Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo.
ilustraciones, diagramas, tablas
- Autores:
-
Montoya Cardona, José Fernando
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80568
- Palabra clave:
- 330 - Economía::333 - Economía de la tierra y de la energía
Demanda de energía eléctrica
Energy consumption
Consumo de energía
Fourier
Edemand
Forecasting Accuracy
Clustering
Time series
Energy demand
Demanda de energía
Precisión del pronóstico
Agrupamiento
Series de tiempo
K-means
ARIMA
Fourier
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| dc.title.translated.eng.fl_str_mv |
The forecasting energy demand in Colombia in the short term based on an adaptive hybrid model. |
| title |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| spellingShingle |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. 330 - Economía::333 - Economía de la tierra y de la energía Demanda de energía eléctrica Energy consumption Consumo de energía Fourier Edemand Forecasting Accuracy Clustering Time series Energy demand Demanda de energía Precisión del pronóstico Agrupamiento Series de tiempo K-means ARIMA Fourier |
| title_short |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| title_full |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| title_fullStr |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| title_full_unstemmed |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| title_sort |
Pronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo. |
| dc.creator.fl_str_mv |
Montoya Cardona, José Fernando |
| dc.contributor.advisor.none.fl_str_mv |
Velásquez Henao, Juan David |
| dc.contributor.author.none.fl_str_mv |
Montoya Cardona, José Fernando |
| dc.subject.ddc.spa.fl_str_mv |
330 - Economía::333 - Economía de la tierra y de la energía |
| topic |
330 - Economía::333 - Economía de la tierra y de la energía Demanda de energía eléctrica Energy consumption Consumo de energía Fourier Edemand Forecasting Accuracy Clustering Time series Energy demand Demanda de energía Precisión del pronóstico Agrupamiento Series de tiempo K-means ARIMA Fourier |
| dc.subject.lemb.none.fl_str_mv |
Demanda de energía eléctrica Energy consumption Consumo de energía |
| dc.subject.proposal.eng.fl_str_mv |
Fourier Edemand Forecasting Accuracy Clustering Time series Energy demand |
| dc.subject.proposal.spa.fl_str_mv |
Demanda de energía Precisión del pronóstico Agrupamiento Series de tiempo K-means ARIMA Fourier |
| description |
ilustraciones, diagramas, tablas |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-10-16T16:07:01Z |
| dc.date.available.none.fl_str_mv |
2021-10-16T16:07:01Z |
| dc.date.issued.none.fl_str_mv |
2021-10 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
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http://purl.org/redcol/resource_type/TM |
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https://repositorio.unal.edu.co/handle/unal/80568 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/80568 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
