Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization
This study deals with the minimization of the operational and investment cost in the distribution and operation of the power flow considering the installation of fixed-step capacitor banks. This issue is represented by a nonlinear mixed-integer programming mathematical model which is solved by apply...
- Autores:
-
Riaño, Fabio Edison
Cruz, Jonathan Felipe
Montoya, Oscar Danilo
Chamorro, Harold R.
Alvarado-Barrios, Lázaro
- 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:20.500.12585/10335
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10335
- Palabra clave:
- Chu and Beasley genetic algorithm
Discrete codification
Fixed-step capacitor banks
Operative costs minimization
Combinatorial optimization
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
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Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| title |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| spellingShingle |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization Chu and Beasley genetic algorithm Discrete codification Fixed-step capacitor banks Operative costs minimization Combinatorial optimization LEMB |
| title_short |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| title_full |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| title_fullStr |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| title_full_unstemmed |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| title_sort |
Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimization |
| dc.creator.fl_str_mv |
Riaño, Fabio Edison Cruz, Jonathan Felipe Montoya, Oscar Danilo Chamorro, Harold R. Alvarado-Barrios, Lázaro |
| dc.contributor.author.none.fl_str_mv |
Riaño, Fabio Edison Cruz, Jonathan Felipe Montoya, Oscar Danilo Chamorro, Harold R. Alvarado-Barrios, Lázaro |
| dc.subject.keywords.spa.fl_str_mv |
Chu and Beasley genetic algorithm Discrete codification Fixed-step capacitor banks Operative costs minimization Combinatorial optimization |
| topic |
Chu and Beasley genetic algorithm Discrete codification Fixed-step capacitor banks Operative costs minimization Combinatorial optimization LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This study deals with the minimization of the operational and investment cost in the distribution and operation of the power flow considering the installation of fixed-step capacitor banks. This issue is represented by a nonlinear mixed-integer programming mathematical model which is solved by applying the Chu and Beasley genetic algorithm (CBGA). While this algorithm is a classical method for resolving this type of optimization problem, the solutions found using this approach are better than those reported in the literature using metaheuristic techniques and the General Algebraic Modeling System (GAMS). In addition, the time required for the CBGA to get results was reduced to a few seconds to make it a more robust, efficient, and capable tool for distribution system analysis. Finally, the computational sources used in this study were developed in the MATLAB programming environment by implementing test feeders composed of 10, 33, and 69 nodes with radial and meshed configurations. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-07-29T19:16:53Z |
| dc.date.available.none.fl_str_mv |
2021-07-29T19:16:53Z |
| dc.date.issued.none.fl_str_mv |
2021-02-09 |
| dc.date.submitted.none.fl_str_mv |
2021-07-29 |
| 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 |
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Riaño, F.E.; Cruz, J.F.; Montoya, O.D.; Chamorro, H.R.; Alvarado-Barrios, L. Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization. Electronics 2021, 10, 419. https://doi.org/10.3390/electronics10040419 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10335 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/electronics10040419 |
| 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 |
Riaño, F.E.; Cruz, J.F.; Montoya, O.D.; Chamorro, H.R.; Alvarado-Barrios, L. Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization. Electronics 2021, 10, 419. https://doi.org/10.3390/electronics10040419 10.3390/electronics10040419 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/10335 |
