Shaft power estimation in induction motor operating under unbalanced and harmonics voltages

In this work the application of a method to estimate the shaft power of induction motors operating in the presences of unbalanced and harmonics voltages is presented. The method uses the steady state equivalent circuits, with some considerations for the analysis of motor performance, fed with unbala...

Full description

Autores:
Quispe Oqueña, Enrique Ciro
Sousa Santos, Vladimir
Viego Felipe, Percy R.
Gómez Sarduy, Julio Rafael
Balbis Morejón, Milen
Tipo de recurso:
Article of journal
Fecha de publicación:
2016
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
spa
OAI Identifier:
oai:red.uao.edu.co:10614/11088
Acceso en línea:
http://hdl.handle.net/10614/11088
Palabra clave:
Análisis armónico
Motores eléctricos de inducción
Electric motors, Induction
Equivalent circuits
Harmonic analysis
Induction motors
Industrial power systems
Parameter estimation
Power quality
Unbalanced voltage
Rights
openAccess
License
Derechos Reservados - Universidad Autónoma de Occidente
id REPOUAO2_ce46cfba237b7c3ec2747941605be60d
oai_identifier_str oai:red.uao.edu.co:10614/11088
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
title Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
spellingShingle Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
Análisis armónico
Motores eléctricos de inducción
Electric motors, Induction
Equivalent circuits
Harmonic analysis
Induction motors
Industrial power systems
Parameter estimation
Power quality
Unbalanced voltage
title_short Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
title_full Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
title_fullStr Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
title_full_unstemmed Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
title_sort Shaft power estimation in induction motor operating under unbalanced and harmonics voltages
dc.creator.fl_str_mv Quispe Oqueña, Enrique Ciro
Sousa Santos, Vladimir
Viego Felipe, Percy R.
Gómez Sarduy, Julio Rafael
Balbis Morejón, Milen
dc.contributor.author.none.fl_str_mv Quispe Oqueña, Enrique Ciro
Sousa Santos, Vladimir
Viego Felipe, Percy R.
Gómez Sarduy, Julio Rafael
Balbis Morejón, Milen
dc.subject.armarc.spa.fl_str_mv Análisis armónico
Motores eléctricos de inducción
topic Análisis armónico
Motores eléctricos de inducción
Electric motors, Induction
Equivalent circuits
Harmonic analysis
Induction motors
Industrial power systems
Parameter estimation
Power quality
Unbalanced voltage
dc.subject.armarc.eng.fl_str_mv Electric motors, Induction
dc.subject.proposal.eng.fl_str_mv Equivalent circuits
Harmonic analysis
Induction motors
Industrial power systems
Parameter estimation
Power quality
Unbalanced voltage
description In this work the application of a method to estimate the shaft power of induction motors operating in the presences of unbalanced and harmonics voltages is presented. The method uses the steady state equivalent circuits, with some considerations for the analysis of motor performance, fed with unbalanced and harmonic voltages. The parameters of circuits are determined with low invasiveness, by applying a Bacterial Foraging Algorithm as technique of evolutionary search. With this, the shaft power can be estimated at any operating point. The method was tested in a 12.6 kW motor working in an industrial power supply grid, with harmonics and unbalanced voltage
publishDate 2016
dc.date.issued.none.fl_str_mv 2016-05
dc.date.accessioned.none.fl_str_mv 2019-09-10T18:47:55Z
dc.date.available.none.fl_str_mv 2019-09-10T18:47:55Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.eng.fl_str_mv Text
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dc.identifier.citation.eng.fl_str_mv Santos, V. S., Felipe, P. R. V., Sarduy, J. R. G., Quispe, E. C., & Balbis, M. (2016). Shaft power estimation in induction motor operating under unbalanced and harmonics voltages. IEEE Latin America Transactions, 14(5), 2309-2315
dc.identifier.issn.spa.fl_str_mv 1548-0992 (en línea)
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10614/11088
dc.identifier.doi.spa.fl_str_mv doi: 10.1109/TLA.2016.7530427
