Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos
El desarrollo de estrategias de control para convertidores conectados en paralelo es de importancia para la investigación en aplicaciones como la carga rápida de vehículos eléctricos. Este trabajo se enfoca en el análisis de la conexión en paralelo de convertidores Ćuk como una topología simple y ro...
- Autores:
-
Salas Castaño, Maria Claudia
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad de Ibagué
- Repositorio:
- Repositorio Universidad de Ibagué
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unibague.edu.co:20.500.12313/3916
- Acceso en línea:
- https://hdl.handle.net/20.500.12313/3916
- Palabra clave:
- Vehículos eléctricos - Carga rápida
Vehículos eléctricos - Convertidores de potencia - Control
Convertidor de potencia
Estrategia de control
Cargador de vehículos eléctricos
Convertidores de potencia en paralelo
Power converter
Control strategy
Array of power converters
Parallel power converters
- Rights
- openAccess
- License
- http://purl.org/coar/access_right/c_abf2
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dc.title.spa.fl_str_mv |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
title |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
spellingShingle |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos Vehículos eléctricos - Carga rápida Vehículos eléctricos - Convertidores de potencia - Control Convertidor de potencia Estrategia de control Cargador de vehículos eléctricos Convertidores de potencia en paralelo Power converter Control strategy Array of power converters Parallel power converters |
title_short |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
title_full |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
title_fullStr |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
title_full_unstemmed |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
title_sort |
Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos |
dc.creator.fl_str_mv |
Salas Castaño, Maria Claudia |
dc.contributor.advisor.none.fl_str_mv |
López Santos, Oswaldo |
dc.contributor.author.none.fl_str_mv |
Salas Castaño, Maria Claudia |
dc.contributor.jury.none.fl_str_mv |
Barrero Mendoza, Oscar Suárez Sierra, Oscar Javier |
dc.subject.armarc.none.fl_str_mv |
Vehículos eléctricos - Carga rápida Vehículos eléctricos - Convertidores de potencia - Control |
topic |
Vehículos eléctricos - Carga rápida Vehículos eléctricos - Convertidores de potencia - Control Convertidor de potencia Estrategia de control Cargador de vehículos eléctricos Convertidores de potencia en paralelo Power converter Control strategy Array of power converters Parallel power converters |
dc.subject.proposal.spa.fl_str_mv |
Convertidor de potencia Estrategia de control Cargador de vehículos eléctricos Convertidores de potencia en paralelo |
dc.subject.proposal.eng.fl_str_mv |
Power converter Control strategy Array of power converters Parallel power converters |
description |
El desarrollo de estrategias de control para convertidores conectados en paralelo es de importancia para la investigación en aplicaciones como la carga rápida de vehículos eléctricos. Este trabajo se enfoca en el análisis de la conexión en paralelo de convertidores Ćuk como una topología simple y robusta, conveniente para la aplicación deseada. Para ello, se define una función de transferencia que describe el comportamiento de los convertidores teniendo en el sistema de control propuesto. Este sistema consiste en controladores proporcional-integral (PI) dispuestos así: un lazo interno, que controla la corriente de entrada de cada convertidor individualmente, garantizando su estabilidad. Un lazo externo, que controla la corriente de salida de cada convertidor, buscando el intercambio de corriente