| 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/4.0/ |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ Atribución-NoComercial 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
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openAccess |
| dc.format.extent.none.fl_str_mv |
21 páginas |
| dc.format.medium.none.fl_str_mv |
Recurso en línea / Electrónico |
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application/pdf |
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Cartagena de Indias |
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Campus Tecnológico |
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Ingeniería Eléctrica |
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Electronics 2021, 10, 419. |
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Universidad Tecnológica de Bolívar |
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Riaño, Fabio Edison5cd06b0b-a717-41a2-93b6-014b12b94514Cruz, Jonathan Feliped912e07c-2f1c-4893-a558-03edebe4b063Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Chamorro, Harold R.59e2dcd8-f603-4e1f-8459-da694d5a324dAlvarado-Barrios, Lázaro57fdbc12-9b16-4b46-abf4-0ba206be47002021-07-29T19:16:53Z2021-07-29T19:16:53Z2021-02-092021-07-29Riaño, F.E.; Cruz, J.F.; Montoya, O.D.; Chamorro, H.R.; Alvarado-Barrios, L. Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization. Electronics 2021, 10, 419. https://doi.org/10.3390/electronics10040419https://hdl.handle.net/20.500.12585/1033510.3390/electronics10040419Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis study deals with the minimization of the operational and investment cost in the distribution and operation of the power flow considering the installation of fixed-step capacitor banks. This issue is represented by a nonlinear mixed-integer programming mathematical model which is solved by applying the Chu and Beasley genetic algorithm (CBGA). While this algorithm is a classical method for resolving this type of optimization problem, the solutions found using this approach are better than those reported in the literature using metaheuristic techniques and the General Algebraic Modeling System (GAMS). In addition, the time required for the CBGA to get results was reduced to a few seconds to make it a more robust, efficient, and capable tool for distribution system analysis. Finally, the computational sources used in this study were developed in the MATLAB programming environment by implementing test feeders composed of 10, 33, and 69 nodes with radial and meshed configurations.Universidad Tecnológica de Bolívar21 páginasRecurso en línea / Electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Electronics 2021, 10, 419.Reduction of losses and operating costs in distribution networks using a genetic algorithm and mathematical optimizationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Chu and Beasley genetic algorithmDiscrete codificationFixed-step capacitor banksOperative costs minimizationCombinatorial optimizationLEMBCartagena de IndiasCampus TecnológicoIngeniería EléctricaInvestigadoresAlvarado-Barrios, L.; Alvarez-Arroyo, C.; Escano, J.M.; Gonzalez-Longatt, F.M.; Martinez-Ramos, J.L. Two-Level Optimisation and Control Strategy for Unbalanced Active Distribution Systems Management. IEEE Access 2020, 8, 197992–198009Orosz, T.; Sleisz, A.; Tamus, Z.A. Metaheuristic Optimization Preliminary Design Process of Core-Form Autotransformers. IEEE Trans. Magn. 2016, 52, 1–10Lohia, S.; Mahela, O.P.; Ola, S.R. Optimal capacitor placement in distribution system using genetic algorithm. In Proceedings of the 2016 IEEE 7th Power India International Conference (PIICON), Bikaner, India, 25–27 November 2016Montoya, 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, 26Ramírez, S. Electric Distribution Networks; Universidad Nacional de Colombia: Manizales, Colombia, 2009; pp. 653–843. (In Spanish)Bula, I.; Hoxha, V.; Shala, M.; Hajrizi, E. Minimizing non-technical losses with point-to-point measurement of voltage drop between “SMART” meters. IFAC-PapersOnLine 2016, 49, 206–211Fragkioudaki, A.; Cruz-Romero, P.; Gómez-Expósito, A.; Biscarri, J.; de Tellechea, M.J.; Arcos, Á. Detection of Non-technical Losses in Smart Distribution Networks: A Review. In Advances in Intelligent Systems and Computing; Springer: Berlin/Heisenberg, Germany, 2016; pp. 43–54Devi, S.; Geethanjali, M. Optimal location and sizing determination of Distributed Generation and DSTATCOM using Particle Swarm Optimization algorithm. Int. J. Electr. Power Energy Syst. 2014, 62, 562–570Rafael Lozano, C.; Jaimes, S.; Obando, J.D. Assessment Methodology Energy Efficiency: A Proposal. Rev. Teinnova 2016, 1, 22–41Montoya, 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. 