identifier_str_mv Santos, V. S., Felipe, P. R. V., Sarduy, J. R. G., Quispe, E. C., & Balbis, M. (2016). Shaft power estimation in induction motor operating under unbalanced and harmonics voltages. IEEE Latin America Transactions, 14(5), 2309-2315
1548-0992 (en línea)
doi: 10.1109/TLA.2016.7530427
url http://hdl.handle.net/10614/11088
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.eng.fl_str_mv IEEE Latin America Transactions, volumen 14, issue 5, páginas 2309-2315, (may, 2016)
dc.relation.cites.eng.fl_str_mv Santos, V. S., Felipe, P. R. V., Sarduy, J. R. G., Quispe, E. C., & Balbis, M. (2016). Shaft power estimation in induction motor operating under unbalanced and harmonics voltages. IEEE Latin America Transactions, 14(5), 2309-2315
dc.relation.references.spa.fl_str_mv Quispe, E.C., Lopez-Fernandez, X.M., Mendes, A.M.S., Marques Cardoso, A.J., Palacios, J.A. Influence of the positive sequence voltage on the derating of three-phase induction motors under voltage unbalance (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556239, pp. 100-105. Cited 15 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556239
Siraki, A.G., Pillay, P. An in situ efficiency estimation technique for induction machines working with unbalanced supplies (2012) IEEE Transactions on Energy Conversion, 27 (1), art. no. 6042327, pp. 85-95. Cited 29 times. doi: 10.1109/TEC.2011.2168563
Phumiphak, P., Chat-uthai, C. Nonintrusive method for estimating field efficiency of inverter- fed induction motor using measured values (2008) 2008 IEEE International Conference on Sustainable Energy Technologies, ICSET 2008, art. no. 4747074, pp. 580-583. Cited 15 times. ISBN: 978-142441888-6 doi: 10.1109/ICSET.2008.4747074
(1995) IEEE Recommended Practice for Monitoring Electric Power Quality. Cited 1243 times. IEEE Std 1159
(1993) IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems. Cited 2358 times. IEEE Standard 519
(2004) IEEE Standard Test Procedure for Polyphase Induction Motors and Generators. Cited 523 times. IEEE Standard 112
(2014) IEC Standard Methods for Determining Losses and Efficiency from Tests. Cited 2 times. IEC Standard 60034-2-1
Lu, B., Habetler, T.G., Harley, R.G. A nonintrusive and in-service motor-efficiency estimation method using air-gap torque with considerations of condition monitoring (2008) IEEE Transactions on Industry Applications, 44 (6), pp. 1666-1674. Cited 65 times. doi: 10.1109/TIA.2008.2006297
Çunkaş, M., Saǧ, T. Efficiency determination of induction motors using multi-objective evolutionary algorithms (2010) Advances in Engineering Software, 41 (2), pp. 255-261. Cited 26 times. http://www.journals.elsevier.com/advances-in-engineering-software/ doi: 10.1016/j.advengsoft.2009.07.008
Salomon, C.P., Santana, W.C., Da Silva, L.E.B., Bonaldi, E.L., De Oliveira, L.E.L., Da Silva, J.G.B., Lambert-Torres, G., (...), Donadon, A.R. A stator flux synthesis approach for torque estimation of induction motors using a modified stator resistance considering the losses effect (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556315, pp. 1369-1375. Cited 6 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556315
Bae, D., Kim, D., Jung, H.-K., Hahn, S.-Y., Koh, C.S. Determination of induction motor parameters by using neural network based on FEM results (1997) IEEE Transactions on Magnetics, 33 (2 PART 2), pp. 1924-1927. Cited 16 times
Grewal, G.S., Rajpurohit, B.S. Comparison of efficiencies of in situ induction motor in unbalanced field conditions (2015) Proceedings of the 2015 IEEE International Conference on Power and Advanced Control Engineering, ICPACE 2015, art. no. 7274919, pp. 70-74. Cited 2 times. ISBN: 978-147998370-4 doi: 10.1109/ICPACE.2015.7274919
Liu, Y., Passino, K.M. Biomimicry of social foraging bacteria for distributed optimization: Models, principles, and emergent behaviors (2002) Journal of Optimization Theory and Applications, 115 (3), pp. 603-628. Cited 232 times. doi: 10.1023/A:1021207331209
Sakthivel, V.P., Bhuvaneswari, R., Subramanian, S. An accurate and economical approach for induction motor field efficiency estimation using bacterial foraging algorithm (2011) Measurement: Journal of the International Measurement Confederation, 44 (4), pp. 674-684. Cited 25 times. doi: 10.1016/j.measurement.2010.12.008
