Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks

This article addresses the problem of the optimal selection of conductors in asymmetric three-phase distribution networks from a combinatorial optimization perspective, where the problem is represented by a mixed-integer nonlinear programming (MINLP) model that is solved using a master-slave (MS) op...

Full description

Autores:
Vega-Forero, Julián Alejandro
Ramos-Castellanos, Jairo Stiven
Montoya, Oscar Danilo
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/12274
Acceso en línea:
https://hdl.handle.net/20.500.12585/12274
https://doi.org/10.3390/en16031311
Palabra clave:
Distribution Network;
Electric Power Distribution;
Distributed Generation
LEMB
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
id UTB2_c0098caed3db94e12174b9d25ad94088
oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/12274
network_acronym_str UTB2
network_name_str Repositorio Institucional UTB
repository_id_str
dc.title.spa.fl_str_mv Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
title Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
spellingShingle Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
Distribution Network;
Electric Power Distribution;
Distributed Generation
LEMB
title_short Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
title_full Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
title_fullStr Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
title_full_unstemmed Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
title_sort Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks
dc.creator.fl_str_mv Vega-Forero, Julián Alejandro
Ramos-Castellanos, Jairo Stiven
Montoya, Oscar Danilo
dc.contributor.author.none.fl_str_mv Vega-Forero, Julián Alejandro
Ramos-Castellanos, Jairo Stiven
Montoya, Oscar Danilo
dc.subject.keywords.spa.fl_str_mv Distribution Network;
Electric Power Distribution;
Distributed Generation
topic Distribution Network;
Electric Power Distribution;
Distributed Generation
LEMB
dc.subject.armarc.none.fl_str_mv LEMB
description This article addresses the problem of the optimal selection of conductors in asymmetric three-phase distribution networks from a combinatorial optimization perspective, where the problem is represented by a mixed-integer nonlinear programming (MINLP) model that is solved using a master-slave (MS) optimization strategy. In the master stage, an optimization model known as the generalized normal distribution optimization (GNDO) algorithm is proposed with an improvement stage based on the vortex search algorithm (VSA). Both algorithms work with discrete-continuous coding that allows us to represent the locations and gauges of the different conductors in the electrical distribution system. For the slave stage, the backward/forward sweep (BFS) algorithm is adopted. The numerical results obtained in the IEEE 8- and 27-bus systems demonstrate the applicability, efficiency, and robustness of this optimization methodology, which, in comparison with current methodologies such as the Newton metaheuristic algorithm, shows significant improvements in the values of the objective function regarding the balanced demand scenario for the 8- and 27-bus test systems (i.e., 10.30% and 1.40% respectively). On the other hand, for the unbalanced demand scenario, a reduction of 1.43% was obtained in the 27-bus system, whereas no improvement was obtained in the 8-bus grid. An additional simulation scenario associated with the three-phase version of the IEEE33-bus grid under unbalanced operating conditions is analyzed considering three possible load profiles. The first load profile corresponds to the yearly operation under the peak load conduction, the second case is associated with a daily demand profile, and the third operation case discretizes the demand profile in three periods with lengths of 1000 h, 6760 h, and 1000 h with demands of 100%, 60% and 30% of the peak load case. Numerical results show the strong influence of the expected demand behavior on the plan’s total costs, with variations upper than USD/year 260,000.00 between different cases of analysis. All implementations were developed in the MATLAB® programming environment. © 2023 by the authors.