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P. Ledesma, «Regulacion de frecuencia y potencia», p. 33. T.-Y. Kim y S.-B. Cho, «Predicting residential energy consumption using CNN-LSTM neural networks», Energy, vol. 182, pp. 72-81, 2019, doi: 10.1016/j.energy.2019.05.230. J. Davidvelásquez, C. J. Franco, y H. A. García, «A non-linear model for forecasting the monthly demand for electricity in Colombia», Estud. Gerenciales, vol. 25, n.o 112, pp. 37-54, 2009, doi: 10.1016/S0123-5923(09)70079-8. A. S. Ahmad et al., «A review on applications of ANN and SVM for building electrical energy consumption forecasting», Renew. Sustain. Energy Rev., vol. 33, pp. 102-109, 2014, doi: 10.1016/j.rser.2014.01.069. R. Y. M. Li, S. Fong, y K. W. S. Chong, «Forecasting the REITs and stock indices: Group method of data handling neural network approach», Pac. Rim Prop. Res. J., vol. 23, n.o 2, pp. 123-160, 2017, doi: 10.1080/14445921.2016.1225149. «Acuerdo 1303 Por el cual se actualizan los procedimientos para la gestión integral de la demanda C.N.O». https://www.cno.org.co/content/acuerdo-1303-por-el-cual-se-actualizan-los-procedimientos-para-la-gestion-integral-de-la (accedido jun. 29, 2020) E. G. Tajeuna, M. Bouguessa, y S. Wang, «A network-based approach to enhance electricity load forecasting», 2019, vol. 2018-November, pp. 266-275. doi: 10.1109/ICDMW.2018.00046. L. N. Ferreira y L. Zhao, «A time series clustering technique based on community detection in networks», 2015, vol. 53, n.o 1, pp. 183-190. doi: 10.1016/j.procs.2015.07.293. M. E. J. Newman, «Fast algorithm for detecting community structure in networks», Phys. Rev. E - Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 69, n.o 6, p. 5, 2004, doi: 10.1103/PhysRevE.69.066133. G. Le Ray y P. Pinson, «Online adaptive clustering algorithm for load profiling», Sustain. Energy Grids Netw., vol. 17, 2019, doi: 10.1016/j.segan.2018.100181. L. F. S. Vilela, R. C. Leme, C. A. M. Pinheiro, y O. A. S. Carpinteiro, «Forecasting financial series using clustering methods and support vector regression», Artif. Intell. Rev., vol. 52, n.o 2, pp. 743-773, 2019, doi: 10.1007/s10462-018-9663-x. K. Gajowniczek y T. Zabkowski, «Simulation Study on Clustering Approaches for Short-Term Electricity Forecasting», Complexity, vol. 2018, 2018, doi: 10.1155/2018/3683969. P. Laurinec, M. Lóderer, M. Lucká, y V. Rozinajová, «Density-based unsupervised ensemble learning methods for time series forecasting of aggregated or clustered electricity consumption», J. Intell. Inf. Syst., vol. 53, n.o 2, pp. 219-239, 2019, doi: 10.1007/s10844-019-00550-3. S. Sun, J. Fu, y A. Li, «A compound wind power forecasting strategy based on clustering, two-stage decomposition, parameter optimization, and optimal combination of multiple machine learning approaches», Energies, vol. 12, n.o 18, 2019, doi: 10.3390/en12183586. Y. Wang, Y. Shen, S. Mao, X. Chen, y H. Zou, «LASSO and LSTM integrated temporal model for short term solar intensity forecasting», IEEE Internet Things J., vol. 6, n.o 2, pp. 2933-2944, 2019, doi: 10.1109/JIOT.2018.2877510. P. Laurinec y M. Lucká, «Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting», Data Min. Knowl. Discov., vol. 33, n.o 2, pp. 413-445, 2019, doi: 10.1007/s10618-018-0598-2. R. Jain, N. Jain, Y. Gupta, T. Chugh, T. Chugh, y D. J. Hemanth, «A Modified Fuzzy Logic Relation Based Approach for Electricity Consumption Forecasting in India», Int. J. Fuzzy Syst., vol. 22, n.o 2, pp. 461-475, 2020, doi: 10.1007/s40815-019-00704-z. S. Singh y A. Yassine, «Big data mining of energy time series for behavioral analytics and energy consumption forecasting», Energies, vol. 11, n.o 2, 2018, doi: 10.3390/en11020452. E. Y. Shchetinin, «Cluster-based energy consumption forecasting in smart grids», Commun. Comput. Inf. Sci., vol. 919, pp. 445-456, 2018, doi: 10.1007/978-3-319-99447-5_38. B. Auder, J. Cugliari, Y. Goude, y J.