2020Gil-González, W.; Montoya, O.D.; Rajagopalan, A.; Grisales-Noreña, L.F.; Hernández, J.C. Optimal Selection and Location of Fixed-Step Capacitor Banks in Distribution Networks Using a Discrete Version of the Vortex Search Algorithm. Energies 2020, 13, 4914.Almabsout, E.A.; El-Sehiemy, R.A.; An, O.N.U.; Bayat, O. A Hybrid Local Search-Genetic Algorithm for Simultaneous Placement of DG Units and Shunt Capacitors in Radial Distribution Systems. IEEE Access 2020, 8, 54465–54481Tamilselvan, V.; Jayabarathi, T.; Raghunathan, T.; Yang, X.S. Optimal capacitor placement in radial distribution systems using flower pollination algorithm. Alex. Eng. J. 2018, 57, 2775–2786Dixit, M.; Kundu, P.; Jariwala, H.R. Optimal integration of shunt capacitor banks in distribution networks for assessment of techno-economic asset. Comput. Electr. Eng. 2018, 71, 331–345Mousavi-Khademi, M.R.; Chamorro, H.R.; Mousavi-Khademi, M.; Zareian-Jahromi, M.; Sood, V.K.; Guerrero, J.M.; Martinez, W. Optimal Value-based Prices Placement of DER and V2G using Planet Search Algorithm. In Proceedings of the 2020 IEEE Electric Power and Energy Conference (EPEC), Edmonton, AB, Canada, 9–10 November 2020; pp. 1–6Lima Pérez, L.; Vasquez Stanescu, C. An intelligent strategy of power utilities for efficient detection of residential customers under fraudulent conditions. REDIP Rev. Digit. Investig. Postgrado 2014, 3, 501–521Comisión de Regulación de Energía y Gas. Gestión del Flujo de Potencia Reactiva; Comisión de Regulación de Energía y Gas, Ministerio de Minas y Energia: Bogotá D.C., Colombia, 2005; p. 43Ministerio de Minas y Energia. Resolucion CREG 015 del 2018; Ministerio de Minas y Energia: Bogotá D.C., Colombia, 2018.Gil-González, W.; Garces, A.; Montoya, O.D.; Hernández, J.C. A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks. Appl. Sci. 2021, 11, 627.Estrada Soria, G.; Tovar Hernández, J.H.; Gutiérrez Alcaraz, G. Metodology for Capacitor Placement in Distribution Systems using Linear Sensitivity Factors. IEEE Lat. Am. Trans. 2005, 3, 185–192Xu, Y.; Dong, Z.Y.; Wong, K.P.; Liu, E.; Yue, B. Optimal capacitor placement to distribution transformers for power loss reduction in radial distribution systems. IEEE Trans. Power Syst. 2013, 28, 4072–4079Joyal Isac, S.; Suresh Kumar, K. Optimal capacitor placement in radial distribution system to minimize the loss using fuzzy logic control and hybrid particle swarm optimization. Lect. Notes Electr. Eng. 2015, 326, 1319–1329Vuletić, J.; Todorovski, M. Optimal capacitor placement in distorted distribution networks with different load models using Penalty Free Genetic Algorithm. Int. J. Electr. Power Energy Syst. 2016, 78, 174–182Mohammedi, R.D.; Mosbah, M.; Hellal, A.; Arif, S. An efficient BBO algorithm for optimal allocation and sizing of shunt capacitors in radial distribution networks. In Proceedings of the 2015 4th International Conference on Electrical Engineering (ICEE), Boumerdes, Algeria, 13–15 December 2015Szultka, A.; Malkowski, R. Selection of optimal location and rated power of capacitor banks in distribution network using genetic algorithm. In Proceedings of the 2017 18th International Scientific Conference on Electric Power Engineering (EPE), Kouty nad Desnou, Czech Republic, 17–19 May 2017; pp. 1–6.Tolba, M.A.; Tulsky, V.N.; Vanin, A.S.; Diab, A.A. Comprehensive analysis of optimal allocation of capacitor banks in various distribution networks using different hybrid optimization algorithms. In Proceedings of the 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC/I and CPS Europe 2017, Milan, Italy, 6–9 June 2017; pp. 16–22George, T.; Youssef, A.R.; Ebeed, M.; Kamel, S. Ant lion optimization technique for optimal capacitor placement based on total cost and power loss minimization. In Proceedings of the 2018 International Conference on Innovative Trends in Computer Engineering (ITCE), Aswan, Egypt, 19–21 February 2018; pp. 350–356Shwehdi, M.H.; Mohamed, S.R.; Devaraj, D. Optimal capacitor placement on West–East inter-tie in Saudi Arabia using genetic algorithm. Comput. Electr. Eng. 2018, 68, 156–169.Abdelsalam, A.A.; Gabbar, H.A. Shunt