Sousa Santos, V., Viego Felipe, P., Gómez Sarduy, J. Bacterial foraging algorithm application for induction motor field efficiency estimation under unbalanced voltajes (2013) Measurement: Journal of the International Measurement Confederation, 46 (7), pp. 2232-2237. Cited 16 times. doi: 10.1016/j.measurement.2013.03.019
Sousa, V., Viego, P.R., Gómez, J., Lemozy, N., Jurado, A., Quispe, E.C. Procedure for determining induction motor efficiency working under distorted grid voltajes (2014) IEEE Trans. Energy Convers., PP (99), pp. 1-9. Cited 2 times
Sousa Santos, V., Quispe, E.C., Gomez Sarduy, J.R., Viego, P.R., Lemozy, N., Jurado, A., Brugnoni, M. Bacterial Foraging Algorithm application for induction motor field efficiency estimation under harmonics and unbalanced voltajes (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556235, pp. 1108-1111. Cited 6 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556235
(1993) IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems. Cited 2358 times. IEEE Standard 519
Pedra, J., Sainz, L., Córcoles, F. Harmonic modeling of induction motors (2006) Electric Power Systems Research, 76 (11), pp. 936-944. Cited 10 times. doi: 10.1016/j.epsr.2005.10.015
Escobar, J.C.A., De La Rosa, F. Shaft torsional vibration due to non-linear loads in low capacity turbine units (2001) Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, 3 (SUMMER), art. no. 22, pp. 1403-1408. Cited 13 times. doi: 10.1109/PESS.2001.970282
Cummings, Paul G. ESTIMATING EFFECT OF SYSTEM HARMONICS ON LOSSES AND TEMPERATURE RISE OF SQUIRREL-CAGE MOTORS. (1986) IEEE Transactions on Industry Applications, IA-22 (6), pp. 1121-1126. Cited 37 times. doi: 10.1109/TIA.1986.4504843
Ivanov-Smolenski, V. (1984) Electrical Machines, 2. Cited 78 times. Moscú: Mir
Emanuel, A.E., Orr, J.A., Cyganski, D., Gulachenski, E.M. A survey of harmonic voltages and currents at distribution substations (1991) IEEE Transactions on Power Delivery, 6 (4), pp. 1883-1890. Cited 70 times. doi: 10.1109/61.97736
Baghzouz, Y., Burch, R.F., Capasso, A., Cavallini, A., Emanuel, A.E., Halpin, M., Imece, A., (...), Verde, P. Time-varying harmonics: Part I - Characterizing measured data (1998) IEEE Transactions on Power Delivery, 13 (3), pp. 938-944. Cited 122 times. doi: 10.1109/61.686996
WEKA MOTORENPRÜFSTÄNDE Manufacturer [Online] http://www.weka-motorenpruefstaende.de/
(2006) IEC Standard Rotating Electrical machines-Part26: Effects of Unbalanced Voltages on the Performance of Three-phase Cage Induction Motors. Cited 6 times. IEC Standard 60034-26
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rights_invalid_str_mv Derechos Reservados - Universidad Autónoma de Occidente
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spelling Quispe Oqueña, Enrique Cirovirtual::18-1Sousa Santos, Vladimir7d49f4c6dc5688b53999d936638b4426Viego Felipe, Percy R.73e56a4005be0f470f4dcea62618197bGómez Sarduy, Julio Rafael77a5057c8e70b9722f27cf7e3c088d69Balbis Morejón, Milenfca32cf89bcc056365f1b795d060836cUniversidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-09-10T18:47:55Z2019-09-10T18:47:55Z2016-05Santos, V. S., Felipe, P. R. V., Sarduy, J. R. G., Quispe, E. C., & Balbis, M. (2016). Shaft power estimation in induction motor operating under unbalanced and harmonics voltages. IEEE Latin America Transactions, 14(5), 2309-23151548-0992 (en línea)http://hdl.handle.net/10614/11088doi: 10.1109/TLA.2016.7530427In this work the application of a method to estimate the shaft power of induction motors operating in the presences of unbalanced and harmonics voltages is presented. The method uses the steady state equivalent circuits, with some considerations for the analysis of motor performance, fed with unbalanced and harmonic voltages. The parameters of circuits are determined with low invasiveness, by applying a Bacterial Foraging Algorithm as technique of evolutionary search. With this, the shaft power can be estimated at any operating point. The method was tested in a 12.6 kW motor working in an industrial power supply grid, with harmonics and unbalanced voltageEn este trabajo se aplica un método para estimar la potencia de inducción del eje. Los motores que funcionan en presencia de