-M. Poggi, «Scalable clustering of individual electrical curves for profiling and bottom-up forecasting», Energies, vol. 11, n.o 7, 2018, doi: 10.3390/en11071893. L. Li, K. Ota, y M. Dong, «Everything is image: CNN-based short-term electrical load forecasting for smart grid», 2017, vol. 2017-November, pp. 344-351. doi: 10.1109/ISPAN-FCST-ISCC.2017.78. M. Ghofrani, R. Azimi, F. M. Najafabadi, y N. Myers, «A new day-ahead hourly electricity price forecasting framework», presentado en 2017 North American Power Symposium, NAPS 2017, 2017. doi: 10.1109/NAPS.2017.8107269. J. Yang et al., «k-Shape clustering algorithm for building energy usage patterns analysis and forecasting model accuracy improvement», Energy Build., vol. 146, pp. 27-37, 2017, doi: 10.1016/j.enbuild.2017.03.071. I. P. Panapakidis, «Clustering based day-ahead and hour-ahead bus load forecasting models», Int. J. Electr. Power Energy Syst., vol. 80, pp. 171-178, 2016, doi: 10.1016/j.ijepes.2016.01.035. X. Liang, T. Hong, y G. Q. Shen, «Occupancy data analytics and prediction: A case study», Build. Environ., vol. 102, pp. 179-192, 2016, doi: 10.1016/j.buildenv.2016.03.027. Y. H. Chen, W.-C. Hong, W. Shen, y N. N. Huang, «Electric load forecasting based on a least squares support vector machine with fuzzy time series and global harmony search algorithm», Energies, vol. 9, n.o 2, pp. 1-13, 2016, doi: 10.3390/en9020070. M. Chaouch, «Clustering-based improvement of nonparametric functional time series forecasting: Application to intra-day household-level load curves», IEEE Trans. Smart Grid, vol. 5, n.o 1, pp. 411-419, 2014, doi: 10.1109/TSG.2013.2277171. H. Mori y M. Takahashi, «Application of preconditioned Generalized radial Basis Function Network to prediction of photovoltaic power generation», presentado en IEEE PES Innovative Smart Grid Technologies Conference Europe, 2012. doi: 10.1109/ISGTEurope.2012.6465877. B. Kitchenham, «Procedures for Performing Systematic Reviews», p. 33. M. R. Cogollo y J. D. Velásquez, «Methodological advances in artificial neural networks for time series forecasting», IEEE Lat. Am. Trans., vol. 12, n.o 4, pp. 764-771, 2014, doi: 10.1109/TLA.2014.6868881. W. Zhang, G. Mu, C. Song, G. Yan, y V. Heuveline, «Extraction of Spatialoral Features of Bus Loads in Electric Grids Through Clustering in a Dynamic Model Space», IEEE Access, vol. 8, pp. 5852-5861, 2020, doi: 10.1109/ACCESS.2019.2963071. W. Sun y C. Zhang, «A hybrid BA-ELM model based on factor analysis and similar-day approach for short-term load forecasting», Energies, vol. 11, n.o 5, 2018, doi: 10.3390/en11051282. M. Ghofrani, D. Carson, y M. Ghayekhloo, «Hybrid clustering-time series-Bayesian neural network short term load forecasting method», presentado en NAPS 2016 - 48th North American Power Symposium, Proceedings, 2016. doi: 10.1109/NAPS.2016.7747865. P. Laurinec, M. Loderer, P. Vrablecova, M. Lucka, V. Rozinajova, y A. B. Ezzeddine, «Adaptive Time Series Forecasting of Energy Consumption Using Optimized Cluster Analysis», 2016, vol. 0, pp. 398-405. doi: 10.1109/ICDMW.2016.0063. A. Laouafi, M. Mordjaoui, F. Laouafi, y T. E. Boukelia, «Daily peak electricity demand forecasting based on an adaptive hybrid two-stage methodology», Int. J. Electr. Power Energy Syst., vol. 77, pp. 136-144, 2016, doi: 10.1016/j.ijepes.2015.11.046. R. L. Talavera-Llames, R. Pérez-Chacón, M. Martínez-Ballesteros, A. Troncoso, y F. Martínez-Álvarez, «A nearest neighbours-based algorithm for big time series data forecasting», Lect. Notes Comput. Sci. Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinforma., vol. 9648, pp. 174-185, 2016, doi: 10.1007/978-3-319-32034-2_15. W. Wang, W. Pedrycz, y X. Liu, «Time series long-term forecasting model based on information granules and fuzzy clustering», Eng. Appl. Artif. Intell., vol. 41, pp. 17-24, 2015, doi: 10.1016/j.engappai.2015.01.006. C. J. Bennett, R. A. Stewart, y J. W. Lu, «Forecasting low voltage distribution network demand profiles using a pattern recognition based expert system», Energy, vol. 67, pp. 200-212, 2014, doi: 10.1016/j.energy.2014.01.032. S. Humeau, T. K. Wijaya, M. Vasirani, y K. Aberer, «Electricity load forecasting for residential customers: Exploiting aggregation and correlation between households», presentado en 2013 Sustainable Internet and ICT for Sustainability, SustainIT 2013, 2013. doi: 10.1109/SustainIT.2013.6685208. Z. Ding, P. Yang, X. Yang, y Z. Zhang, «Wind power prediction method based on sequential time clustering support vector machine», Dianli Xitong ZidonghuaAutomation Electr. Power Syst., vol. 36, n.o 14, pp. 131-135+149, 2012, doi: 10.3969/j.issn.1000-1026.2012.14.025. «Complex Fourier Series». 2020. [En línea]. Disponible en: https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Book%3A_Electrical_Engineering_(Johnson)/04%3A_Frequency_Domain/4.02%3A_Complex_Fourier_Series M. Charrad, N. Ghazzali, V. Boiteau, y A. Niknafs, «NbClust: An R Package for Determining the Relevant Number of Clusters in a Data Set», J. Stat. Softw., vol. 61, n.o 1, Art. n.o 1, nov. 2014, doi: 10.18637/jss.v061.i06. «pmdarima», API Reference. https://alkaline-ml.com/pmdarima/modules/classes.html |
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Medellín - Minas - Maestría en Ingeniería - Analítica |
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Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Velásquez Henao, Juan David7b16d4a5377f0f1b1f90d3c8c6fd9f8bMontoya Cardona, José Fernandob066ccddbc295e4f5d5ea0ee6339f8942021-10-16T16:07:01Z2021-10-16T16:07:01Z2021-10https://repositorio.unal.edu.co/handle/unal/80568Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramas, tablasLa precisión del pronóstico de la demanda horaria de energía eléctrica es fundamental para realizar una planificación adecuada de los recursos de generación, ya que las desviaciones altas en el pronóstico generan sobrecostos en la operación del sistema. En este trabajo se propone una metodología novedosa de pronóstico basada en el agrupamiento de series de tiempo y los modelos ARIMA; específicamente, el modelo realiza el agrupamiento por tipos de día; seguidamente, agrega las series pertenecientes a un mismo grupo; luego, descompone las series agregadas usando descomposición aditiva; después, se pronostican las series con modelos ARIMA donde se utilizan como variables exógenas las componentes espectrales de Fourier para considerar la estacionalidad y finalmente, se combinan los pronósticos. El modelo propuesto fue utilizado para pronosticar la demanda horaria desde el 13 de enero de 2020 hasta el 15 de marzo de 2020. Los pronósticos del modelo propuesto fueron comparados con los pronósticos del modelo del Centro Nacional de Despacho (Colombia), encontrándose mejoras de hasta un 50% en la precisión con el modelo propuesto. (Texto tomado de la fuente)The forecasting accuracy of the hourly electricity demand is essential for planning the resources of generation, since high deviations in the forecast generate cost overruns in the system’s