homogéneo en el sistema y un lazo de balance de potencia que se encarga de obtener una adecuada distribución de corriente entre los convertidores. Se propone un diseño para el convertidor Ćuk y, con base en la función de transferencia, se realiza la sintonización de los controladores usando el lugar geométrico de las raíces. Finalmente, se implementan los convertidores con los respectivos controladores en PSIM para efectuar pruebas de estabilidad, de rechazo a perturbaciones y de distribución de corriente. Los resultados muestran que con el sistema de control propuesto se garantiza la estabilidad del sistema y se logra una distribución de corriente balanceada entre los convertidores, lo que es importante para aplicaciones de carga rápida de vehículos eléctricos. |
publishDate |
2023 |
dc.date.accessioned.none.fl_str_mv |
2023-11-01T19:13:21Z |
dc.date.available.none.fl_str_mv |
2023-11-01T19:13:21Z |
dc.date.issued.none.fl_str_mv |
2023 |
dc.type.none.fl_str_mv |
Trabajo de grado - Maestría |
dc.type.content.none.fl_str_mv |
Text |
dc.type.driver.none.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.redcol.none.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
dc.type.version.none.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
status_str |
acceptedVersion |
dc.identifier.citation.none.fl_str_mv |
Salas-Castano, M.C., (2023). Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos. [Tesis Maestría, Universidad de Ibagué]. https://hdl.handle.net/20.500.12313/3916 |
dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12313/3916 |
identifier_str_mv |
Salas-Castano, M.C., (2023). Estrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricos. [Tesis Maestría, Universidad de Ibagué]. https://hdl.handle.net/20.500.12313/3916 |
url |
https://hdl.handle.net/20.500.12313/3916 |
dc.language.iso.none.fl_str_mv |
spa |
language |
spa |
dc.relation.references.none.fl_str_mv |
D. W. Kweku et al., “Greenhouse Effect: Greenhouse Gases and Their Impact on Global Warming,” Journal of Scientific Research and Reports, vol. 17, no. 6, pp. 1–9, 2018. M. Allen, M. Babiker, Y. Chen, H. de Coninck, and S. Conors, “Global Warming of 15°C. An IPCC Special Report on the impacts of global warming of 15°C above pre-industrial levels and related global greenhouse gas emission pathways,” IPCC Special Report, 2018. U.S. Energy Information Administration, “U.S. CO2 emissions from energy consumption by source and sector,” 2021. https://www.eia.gov/energyexplained/energy-and-the-environment/where-greenhouse-gases-come-from.php. European Parliament, “Air emissions accounts for greenhouse gases by NACE,” 2022. https://ec.europa.eu/eurostat/databrowser/view/ env_ac_aigg_q/default/ table?lang=en. D. Pérez Jaramillo, M. C. Guitiérrez, and R. Mix Vidal, “Electromovilidad. Panorama actual en América Latina y el Caribe,” Banco Interamericano de Desarrollo, 2019. G. Máñes Gomis, E. Bermúdez Forn, J.L. Pardo González and J. Orbea Otazua, “Movilidad eléctrica: Avances en América Latina y el Caribe 2019,” Programa de las Naciones Unidas para el Medio Ambiente (PNUMA), 2020. International Energy Agency (IEA), “Global EV Outlook 2023,” Paris, 2023. ANDEMOS, “Aumentó la penetración de vehículos eléctricos e híbridos en América Latina durante el 2022,” Bogotá, 2023. T. Gnann, S. Funke, N. Jakobsson, P. Plötz, F. Sprei, and A. Bennehag, “Fast charging infrastructure for electric vehicles: Today’s situation and future needs,” Transportation Research Part D: Transport and Environment, vol. 62, pp. 314–329, 2018. M. Li, M. Feng, D. Luo, and Z. Chen, “Fast Charging Li-Ion Batteries for a New Era of Electric Vehicles,” Cell Reports Physical Science, vol. 1, no. 10, p. 100212, 2020. D. Ronanki, A. Kelkar, and S. S. Williamson, “Extreme fast charging technology—prospects