tensiones desequilibradas y armónicas son presentados el método utiliza los circuitos equivalentes de estado estable, con algunas consideraciones para el análisis del rendimiento del motor, alimentadas con desequilibrios y tensiones armónicas. Los parámetros de los circuitos se determinan con bajo. Invasividad, aplicando un algoritmo de forraje bacteriano como técnica de búsqueda evolutiva. Con esto, la potencia del eje se puede estimar en cualquier operación punto. El método fue probado en un motor de 12.6 kw trabajando en una potencia industrial. Red de suministro, con armónicos y tensión desequilibradaapplication/pdfpáginas 2309-2315spaIEEE Computer SocietyIEEE Latin America Transactions, volumen 14, issue 5, páginas 2309-2315, (may, 2016)Santos, V. S., Felipe, P. R. V., Sarduy, J. R. G., Quispe, E. C., & Balbis, M. (2016). Shaft power estimation in induction motor operating under unbalanced and harmonics voltages. IEEE Latin America Transactions, 14(5), 2309-2315Quispe, E.C., Lopez-Fernandez, X.M., Mendes, A.M.S., Marques Cardoso, A.J., Palacios, J.A. Influence of the positive sequence voltage on the derating of three-phase induction motors under voltage unbalance (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556239, pp. 100-105. Cited 15 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556239Siraki, A.G., Pillay, P. An in situ efficiency estimation technique for induction machines working with unbalanced supplies (2012) IEEE Transactions on Energy Conversion, 27 (1), art. no. 6042327, pp. 85-95. Cited 29 times. doi: 10.1109/TEC.2011.2168563Phumiphak, P., Chat-uthai, C. Nonintrusive method for estimating field efficiency of inverter- fed induction motor using measured values (2008) 2008 IEEE International Conference on Sustainable Energy Technologies, ICSET 2008, art. no. 4747074, pp. 580-583. Cited 15 times. ISBN: 978-142441888-6 doi: 10.1109/ICSET.2008.4747074(1995) IEEE Recommended Practice for Monitoring Electric Power Quality. Cited 1243 times. IEEE Std 1159(1993) IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems. Cited 2358 times. IEEE Standard 519(2004) IEEE Standard Test Procedure for Polyphase Induction Motors and Generators. Cited 523 times. IEEE Standard 112(2014) IEC Standard Methods for Determining Losses and Efficiency from Tests. Cited 2 times. IEC Standard 60034-2-1Lu, B., Habetler, T.G., Harley, R.G. A nonintrusive and in-service motor-efficiency estimation method using air-gap torque with considerations of condition monitoring (2008) IEEE Transactions on Industry Applications, 44 (6), pp. 1666-1674. Cited 65 times. doi: 10.1109/TIA.2008.2006297Çunkaş, M., Saǧ, T. Efficiency determination of induction motors using multi-objective evolutionary algorithms (2010) Advances in Engineering Software, 41 (2), pp. 255-261. Cited 26 times. http://www.journals.elsevier.com/advances-in-engineering-software/ doi: 10.1016/j.advengsoft.2009.07.008Salomon, C.P., Santana, W.C., Da Silva, L.E.B., Bonaldi, E.L., De Oliveira, L.E.L., Da Silva, J.G.B., Lambert-Torres, G., (...), Donadon, A.R. A stator flux synthesis approach for torque estimation of induction motors using a modified stator resistance considering the losses effect (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556315, pp. 1369-1375. Cited 6 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556315Bae, D., Kim, D., Jung, H.-K., Hahn, S.-Y., Koh, C.S. Determination of induction motor parameters by using neural network based on FEM results (1997) IEEE Transactions on Magnetics, 33 (2 PART 2), pp. 1924-1927. Cited 16 timesGrewal, G.S., Rajpurohit, B.S. Comparison of efficiencies of in situ induction motor in unbalanced field conditions (2015) Proceedings of the 2015 IEEE International Conference on Power and Advanced Control Engineering, ICPACE 2015, art. no. 7274919, pp. 70-74. Cited 2 times. ISBN: 978-147998370-4 doi: 10.1109/ICPACE.2015.7274919Liu, Y., Passino, K.M. Biomimicry of social foraging bacteria for distributed optimization: Models, principles, and emergent behaviors (2002) Journal of Optimization Theory and Applications, 115 (3), pp. 603-628. Cited 232 times. doi: 10.1023/A:1021207331209Sakthivel, V.P., Bhuvaneswari, R., Subramanian, S. An accurate and