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-07-21T15:40:42Z
dc.date.available.none.fl_str_mv 2023-07-21T15:40:42Z
dc.date.issued.none.fl_str_mv 2023
dc.date.submitted.none.fl_str_mv 2023
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/draft
dc.type.spa.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
status_str draft
dc.identifier.citation.spa.fl_str_mv Vega-Forero, J.A.; Ramos-Castellanos, J.S.; Montoya, O.D. Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks. Energies 2023, 16, 1311. https://doi.org/10.3390/en16031311
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/12274
dc.identifier.doi.none.fl_str_mv https://doi.org/10.3390/en16031311
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 Vega-Forero, J.A.; Ramos-Castellanos, J.S.; Montoya, O.D. Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks. Energies 2023, 16, 1311. https://doi.org/10.3390/en16031311
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/12274
https://doi.org/10.3390/en16031311
dc.language.iso.spa.fl_str_mv eng
language eng
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 35 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.source.spa.fl_str_mv Energies 16, Issue 3
institution Universidad Tecnológica de Bolívar
bitstream.url.fl_str_mv https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/1/energies-16-01311-v3.pdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/2/license_rdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/3/license.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/4/energies-16-01311-v3.pdf.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/5/energies-16-01311-v3.pdf.jpg
bitstream.checksum.fl_str_mv 1d709a65542baebc2b16f19b261f5305
4460e5956bc1d1639be9ae6146a50347
e20ad307a1c5f3f25af9304a7a7c86b6
ffbe88018cc3927627cd596579c0e22f
026b47acd2d3e9bbe0b61d724aa6fa04
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional UTB
repository.mail.fl_str_mv repositorioutb@utb.edu.co
_version_ 1814021756674899968
spelling Vega-Forero, Julián Alejandro0ad14931-4bad-4e9d-9a11-47abeb1bc834Ramos-Castellanos, Jairo Stiven82701298-a6b5-4514-8b8f-46045905e8f5Montoya, Oscar Danilo9fa8a75a-58fa-436d-a6e2-d80f718a4ea82023-07-21T15:40:42Z2023-07-21T15:40:42Z20232023Vega-Forero, J.A.; Ramos-Castellanos, J.S.; Montoya, O.D. Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks. Energies 2023, 16, 1311. https://doi.org/10.3390/en16031311https://hdl.handle.net/20.500.12585/12274https://doi.org/10.3390/en16031311Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis article addresses the problem of the optimal selection of conductors in asymmetric three-phase distribution networks from a combinatorial optimization perspective, where the problem is represented by a mixed-integer nonlinear programming (MINLP) model that is solved using a master-slave (MS) optimization strategy. In the master stage, an optimization model known as the generalized normal distribution optimization (GNDO) algorithm is proposed with an improvement stage based on the vortex search algorithm (VSA). Both algorithms work with discrete-continuous coding that allows us to represent the locations and gauges of the different conductors in the electrical distribution system. For the slave stage, the backward/forward sweep (BFS) algorithm is adopted. The numerical results obtained in the IEEE 8- and 27-bus systems demonstrate the applicability, efficiency, and robustness of this optimization methodology, which, in comparison with current methodologies such as the Newton metaheuristic algorithm, shows significant improvements in the values of the objective function regarding the balanced demand scenario for the 8- and 27-bus test systems (i.e., 10.30% and 1.40% respectively). On the other hand, for the unbalanced demand scenario, a reduction of 1.43% was obtained in the 27-bus system, whereas no improvement was obtained in the 8-bus grid. An additional simulation scenario