to enhance sustainable electric transportation,” Energies, vol. 12, no. 19, pp. 1–17, 2019. M. Ahmadi, N. Mithulananthan, and R. Sharma, “A review on topologies for fast charging stations for electric vehicles,” 2016 IEEE International Conference Power System Technology (POWERCON), pp. 1–6, 2016. M. Safayatullah, M. Tamasas Elrais, G. Sumana, R. Rezaii, and I. Batarseh, “A Comprehensive Review of Power Converter Topologies and Control Methods for Electric Vehicle Fast Charging Applications,” IEEE Access, vol. 10, pp. 40753–40793, 2022. K. Shi, F. Shen, D. Lv, P. Lin, M. Chen, and D. Xu, “A novel start-up scheme for modular multilevel converter,” 2012 IEEE Energy Conversion Congress and Expostion (ECCE), pp. 4180–4187, 2012. M. Norambuena, S. Kouro, S. Dieckerhoff, and J. Rodriguez, “Reduced Multilevel Converter: A Novel Multilevel Converter with a Reduced Number of Active Switches,” IEEE Transactions on Industrial Electronics, vol. 65, no. 5, pp. 3636–3645, 2018. P. Yang, Y. Xia, M. Yu, W. Wei, and Y. 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RAE, “Vehículo de motor eléctrico.”. J. Trashorras Montecelos, Vehículos eléctricos, Madrid, 2019. IEEE Standard for Technical Specifications of a DC Quick Charger for Use with Electric Vehicles, IEEE 2030.1.1-2021, 2021. J. M. Kim, J. Lee, T. H. Eom, K. H. Bae, M. H. Shin, and C. Y. Won, “Design and Control Method of 25kW High Efficient EV Fast Charger,” 2018 21st International Conference on Electrical Machines and Systems (ICEMS), pp. 2603–2607, 2018. X. Liang, S. Srdic, J. Won, E. Aponte, K. Booth, and S. Lukic, “A 12.47 kV medium voltage input 350 kW EV fast charger using 10 kV SiC MOSFET,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 581–587, 2019. M. Ehsani, K. V. Singh, H. O. Bansal, and R. T. Mehrjardi, “State of the Art and Trends in Electric and Hybrid Electric Vehicles,” Proceedings of the IEEE, vol. 109, no. 6, pp. 967–984, 2021. SAE Electric Vehicle and Plug in Hybrid Electric Vehicle Conductive Coupler, SAE J1772, 2010. G. Joos, M. De Freige, and M. Dubois, “Design and simulation of a fast charging station for PHEV/EV batteries,” 2010 IEEE Electrical Power & Energy Conference (EPEC), pp. 1-5, 2010. M. Brenna, F. Foiadelli, C. Leone, and M. Longo, “Electric Vehicles Charging Technology Review and Optimal Size Estimation,” Journal of Electrical Engineering & Technology, vol. 15, no. 6, pp. 2539–2552, 2020. S. N. Manias, “DC-DC Converters,” in Power Electronics and Motor Drive Systems, cap. 7, pp. 501–534, 2017. F. Bordry, “Power converters : definitions , classification and converter topologies,” Specialised CERN Accelerator Course on Power Converters, Warrington, UK, pp. 13–42, 2004. D. Czarkowski, “DC-DC Converters,” in Power Electronics Handbook, 4th ed., Butterworth-Heinemann, NY, United States, cap. 10, pp. 275–288, 2018. M. Andresen, V. Raveendran, G. Buticchi, and M. Liserre, “Lifetime-based power routing in parallel converters for smart transformer application,” IEEE Transactions on Industrial Electronics, vol. 65, no. 2, pp. 1675–1684, 2017. A. Cid-Pastor, L. Martinez-Salamero, C. Alonso, R. Leyva, and S. Singer, “Paralleling DC-DC switching converters by means of power gyrators,” IEEE Transactions on Power Electronics, vol. 22, no. 6, pp. 2444–2453, 2007 F. Cavenago et al., “Control,” in Modern Spacecraft Guidance, Navigation, and Control: From System Modeling to AI and Innovative Applications, Elsevier, cap. 10, pp. 543–630, 2023. Electric Vehicle Conductive Charging System-Part 1: General Requirements, IEC 61851-1:2017, 2017. Residual Direct Current Detecting Device (RDC-DD) to be Used for Mode 3 Charging of Electric Vehicles, IEC 62955:2018, 2018. H. Tu, H. Feng, S. Srdic, and S. Lukic, “Extreme Fast Charging of Electric Vehicles : A Technology Overview,” IEEE Transactions on Transportation Electrification, vol. 5, no. 4, pp. 861–878, 2019. L. A. D. Ta, N. D. Dao, and D.