economical approach for induction motor field efficiency estimation using bacterial foraging algorithm (2011) Measurement: Journal of the International Measurement Confederation, 44 (4), pp. 674-684. Cited 25 times. doi: 10.1016/j.measurement.2010.12.008Sousa Santos, V., Viego Felipe, P., Gómez Sarduy, J. Bacterial foraging algorithm application for induction motor field efficiency estimation under unbalanced voltajes (2013) Measurement: Journal of the International Measurement Confederation, 46 (7), pp. 2232-2237. Cited 16 times. doi: 10.1016/j.measurement.2013.03.019Sousa, V., Viego, P.R., Gómez, J., Lemozy, N., Jurado, A., Quispe, E.C. Procedure for determining induction motor efficiency working under distorted grid voltajes (2014) IEEE Trans. Energy Convers., PP (99), pp. 1-9. Cited 2 timesSousa Santos, V., Quispe, E.C., Gomez Sarduy, J.R., Viego, P.R., Lemozy, N., Jurado, A., Brugnoni, M. Bacterial Foraging Algorithm application for induction motor field efficiency estimation under harmonics and unbalanced voltajes (2013) Proceedings of the 2013 IEEE International Electric Machines and Drives Conference, IEMDC 2013, art. no. 6556235, pp. 1108-1111. Cited 6 times. ISBN: 978-146734975-8 doi: 10.1109/IEMDC.2013.6556235(1993) IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems. Cited 2358 times. IEEE Standard 519Pedra, J., Sainz, L., Córcoles, F. Harmonic modeling of induction motors (2006) Electric Power Systems Research, 76 (11), pp. 936-944. Cited 10 times. doi: 10.1016/j.epsr.2005.10.015Escobar, J.C.A., De La Rosa, F. Shaft torsional vibration due to non-linear loads in low capacity turbine units (2001) Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, 3 (SUMMER), art. no. 22, pp. 1403-1408. Cited 13 times. doi: 10.1109/PESS.2001.970282Cummings, Paul G. ESTIMATING EFFECT OF SYSTEM HARMONICS ON LOSSES AND TEMPERATURE RISE OF SQUIRREL-CAGE MOTORS. (1986) IEEE Transactions on Industry Applications, IA-22 (6), pp. 1121-1126. Cited 37 times. doi: 10.1109/TIA.1986.4504843Ivanov-Smolenski, V. (1984) Electrical Machines, 2. Cited 78 times. Moscú: MirEmanuel, A.E., Orr, J.A., Cyganski, D., Gulachenski, E.M. A survey of harmonic voltages and currents at distribution substations (1991) IEEE Transactions on Power Delivery, 6 (4), pp. 1883-1890. Cited 70 times. doi: 10.1109/61.97736Baghzouz, Y., Burch, R.F., Capasso, A., Cavallini, A., Emanuel, A.E., Halpin, M., Imece, A., (...), Verde, P. Time-varying harmonics: Part I - Characterizing measured data (1998) IEEE Transactions on Power Delivery, 13 (3), pp. 938-944. Cited 122 times. doi: 10.1109/61.686996WEKA MOTORENPRÜFSTÄNDE Manufacturer [Online] http://www.weka-motorenpruefstaende.de/(2006) IEC Standard Rotating Electrical machines-Part26: Effects of Unbalanced Voltages on the Performance of Three-phase Cage Induction Motors. Cited 6 times. IEC Standard 60034-26Derechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2https://ieeexplore.ieee.org/document/7530427Shaft power estimation in induction motor operating under unbalanced and harmonics voltagesArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Análisis armónicoMotores eléctricos de inducciónElectric motors, InductionEquivalent circuitsHarmonic analysisInduction motorsIndustrial power systemsParameter estimationPower qualityUnbalanced voltagePublicationc6bf35c2-a499-44cd-abc3-eb4b458d7de5virtual::18-1c6bf35c2-a499-44cd-abc3-eb4b458d7de5virtual::18-1c6bf35c2-a499-44cd-abc3-eb4b458d7de5https://scholar.google.com.co/citations?user=8WM_SB8AAAAJ&hl=envirtual::18-1https://scholar.google.com.co/citations?user=8WM_SB8AAAAJ&hl=enhttps://orcid.org/0000-0003-3223-1834virtual::18-1https://orcid.org/0000-0003-3223-1834https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000144304virtual::18-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/8685cdf0-da7a-4478-99ae-7d08909e1e64/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/bd10d111-99af-4f1b-b028-135315946bdc/download20b5ba22b1117f71589c7318baa2c560MD5310614/11088oai:red.uao.edu.co:10614/110882024-03-01 11:47:27.86https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidentemetadata.onlyhttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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