Capacitors Optimal Placement in Distribution Networks Using Artificial Electric Field Algorithm. In Proceedings of the 2019 IEEE 7th International Conference on Smart Energy Grid Engineering (SEGE), Oshawa, ON, Canada, 12–14 August 2019; pp. 77–85.Quezada, C.; Torres, J.; Quizhpi, F. Optimal Location of Capacitor Banks by Implementing Heuristic Methods in Distribution Networks. In Proceedings of the 2019 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), Valparaiso, Chile, 13–27 November 2019; pp. 1–6.Montoya, O.D.; Ramírez, C.A.; Grisales, L.F. Location and Optimal Sizing of Distributed Generators and Banks Capacitors in Distribution Systems. Sci. Tech. 2018, 23, 308–314Abul’Wafa, A.R. Optimal capacitor allocation in radial distribution systems for loss reduction: A two stage method. Electr. Power Syst. Res. 2013, 95, 168–174Wilson, J.M. A Genetic Algorithm for the Generalised Assignment Problem. J. Oper. Res. Soc. 1997, 48, 804Dunn, A.M.; Hofmann, O.S.; Waters, B.; Witchel, E. Cloaking Malware with the Trusted Platform Module. In Proceedings of the 20th USENIX Security Symposium, San Francisco, CA, USA, 8–12 August 2011.Gallego-Londoño, J.P.; Montoya-Giraldo, O.D.; Hincapié-Isaza, R.A.; Granada-Echeverri, M. Optimal location of reclosers and fuses in distribution systems. ITECKNE 2016, 13, 113Montoya, 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, 106454Montoya, O.D.; Grisales-Noreña, L.F.; Amin, W.T.; Rojas, L.A.; Campillo, J. Vortex Search Algorithm for Optimal Sizing of Distributed Generators in AC Distribution Networks with Radial Topology. Commun. Comput. Inf. Sci. 2019, 1052, 235–249Da Rosa, W.M.; Rossoni, P.; Teixeira, J.C.; Belati, E.A.; Asano, P.T.L. Optimal allocation of capacitor banks using genetic algorithm and sensitivity analysis. IEEE Lat. Am. Trans. 2016, 14, 3702–3707Osorio Cruz, F.A. Optimal Location of Electric Power Recharging Stations for Exchange of Batteries for Electric Vehicles; Universidad Tecnológica de Pereira: Pereira, Colombia, 2017; Available online: http://repositorio.utp.edu.co/dspace/handle/11059/8019 (accessed on 5 February 2021). (In Spanish)Serna, M.A.; Marín, J.L. Genetic Algorithms: An Alternative Solution to Optimize the Inventory Model (Q; r). Master’s Thesis, Universidad Eafit, Medellín, Colombia, 2009. Available online: https://repository.eafit.edu.co/handle/10784/125 (accessed on 5 February 2021). (In Spanish)Montoya, O.D.; Gil-González, W.; Orozco-Henao, C. On the convergence of the power flow methods for DC networks with mesh and radial structures. Electr. Power Syst. Res. 2021, 191, 106881.Shen, T.; Li, Y.; Xiang, J. A graph-based power flow method for balanced distribution systems. Energies 2018, 11, 511Rao, R.S.; Narasimham, S.V.; Ramalingaraju, M. Optimal capacitor placement in a radial distribution system using Plant Growth Simulation Algorithm. Int. J. Electr. Power Energy Syst. 2011, 33, 1133–1139.Vita, V. Development of a decision-making algorithm for the optimum size and placement of distributed generation units in distribution networks. Energies 2017, 10, 1433.Taher, S.A.; Afsari, S.A. Optimal location and sizing of UPQC in distribution networks using differential evolution algorithm. Math. Probl. Eng. 2012, 2012, 838629Davoudi, M.; Cecchi, V.; Aguero, J.R. Investigating the ability of meshed distribution systems to increase penetration levels of Distributed Generation. In Proceedings of the Conference Proceedings—IEEE SOUTHEASTCON, Lexington, KY, USA, 13–16 March 2014.Savier, J.S.; Das, D. Impact of network reconfiguration on loss allocation of radial distribution systems. IEEE Trans. Power Deliv. 2007, 22, 2473–2480Das, B.; Kumar, A. Cost optimization of a hybrid energy storage system using GAMS. In Proceedings of the 2017 International Conference on Power and Embedded Drive Control (ICPEDC), Chennai, India, 16–18 March 2017; pp. 89–92Montoya, O.D.; Garrido, V.M.; Grisales-Noreña, L.F.; Gil-González, W.; Garces, A.; Ramos-Paja, C.A. Optimal Location of DGs in DC Power Grids Using a MINLP Model Implemented in GAMS. In Proceedings of the 2018 IEEE 9th Power, Instrumentation and Measurement Meeting (EPIM), Salto, Uruguay, 14–16 November 2018; pp. 1–5.Hijazi, H.; Thiébaux, S. Optimal distribution systems reconfiguration for radial and meshed grids. Int. J. Electr. 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