-C. Lee, “High-Efficiency Hybrid LLC Resonant Converter for On-board Chargers of Plug-in Electric Vehicles,” IEEE Transactions on Power Electronics, vol. 35, no. 8, pp. 8324–8334, 2020. H. Li, Z. Zhang, S. Wang, J. Tang, X. Ren, and Q. Chen, “A 300-kHz 6.6-kW SiC Bidirectional LLC On-board Charger,” IEEE Transactions on Industrial Electronics, vol. 67, no. 2, pp. 1435–1445, 2020. H. Haga and F. Kurokawa, “Modulation Method of a Full - Bridge Three - level LLC Resonant Converter for Battery Charger of Electrical Vehicles,” IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 2498–2507, 2017. R. W. A. A. De Donker, D. M. Divan and M. H. Kheraluwala, “A three-phase soft-switched high power density DC/DC converter for high power applications,” IEEE Transactions on Industry Applications, vol. 27, no. 1, pp. 63–73, 1991. Y. Yan, H. Bai, A. Foote and W. 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Singh, “A Power Factor Corrected LLC Resonant Converter for Electric Vehicle Charger Using Cuk Converter,” IEEE Transactons on Industry Applications, vol. 55, no. 6, pp. 6278–6286, 2019. P. Prem, P. Sivaraman, J. S. Sakthi Suriya Raj, M. Jagabar Sathik and D. Almakhles, “Fast charging converter and control algorithm for solar PV battery and electrical grid integrated electric vehicle charging station,” Automatika, vol. 61, no. 4, pp. 614–625, Aug 2020. S. Cuoghi, R. Mandrioli, L. Ntogrmarzidis, and G. Gabriele, “Multileg Interleaved Buck Converter for EV Charging : Discrete-Time Model and Direct Control Design,” Energies, vol. 13, no. 2, p. 466, Jan 2020. A. K. Seth and M. Singh, “Unified adaptive neuro-fuzzy inference system control for OFF board electric vehicle charger,” International Journal of Electrical Power & Energy Systems, vol. 130, p. 106896, Sep 2021. A. M. Mohammed, S. N. H. Alalwan, A. Taşcıkaraoğlu and J. P. S. Catalão, “Sliding mode-based control of an electric vehicle fast charging station in a DC microgrid,” Sustainable Energy, Grids and Networks, vol. 32, p. 100820, Dec 2022. S. Luo, Z. Ye, R-L. Lin, and F. C. Lee, “A classification and evaluation of paralleling methods for power supply modules,” 30th Annual IEEE Power Electronics Specialists Conference, vol. 2, pp. 901–908, Jul 1999. K. Siri, C. Q. Lee, and T-E. Wu, “Current Distribution Control For Parallel Connected Converters : Part I,” IEEE Transactions on Aerospace and Electronics Systems, vol. 28, no. 3, pp. 829–840, Jul 1992. P. J. Grbovic, “A Novel Current Sharing Control for Modular Parallel Connected Power Converters,” 2014 IEEE 15th Workshop on Control and Modeling for Power Electronics (COMPEL), pp. 1–6, Jun 2014. M. Cousineau and Z. Xiao, “Fully Masterless Control of Parallel Converter,” 2013 15th European Conference on Power Electronics and Applications (EPE), pp. 1–10, Sep 2013. H. Du, C. Jiang, G. Wen, W. Zhu and Y. Cheng, “Current Sharing Control for Parallel DC-DC Buck Converters Based on Finite-Time Control Technique,” IEEE Transactions on Industrial Informatics, vol. 15, no. 4, pp. 2186–2198, Apr 2019. Nissan Leaf specifications, Nissan, 2013, [Online]. Available: http://www.leftlanenews.com/new-car-buying/nissan/leaf/specifications/. |