associated with the three-phase version of the IEEE33-bus grid under unbalanced operating conditions is analyzed considering three possible load profiles. The first load profile corresponds to the yearly operation under the peak load conduction, the second case is associated with a daily demand profile, and the third operation case discretizes the demand profile in three periods with lengths of 1000 h, 6760 h, and 1000 h with demands of 100%, 60% and 30% of the peak load case. Numerical results show the strong influence of the expected demand behavior on the plan’s total costs, with variations upper than USD/year 260,000.00 between different cases of analysis. All implementations were developed in the MATLAB® programming environment. © 2023 by the authors.35 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_abf2Energies 16, Issue 3Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1Distribution Network;Electric Power Distribution;Distributed GenerationLEMBCartagena de IndiasRamírez Castaño, S. (2004) Power Distribution Networks Departamento de Ingeniería Eléctrica, Electrónica y Computación, Universidad Nacional de Colombia, Manizalez, Colombia, Available online https://repositorio.unal.edu.co/handle/unal/57581Denton, W., Reps, D. Distribution-substation and primary-feeder planning (1955) Electr. Eng, 74, pp. 804-809.Agarwal, U., Jain, N. Distributed Energy Resources and Supportive Methodologies for their Optimal Planning under Modern Distribution Network: a Review (2019) Technology and Economics of Smart Grids and Sustainable Energy, 4 (1), art. no. 3. Cited 16 times. https://link.springer.com/journal/40866 doi: 10.1007/s40866-019-0060-6Koziel, S., Hilber, P., Westerlund, P., Shayesteh, E. Investments in data quality: Evaluating impacts of faulty data on asset management in power systems (2021) Applied Energy, 281, art. no. 116057. Cited 15 times. https://www.journals.elsevier.com/applied-energy doi: 10.1016/j.apenergy.2020.116057Ahmadian, A., Elkamel, A., Mazouz, A. An improved hybrid particle swarm optimization and tabu search algorithm for expansion planning of large dimension electric distribution network (2019) Energies, 12 (16), art. no. 3052. Cited 25 times. https://www.mdpi.com/1996-1073/12/16 doi: 10.3390/en12163052Kazmi, S.A.A., Shahzad, M.K., Khan, A.Z., Shin, D.R. Smart distribution networks: A review of modern distribution concepts from a planning perspective (2017) Energies, 10 (4), art. no. 501. Cited 58 times. http://www.mdpi.com/journal/energies/ doi: 10.3390/en10040501Ponnavaikko, M., Prakasa Rao, K.S. Optimal distribution system planning (1981) IEEE Transactions on Power Apparatus and Systems, PAS-100 (6), pp. 2969-2977. Cited 37 times. doi: 10.1109/TPAS.1981.316370Ponnavaikko, M., Rao, K.S.P., Venkata, S.S. Distribution system planning through a quadratic mixed integer programming approach (1987) IEEE Transactions on Power Delivery, 2 (4), pp. 1157-1163. Cited 62 times. doi: 10.1109/TPWRD.1987.4308237Adams, R.N., Laughton, M.A. OPTIMAL PLANNING OF POWER NETWORKS USING MIXED-INTEGER PROGRAMMING. (1974) Proceedings of the Institution of Electrical Engineers, 121 (2), pp. 139-147. Cited 131 times. doi: 10.1049/piee.1974.0024Islam, Shah Jahirul, Abd. Ghani, Mohd.Ruddin Economical optimization of conductor selection in planning radial distribution networks (1999) Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, 2, pp. 858-863. Cited 6 times.Joshi, D., Burada, S., Mistry, K.D. Distribution system planning with optimal conductor selection (2017) 2017 Recent Developments in Control, Automation and Power Engineering, RDCAPE 2017, pp. 263-268. Cited 4 times. http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8356462 ISBN: 978-150903978-4 doi: 10.1109/RDCAPE.2017.8358279Falaghi, H., Ramezani, M., Haghifam, M.R., Milani, K.R. Optimal selection of conductors in radial distribution systems with time varying load Proceedings of the CIRED 2005-18th