Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks
With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied b...
- Autores:
-
Montoya, Oscar Danilo
Grisales-Noreña, Luis Fernando
Rivas-Trujillo, Edwin
- 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:20.500.12585/10418
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10418
https://doi.org/10.3390/computers10090109
- Palabra clave:
- Approximated mixed-integer quadratic convex model
Phase balancing problem
Asymmetric distribution networks
Triangular-based power flow method
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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| dc.title.spa.fl_str_mv |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| spellingShingle |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks Approximated mixed-integer quadratic convex model Phase balancing problem Asymmetric distribution networks Triangular-based power flow method LEMB |
| title_short |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_full |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_fullStr |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_full_unstemmed |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_sort |
Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Grisales-Noreña, Luis Fernando Rivas-Trujillo, Edwin |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Grisales-Noreña, Luis Fernando Rivas-Trujillo, Edwin |
| dc.subject.keywords.spa.fl_str_mv |
Approximated mixed-integer quadratic convex model Phase balancing problem Asymmetric distribution networks Triangular-based power flow method |
| topic |
Approximated mixed-integer quadratic convex model Phase balancing problem Asymmetric distribution networks Triangular-based power flow method LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3 × 3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver. |
| publishDate |
2021 |
| dc.date.issued.none.fl_str_mv |
2021-08-31 |
| dc.date.accessioned.none.fl_str_mv |
2022-01-28T20:00:12Z |
| dc.date.available.none.fl_str_mv |
2022-01-28T20:00:12Z |
| dc.date.submitted.none.fl_str_mv |
2022-01-27 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
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info:eu-repo/semantics/restrictedAccess |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Montoya, O.D.; Grisales-Noreña, L.F.; Rivas-Trujillo, E. Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks. Computers 2021, 10, 109. https://doi.org/10.3390/computers10090109 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10418 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.3390/computers10090109 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya, O.D.; Grisales-Noreña, L.F.; Rivas-Trujillo, E. Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks. Computers 2021, 10, 109. https://doi.org/10.3390/computers10090109 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10418 https://doi.org/10.3390/computers10090109 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
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 |
| dc.format.extent.none.fl_str_mv |
12 Páginas |
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application/pdf |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
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Computers - vol. 10 n° 9 (2021) |
| institution |
Universidad Tecnológica de Bolívar |
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Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Grisales-Noreña, Luis Fernando7c27cda4-5fe4-4686-8f72-b0442c58a5d1Rivas-Trujillo, Edwin0720b1ee-acdc-4aea-b24b-fc319c4dd61c2022-01-28T20:00:12Z2022-01-28T20:00:12Z2021-08-312022-01-27Montoya, O.D.; Grisales-Noreña, L.F.; Rivas-Trujillo, E. Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks. Computers 2021, 10, 109. https://doi.org/10.3390/computers10090109https://hdl.handle.net/20.500.12585/10418https://doi.org/10.3390/computers10090109Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarWith this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3 × 3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver.12 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_abf2Computers - vol. 10 n° 9 (2021)Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Approximated mixed-integer quadratic convex modelPhase balancing problemAsymmetric distribution networksTriangular-based power flow methodLEMBCartagena de IndiasGarces, 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/app11051972Ma, K.; Fang, L.; Kong, W. Review of distribution network phase unbalance: Scale, causes, consequences, solutions, and future research direction. CSEE J. Power Energy Syst. 2020, 6, 479–488, doi:10.17775/cseejpes.2019.03280.Montoya, O.D.; Molina-Cabrera, A.; Grisales-Noreña, L.F.; Hincapié, R.A.; Granada, M. Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach. Computation 2021, 9, 67, doi:10.3390/computation9060067.Kong, W.; Ma, K.; Fang, L.; Wei, R.; Li, F. Cost-Benefit Analysis of Phase Balancing Solution for Data-Scarce LV Networks by Cluster-Wise Gaussian Process Regression. IEEE Trans. Power Syst. 2020, 35, 3170–3180, doi:10.1109/tpwrs.2020.2966601.Granada, M.; Gallego, R.A.; López, J.M. Optimal Phase Balancing Planning for Loss Reduction in Distribution Systems using a Specialized Genetic Algorithm. Ing. Y Cienc. 2012, 8, 121–140, doi:10.17230/ingciencia.8.15.6Montoya, 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/computation9060061.Tuppadung, Y.; Kurutach, W. The Modified Particle Swarm Optimization for Phase Balancing. In Proceedings of the TENCON 2006-2006 IEEE Region 10 Conference, Hong Kong, China, 14–17 November 2006; doi:10.1109/tencon.2006.344014.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/en14051282Zhu, J.; Bilbro, G.; Chow, M.Y. Phase balancing using simulated annealing. IEEE Trans. Power Syst. 1999, 14, 1508–1513, doi:10.1109/59.801943.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.2012.03.029Montoya, O.D.; Arias-Londoño, A.; Grisales-Noreña, L.F.; Barrios, J.Á.; Chamorro, H.R. Optimal Demand Reconfiguration in Three-Phase Distribution Grids Using an MI-Convex Model. Symmetry 2021, 13, 1124, doi:10.3390/sym13071124Sur, U.; Sarkar, G. A Sufficient Condition for Multiple Load Flow Solutions Existence in Three Phase Unbalanced Active Distribution Networks. IEEE Trans. Circuits Syst. II Express Briefs 2018, 65, 784–788, doi:10.1109/tcsii.2017.2751542Cortés-Caicedo, B.; Avellaneda-Gómez, L.S.; Montoya, O.D.; Alvarado-Barrios, L.; Álvarez-Arroyo, C. An Improved Crow Search Algorithm Applied to the Phase Swapping Problem in Asymmetric Distribution Systems. Symmetry 2021, 13, 1329, doi:10.3390/sym13081329.Benson, H.Y.; Sa ˘glam, Ü. Mixed-Integer Second-Order Cone Programming: A Survey. In Theory Driven by Influential Applications; INFORMS: Catonsville, MD, USA, 2013; pp. 13–36, doi:10.1287/educ.2013.0115.Sereeter, B.; Vuik, K.; Witteveen, C. Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks. Energies 2017, 10, 1658, doi:10.3390/en10101658.Shen, T.; Li, Y.; Xiang, J. A Graph-Based Power Flow Method for Balanced Distribution Systems. Energies 2018, 11, 511, doi:10.3390/en11030511Marini, A.; Mortazavi, S.; Piegari, L.; Ghazizadeh, M.S. An efficient graph-based power flow algorithm for electrical distribution systems with a comprehensive modeling of distributed generations. Electr. Power Syst. Res. 2019, 170, 229–243, doi:10.1016/j.epsr.2018.12.026.Montoya, O.D.; Alarcon-Villamil, J.A.; Hernández, J.C. Operating Cost Reduction in Distribution Networks Based on the Optimal Phase-Swapping including the Costs of the Working Groups and Energy Losses. Energies 2021, 14, 4535, doi:10.3390/en1415453. Kayabekir, A.E.; Nigdeli, M. Statistical Evaluation of Metaheuristic Algorithm: An Optimum Reinforced Concrete T-beam Problem. In Advances in Structural Engineering—Optimization; Springer International Publishing: Berlin/Heidelberg, Germany, 2020; pp. 299–310, doi:10.1007/978-3-030-61848-3_11.Chicco, G.; Mazza, A. Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the ‘Rush to Heuristics’. 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