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López Santos, Oswaldoda4d97cf-765b-4ee3-897d-70e80ba0bc58-1Salas Castaño, Maria Claudia099021de-34fe-42f3-8e57-ac93626cddc2-1Barrero Mendoza, Oscar2d7e2643-9c20-40f0-a36b-4ecd5bf1e652-1Suárez Sierra, Oscar Javier628e2bc6-1281-4c86-b0a5-a472f39eb104-12023-11-01T19:13:21Z2023-11-01T19:13:21Z2023El desarrollo de estrategias de control para convertidores conectados en paralelo es de importancia para la investigación en aplicaciones como la carga rápida de vehículos eléctricos. Este trabajo se enfoca en el análisis de la conexión en paralelo de convertidores Ćuk como una topología simple y robusta, conveniente para la aplicación deseada. Para ello, se define una función de transferencia que describe el comportamiento de los convertidores teniendo en el sistema de control propuesto. Este sistema consiste en controladores proporcional-integral (PI) dispuestos así: un lazo interno, que controla la corriente de entrada de cada convertidor individualmente, garantizando su estabilidad. Un lazo externo, que controla la corriente de salida de cada convertidor, buscando el intercambio de corriente homogéneo en el sistema y un lazo de balance de potencia que se encarga de obtener una adecuada distribución de corriente entre los convertidores. Se propone un diseño para el convertidor Ćuk y, con base en la función de transferencia, se realiza la sintonización de los controladores usando el lugar geométrico de las raíces. Finalmente, se implementan los convertidores con los respectivos controladores en PSIM para efectuar pruebas de estabilidad, de rechazo a perturbaciones y de distribución de corriente. Los resultados muestran que con el sistema de control propuesto se garantiza la estabilidad del sistema y se logra una distribución de corriente balanceada entre los convertidores, lo que es importante para aplicaciones de carga rápida de vehículos eléctricos.The development of control strategies for parallel-connected converters is important for research in applications as fast charging of electric vehicles. This work focuses on the analysis of parallel connection of Ćuk converters as a simple and robust topology, convenient for the selected application. For this purpose, a transfer function that describes the behavior of the converters is defined, considering the proposed control system. This system consists of proportional-integral (PI) controllers arranged as follows: an internal loop that controls the input current of each converter individually, ensuring its stability. An external loop that controls the output current of each converter, for the homogeneous current exchange in the system, and a power balance loop that manages obtaining an adequate current distribution between the converters. A design for the Ćuk converter is proposed and based on the transfer function, the controllers are tuned using the root locus method. Finally, the converters with the respective controllers are implemented in PSIM to run tests of stability, disturbance rejection and current distribution. The results show that with the proposed control system, the stability of the system is guaranteed and a balanced current distribution between the converters is achieved, which is important for fast charging applications of electric vehicles.MaestríaMagister en Ingeniería de Control1. Introducción 1 1.1. Planteamiento del problema y pregunta de investigación 1 1.2. Justificación del estudio 2 1.3. Objetivos 3 1.4. Contenido del documento 3 2. Marco teórico 4 2.1. Vehículos eléctricos 4 2.1.1. Vehículos eléctricos de batería 5 2.1.2. Cargadores rápidos para vehículos eléctricos 5 2.1.3. Unidades de almacenamiento y métodos de carga 6 2.2. Convertidores de potencia DC-DC 6 2.2.1. Tipos de convertidores de potencia DC-DC 6 2.2.2. Convertidores en paralelo 8 2.3. Control de convertidores 9 2.3.1. Control en modo deslizante 9 2.3.2. Modulación por ancho de pulso 9 3. Convertidor de potencia 11 3.1. Topologías de convertidores usadas en cargadores rápidos de vehículos eléctricos 11 3.1.1. Convertidores con aislamiento galvánico 12 3.1.2. Convertidores sin aislamiento galvánico 14 3.2. Convertidor Ćuk 15 3.2.1. Análisis y diseño del convertidor Ćuk 16 3.2.2. Función de transferencia 16 