International Conference and Exhibition on Electricity Distribution, pp. 1-4. Cited 22 times. Turin, Italy, 6–9 June 2005Ponnavaikko, M., Rao, K.S.P. An approach to optical distribution system planning through conductor gradation (1982) IEEE Transactions on Power Apparatus and Systems, PAS-101 (6), pp. 1735-1742. Cited 51 times. doi: 10.1109/TPAS.1982.317227Mendoza, F., Requena, D., Bemal-Agustín, J.L., Domínguez-Navarro, J.A. Optimal conductor size selection in radial power distribution systems using evolutionary strategies (2006) 2006 IEEE PES Transmission and Distribution Conference and Exposition: Latin America, TDC'06, art. no. 4104682. Cited 25 times. ISBN: 1424402883; 978-142440288-5 doi: 10.1109/TDCLA.2006.311451Legha, M.M., Javaheri, H., Legha, M.M. Optimal Conductor Selection in Radial Distribution Systems for Productivity Improvement Using Genetic Algorithm (2013) Iraqi J. Electr. Electron. Eng, 9, pp. 29-35. Cited 13 times.Rao, R.S., Satish, K., Narasimham, S.V.L. Optimal conductor size selection in distribution systems using the harmony search algorithm with a differential operator (2011) Electric Power Components and Systems, 40 (1), pp. 41-56. Cited 31 times. doi: 10.1080/15325008.2011.621922Momoh, I., Jibril, Y., Jimoh, B., Abubakar, A., Ajayi, O., Abubakar, A., Sulaiman, S., (...), Yusuf, S. Effect of an optimal conductor size selection scheme for single wire earth return power distribution networks for rural electrification (2019) ATBU J. Sci. Technol. Educ, 7, pp. 286-295. Cited 3 times.Manikandan, S., Sasitharan, S., Rao, J.V., Moorthy, V. Analysis of optimal conductor selection for radial distribution systems using DPSO (2016) 2016 3rd International Conference on Electrical Energy Systems, ICEES 2016, art. no. 7510623, pp. 96-101. Cited 6 times. ISBN: 978-146738261-8 doi: 10.1109/ICEES.2016.7510623Kalesar, B.M. Conductor selection optimization in radial distribution system considering load growth using MDE algorithm (2014) World Journal of Modelling and Simulation, 10 (3), pp. 175-184. Cited 9 times. http://www.worldacademicunion.com/journal/1746-7233WJMS/wjmsvol10no03paper02.pdfAbdelaziz, A.Y., Fathy, A. A novel approach based on crow search algorithm for optimal selection of conductor size in radial distribution networks (2017) Engineering Science and Technology, an International Journal, 20 (2), pp. 391-402. Cited 95 times. www.journals.elsevier.com/engineering-science-and-technology-an-international-journal/ doi: 10.1016/j.jestch.2017.02.004Ismael, S.M., Aleem, S.H.E.A., Abdelaziz, A.Y. Optimal selection of conductors in Egyptian radial distribution systems using sine-cosine optimization algorithm (2018) 2017 19th International Middle-East Power Systems Conference, MEPCON 2017 - Proceedings, 2018-February, pp. 103-107. Cited 24 times. ISBN: 978-153860990-3 doi: 10.1109/MEPCON.2017.8301170Ismael, S.M., Abdel Aleem, S.H.E., Abdelaziz, A.Y., Zobaa, A.F. Practical Considerations for Optimal Conductor Reinforcement and Hosting Capacity Enhancement in Radial Distribution Systems (2018) IEEE Access, 6, pp. 27268-27277. Cited 59 times. http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 doi: 10.1109/ACCESS.2018.2835165Kumari, M., Singh, V.R., Ranjan, R. Optimal selection of conductor in RDS considering weather condition (Open Access) (2018) 2018 International Conference on Computing, Power and Communication Technologies, GUCON 2018, art. no. 8675051, pp. 647-651. Cited 5 times. http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8671767 ISBN: 978-153864491-1 doi: 10.1109/GUCON.2018.8675051Ismael, S.M., Abdel Aleem, S.H.E., Abdelaziz, A.Y. Optimal conductor selection in radial distribution systems using whale optimization algorithm (Open Access) (2019) Journal of Engineering Science and Technology, 14 (1), pp. 87-107. Cited 7 times. http://jestec.taylors.edu.my/Vol%2014%20issue%201%20February%202019/14_1_07.pdfRamana, T., Nararaju, K., Ganesh, V., Sivanagaraju, S. Customer