operation. In this research, a novel forecasting methodology based in clustering time series and ARIMA models is proposed; specifically, the model performs the clustering by types of day, then adds the time series belonging to the same cluster; it later decomposes the aggregate series using additive decomposition, then time series are forecasted with ARIMA models where the Fourier spectral components are used as exogenous variables to consider seasonality and finally, the results of the forecast are combined. The proposed model was used to forecast hourly demand from January 13, 2020 to March 15, 2020. The results of the proposed model were compared with the model of the National Dispatch Center (Colombia), getting improvements of up to 50% of accuracy with the proposed model.MaestríaMagíster en Ingeniería - AnalíticaAnalítica de Mercados de Energíaxiv, 39 páginasapplication/pdfspaUniversidad Nacional de ColombiaMedellín - Minas - Maestría en Ingeniería - AnalíticaDepartamento de la Computación y la DecisiónFacultad de MinasMedellín, ColombiaUniversidad Nacional de Colombia - Sede Medellín330 - Economía::333 - Economía de la tierra y de la energíaDemanda de energía eléctricaEnergy consumptionConsumo de energíaFourierEdemandForecasting AccuracyClusteringTime seriesEnergy demandDemanda de energíaPrecisión del pronósticoAgrupamientoSeries de tiempoK-meansARIMAFourierPronóstico de la demanda de energía en Colombia a corto plazo basado en un modelo híbrido adaptativo.The forecasting energy demand in Colombia in the short term based on an adaptive hybrid model.Trabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMColombiaP. Ledesma, «Regulacion de frecuencia y potencia», p. 33.T.-Y. Kim y S.-B. Cho, «Predicting residential energy consumption using CNN-LSTM neural networks», Energy, vol. 182, pp. 72-81, 2019, doi: 10.1016/j.energy.2019.05.230.J. Davidvelásquez, C. J. Franco, y H. A. García, «A non-linear model for forecasting the monthly demand for electricity in Colombia», Estud. Gerenciales, vol. 25, n.o 112, pp. 37-54, 2009, doi: 10.1016/S0123-5923(09)70079-8.A. S. Ahmad et al., «A review on applications of ANN and SVM for building electrical energy consumption forecasting», Renew. Sustain. Energy Rev., vol. 33, pp. 102-109, 2014, doi: 10.1016/j.rser.2014.01.069.R. Y. M. Li, S. Fong, y K. W. S. Chong, «Forecasting the REITs and stock indices: Group method of data handling neural network approach», Pac. Rim Prop. Res. J., vol. 23, n.o 2, pp. 123-160, 2017, doi: 10.1080/14445921.2016.1225149.«Acuerdo 1303 Por el cual se actualizan los procedimientos para la gestión integral de la demanda C.N.O». https://www.cno.org.co/content/acuerdo-1303-por-el-cual-se-actualizan-los-procedimientos-para-la-gestion-integral-de-la (accedido jun. 29, 2020)E. G. Tajeuna, M. Bouguessa, y S. Wang, «A network-based approach to enhance electricity load forecasting», 2019, vol. 2018-November, pp. 266-275. doi: 10.1109/ICDMW.2018.00046.L. N. Ferreira y L. Zhao, «A time series clustering technique based on community detection in networks», 2015, vol. 53, n.o 1, pp. 183-190. doi: 10.1016/j.procs.2015.07.293.M. E. J. Newman, «Fast algorithm for detecting community structure in networks», Phys. Rev. E - Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 69, n.o 6, p. 5, 2004, doi: 10.1103/PhysRevE.69.066133.G. Le Ray y P. Pinson, «Online adaptive clustering algorithm for load profiling», Sustain. Energy Grids Netw., vol. 17, 2019, doi: 