3.2.3. Verificación y ajuste de las funciones de transferencia 20 3.3. Conexión en paralelo 29 4. Estrategia de control 32 4.1. Estrategias para cargadores rápidos de vehículos eléctricos 32 4.2. Estrategias aplicadas a convertidores en paralelo 33 4.3. Estrategia propuesta 34 4.3.1. Lazo interno 34 4.3.2. Lazo externo 35 4.3.3. Lazo de balance de potencia 36 4.4. Diseño de controladores 38 5. Simulación y resultados 42 5.1. Verificación de diseño 42 5.1.1. Simulación del lazo interno 43 5.1.2. Simulación del lazo externo con convertidores iguales 43 5.1.3. Simulación de lazo de balance con convertidores diferentes 44 5.2. Verificación de la respuesta ante perturbaciones 45 5.2.1. Alteraciones en la fuente 45 5.2.2. Alteraciones en la carga 49 5.3. Planteamiento de ajustes del diseño 51 5.3.1. Lazo externo con polo real en el controlador 51 5.3.2. Lazo externo con constante derivativa en el controlador 52 5.4. Escenarios de carga de baterías 53 5.4.1. Caso 1 53 5.4.2. Caso 2 54 5.4.3. Caso 3 55 5.4.4. Caso 4 57 6. Conclusiones y trabajo futuro 59 6.1. Conclusiones 59 6.2. 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Available: http://www.leftlanenews.com/new-car-buying/nissan/leaf/specifications/.info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)https://creativecommons.org/licenses/by-nc-nd/4.0/Vehículos eléctricos - Carga rápidaVehículos eléctricos - Convertidores de potencia - ControlConvertidor de potenciaEstrategia de controlCargador de vehículos eléctricosConvertidores de potencia en paraleloPower converterControl strategyArray of power convertersParallel power convertersEstrategia para el control de convertidores de potencia conectados en paralelo orientados a la carga rápida de vehículos eléctricosTrabajo de grado - MaestríaTextinfo:eu-repo/semantics/masterThesishttp://purl.org/redcol/resource_type/TMinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALTesis de Grado.pdfTesis de Grado.pdfapplication/pdf4380371https://repositorio.unibague.edu.co/bitstreams/26dbf414-5320-4c1a-8e14-365d9789fabe/downloadfd361337fc9b0e2ed79ae1a958548553MD51Autorización de publicación.pdfAutorización de publicación.pdfapplication/pdf150287https://repositorio.unibague.edu.co/bitstreams/3dd7e14f-7758-4877-adc2-c0e57195b2c9/downloadea3fbfc51bfd1a927e5aada01008d853MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-8134https://repositorio.unibague.edu.co/bitstreams/979c4330-11fd-4b52-8433-20f7fa77e2b6/download2fa3e590786b9c0f3ceba1b9656b7ac3MD53TEXTTesis de Grado.pdf.txtTesis de Grado.pdf.txtExtracted texttext/plain101811https://repositorio.unibague.edu.co/bitstreams/95c32388-e393-4255-936a-f144b112a7b9/downloadd28bbf46c4935e68ea02c0f8d504951fMD54Autorización de publicación.pdf.txtAutorización de publicación.pdf.txtExtracted texttext/plain3666https://repositorio.unibague.edu.co/bitstreams/42de9a5e-b977-4b48-a124-c61115599d7e/download18cb3eba65ad933836694df571e75fd0MD56THUMBNAILTesis de Grado.pdf.jpgTesis de Grado.pdf.jpgGenerated Thumbnailimage/jpeg6517https://repositorio.unibague.edu.co/bitstreams/df65816d-614e-4864-a29d-de7e5c13bee7/download79b01109f4516b0e205885c1baf790d1MD55Autorización de publicación.pdf.jpgAutorización de publicación.pdf.jpgGenerated Thumbnailimage/jpeg14166https://repositorio.unibague.edu.co/bitstreams/b1a8a839-0cf6-46f3-a316-d55cc0766093/download7dd30516f8a1e8b75a654329a6ba689dMD5720.500.12313/3916oai:repositorio.unibague.edu.co:20.500.12313/39162023-11-07 11:09:34.627https://creativecommons.org/licenses/by-nc-nd/4.0/https://repositorio.unibague.edu.coRepositorio Institucional Universidad de Ibaguébdigital@metabiblioteca.comQ3JlYXRpdmUgQ29tbW9ucyBBdHRyaWJ1dGlvbi1Ob25Db21tZXJjaWFsLU5vRGVyaXZhdGl2ZXMgNC4wIEludGVybmF0aW9uYWwgTGljZW5zZQ0KaHR0cHM6Ly9jcmVhdGl2ZWNvbW1vbnMub3JnL2xpY2Vuc2VzL2J5LW5jLW5kLzQuMC8= |