.1007/s11047-018-9704-z.Montoya, O.D.; Molina-Cabrera, A.; Chamorro, H.R.; Alvarado-Barrios, L.; Rivas-Trujillo, E. A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks. Electronics 2020, 10, 26. doi:10.3390/electronics10010026.Deeb, H.; Sarangi, A.; Mishra, D.; Sarangi, S.K. Improved Black Hole optimization algorithm for data clustering. J. King Saud Univ. Comput. Inf. Sci. 2020. doi:10.1016/j.jksuci.2020.12.013.Montoya, O.D.; Gil-González, W.; Grisales-Noreña, L.; Orozco-Henao, C.; Serra, F. Economic Dispatch of BESS and Renewable Generators in DC Microgrids Using Voltage-Dependent Load Models. 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