10.1016/j.segan.2018.100181.L. F. S. Vilela, R. C. Leme, C. A. M. Pinheiro, y O. A. S. Carpinteiro, «Forecasting financial series using clustering methods and support vector regression», Artif. Intell. Rev., vol. 52, n.o 2, pp. 743-773, 2019, doi: 10.1007/s10462-018-9663-x.K. Gajowniczek y T. Zabkowski, «Simulation Study on Clustering Approaches for Short-Term Electricity Forecasting», Complexity, vol. 2018, 2018, doi: 10.1155/2018/3683969.P. Laurinec, M. Lóderer, M. Lucká, y V. Rozinajová, «Density-based unsupervised ensemble learning methods for time series forecasting of aggregated or clustered electricity consumption», J. Intell. Inf. Syst., vol. 53, n.o 2, pp. 219-239, 2019, doi: 10.1007/s10844-019-00550-3.S. Sun, J. Fu, y A. Li, «A compound wind power forecasting strategy based on clustering, two-stage decomposition, parameter optimization, and optimal combination of multiple machine learning approaches», Energies, vol. 12, n.o 18, 2019, doi: 10.3390/en12183586.Y. Wang, Y. Shen, S. Mao, X. Chen, y H. Zou, «LASSO and LSTM integrated temporal model for short term solar intensity forecasting», IEEE Internet Things J., vol. 6, n.o 2, pp. 2933-2944, 2019, doi: 10.1109/JIOT.2018.2877510.P. Laurinec y M. Lucká, «Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting», Data Min. Knowl. Discov., vol. 33, n.o 2, pp. 413-445, 2019, doi: 10.1007/s10618-018-0598-2.R. Jain, N. Jain, Y. Gupta, T. Chugh, T. Chugh, y D. J. Hemanth, «A Modified Fuzzy Logic Relation Based Approach for Electricity Consumption Forecasting in India», Int. J. Fuzzy Syst., vol. 22, n.o 2, pp. 461-475, 2020, doi: 10.1007/s40815-019-00704-z.S. Singh y A. Yassine, «Big data mining of energy time series for behavioral analytics and energy consumption forecasting», Energies, vol. 11, n.o 2, 2018, doi: 10.3390/en11020452.E. Y. Shchetinin, «Cluster-based energy consumption forecasting in smart grids», Commun. Comput. Inf. Sci., vol. 919, pp. 445-456, 2018, doi: 10.1007/978-3-319-99447-5_38.B. Auder, J. Cugliari, Y. Goude, y J.-M. Poggi, «Scalable clustering of individual electrical curves for profiling and bottom-up forecasting», Energies, vol. 11, n.o 7, 2018, doi: 10.3390/en11071893.L. Li, K. Ota, y M. Dong, «Everything is image: CNN-based short-term electrical load forecasting for smart grid», 2017, vol. 2017-November, pp. 344-351. doi: 10.1109/ISPAN-FCST-ISCC.2017.78.M. Ghofrani, R. Azimi, F. M. Najafabadi, y N. Myers, «A new day-ahead hourly electricity price forecasting framework», presentado en 2017 North American Power Symposium, NAPS 2017, 2017. doi: 10.1109/NAPS.2017.8107269.J. 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Softw., vol. 61, n.o 1, Art. n.o 1, nov. 2014, doi: 10.18637/jss.v061.i06.«pmdarima», API Reference. https://alkaline-ml.com/pmdarima/modules/classes.htmlInvestigadoresLICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/80568/3/license.txtcccfe52f796b7c63423298c2d3365fc6MD53ORIGINAL1144176600.2021.pdf1144176600.2021.pdfTesis de Maestría en Ingeniería - Analíticaapplication/pdf1479329https://repositorio.unal.edu.co/bitstream/unal/80568/4/1144176600.2021.pdf47bd28035578c803bed86d22edee54b9MD54THUMBNAIL1144176600.2021.pdf.jpg1144176600.2021.pdf.jpgGenerated Thumbnailimage/jpeg4672https://repositorio.unal.edu.co/bitstream/unal/80568/5/1144176600.2021.pdf.jpged2d51e9550cdff71f8ab889b8bf3ed9MD55unal/80568oai:repositorio.unal.edu.co:unal/805682024-07-31 23:13:29.249Repositorio Institucional Universidad Nacional de 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