loss allocation reduction using optimal conductor selection in electrical distribution system (2020) Lecture Notes in Electrical Engineering, 569, pp. 369-379. Cited 2 times. http://www.springer.com/series/7818 doi: 10.1007/978-981-13-8942-9_31Martínez-Gil, J.F., Moyano-García, N.A., Montoya, O.D., Alarcon-Villamil, J.A. Optimal selection of conductors in three-phase distribution networks using a discrete version of the vortex search algorithm (2021) Computation, 9 (7), art. no. 80. Cited 8 times. www.mdpi.com/journal/computation doi: 10.3390/computation9070080Thenepalle, M. A comparative study on optimal conductor selection for radial distribution network using conventional and genetic algorithm approach (2011) Int. J. Comput. Appl, 17, pp. 6-13. Cited 15 times.Samal, P., Mohanty, S., Ganguly, S. Simultaneous capacitor allocation and conductor sizing in unbalanced radial distribution systems using differential evolution algorithm (2016) 2016 National Power Systems Conference, NPSC 2016, art. no. 7858853. Cited 11 times. ISBN: 978-146739968-5 doi: 10.1109/NPSC.2016.7858853Abul'Wafa, A.R. Multi-conductor feeder design for radial distribution networks (2016) Electric Power Systems Research, 140, pp. 184-192. Cited 18 times. doi: 10.1016/j.epsr.2016.06.023Nivia Torres, D.J., Salazar Alarcón, G.A., Montoya, O.D. Selección óptima de conductores en redes de distribución trifásicas utilizando el algoritmo metaheurístico de Newton (2022) Ingeniería, 27, p. e19303. Cited 3 times.Montoya, O.D. Notes on the Dimension of the Solution Space in Typical Electrical Engineering Optimization Problems (2022) Ingeniería, 27, p. e19310. Cited 8 times.Zhang, Y., Jin, Z., Mirjalili, S. Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models (Open Access) (2020) Energy Conversion and Management, 224, art. no. 113301. Cited 79 times. https://www.journals.elsevier.com/energy-conversion-and-management doi: 10.1016/j.enconman.2020.113301Cortés-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 (Open Access) (2021) Energies, 14 (5), art. no. 1282. Cited 22 times. https://www.mdpi.com/1996-1073/14/5/1282/pdf doi: 10.3390/en14051282Abdel-Basset, M., Mohamed, R., Abouhawwash, M., Chang, V., Askar, S.S. A local search-based generalized normal distribution algorithm for permutation flow shop scheduling (Open Access) (2021) Applied Sciences (Switzerland), 11 (11), art. no. 4837. Cited 8 times. https://www.mdpi.com/2076-3417/11/11/4837/pdf doi: 10.3390/app111148375 Wang, C., Liu, P., Zhang, T., Sun, J. The Adaptive Vortex Search Algorithm of Optimal Path Planning for Forest Fire Rescue UAV (Open Access) (2018) Proceedings of 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference, IAEAC 2018, art. no. 8577733, pp. 400-403. Cited 39 times. http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8544134 ISBN: 978-153864508-6 doi: 10.1109/IAEAC.2018.8577733Doğan, B. A modified vortex search algorithm for numerical function optimization (2016) arXiv 1606.02710http://purl.org/coar/resource_type/c_6501ORIGINALenergies-16-01311-v3.pdfenergies-16-01311-v3.pdfapplication/pdf1305377https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/1/energies-16-01311-v3.pdf1d709a65542baebc2b16f19b261f5305MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTenergies-16-01311-v3.pdf.txtenergies-16-01311-v3.pdf.txtExtracted texttext/plain94058https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/4/energies-16-01311-v3.pdf.txtffbe88018cc3927627cd596579c0e22fMD54THUMBNAILenergies-16-01311-v3.pdf.jpgenergies-16-01311-v3.pdf.jpgGenerated Thumbnailimage/jpeg8176https://repositorio.utb.edu.co/bitstream/20.500.12585/12274/5/energies-16-01311-v3.pdf.jpg026b47acd2d3e9bbe0b61d724aa6fa04MD5520.500.12585/12274oai:repositorio.utb.edu.co:20.500.12585/122742023-07-22 00:17:31.204Repositorio Institucional UTBrepositorioutb@utb.edu.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