Unbalanced voltages impacts on the energy performance of induction motors

This paper presents the results of a study about the effects of unbalanced voltages on the energy performance of three-phase induction motors. The principal contribution of this paper is that presents a detailed analysis of the influence of positive and negative sequence voltage components and the a...

Full description

Autores:
Quispe Oqueña, Enrique Ciro
Ferreria, Fernando
Sousa Santos, Vladimir
López, Iván D.
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/11408
Acceso en línea:
http://hdl.handle.net/10614/11408
Palabra clave:
Motores eléctricos de inducción
Electric motors, Induction
Efficiency
Energy performance
Induction motors
Losses
Power factor
Voltage unbalance
Rights
openAccess
License
Derechos Reservados - Universidad Autónoma de Occidente
id REPOUAO2_4392d370e26a7fa789e0db5ca59770d9
oai_identifier_str oai:red.uao.edu.co:10614/11408
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Unbalanced voltages impacts on the energy performance of induction motors
title Unbalanced voltages impacts on the energy performance of induction motors
spellingShingle Unbalanced voltages impacts on the energy performance of induction motors
Motores eléctricos de inducción
Electric motors, Induction
Efficiency
Energy performance
Induction motors
Losses
Power factor
Voltage unbalance
title_short Unbalanced voltages impacts on the energy performance of induction motors
title_full Unbalanced voltages impacts on the energy performance of induction motors
title_fullStr Unbalanced voltages impacts on the energy performance of induction motors
title_full_unstemmed Unbalanced voltages impacts on the energy performance of induction motors
title_sort Unbalanced voltages impacts on the energy performance of induction motors
dc.creator.fl_str_mv Quispe Oqueña, Enrique Ciro
Ferreria, Fernando
Sousa Santos, Vladimir
López, Iván D.
dc.contributor.author.none.fl_str_mv Quispe Oqueña, Enrique Ciro
Ferreria, Fernando
Sousa Santos, Vladimir
López, Iván D.
dc.subject.armarc.spa.fl_str_mv Motores eléctricos de inducción
topic Motores eléctricos de inducción
Electric motors, Induction
Efficiency
Energy performance
Induction motors
Losses
Power factor
Voltage unbalance
dc.subject.armarc.eng.fl_str_mv Electric motors, Induction
dc.subject.proposal.eng.fl_str_mv Efficiency
Energy performance
Induction motors
Losses
Power factor
Voltage unbalance
description This paper presents the results of a study about the effects of unbalanced voltages on the energy performance of three-phase induction motors. The principal contribution of this paper is that presents a detailed analysis of the influence of positive and negative sequence voltage components and the angle between them on several characteristics such as: line currents, losses, efficiency and power factor under different voltage unbalanced conditions. A three-phase induction motor of 3 HP was used as a case study. The results of the investigation show that the positive sequence voltage must be considered together with the voltage unbalance factor (VUF) or percent voltage unbalance (PVU) index to evaluate the performance of the induction motor. It is also shown that the behavior of the motor load influences on the positive sequence parameters next to the voltage, while in the case of negative sequence only influences the negative sequence voltage
publishDate 2018
dc.date.issued.none.fl_str_mv 2018-05-07
dc.date.accessioned.none.fl_str_mv 2019-11-06T14:37:00Z
dc.date.available.none.fl_str_mv 2019-11-06T14:37:00Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.eng.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.eng.fl_str_mv Text
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.eng.fl_str_mv http://purl.org/redcol/resource_type/ARTREF
dc.type.version.eng.fl_str_mv info:eu-repo/semantics/publishedVersion
format http://purl.org/coar/resource_type/c_6501
status_str publishedVersion
dc.identifier.issn.spa.fl_str_mv 2088-8708
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10614/11408
dc.identifier.doi.none.fl_str_mv DOI: 10.11591/ijece.v8i3
identifier_str_mv 2088-8708
DOI: 10.11591/ijece.v8i3
url http://hdl.handle.net/10614/11408
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.none.fl_str_mv 1422
dc.relation.citationissue.none.fl_str_mv 3
dc.relation.citationstartpage.none.fl_str_mv 1412
dc.relation.citationvolume.none.fl_str_mv 8
dc.relation.cites.eng.fl_str_mv Quispe, E. C., López, I. D., Ferreira, F. J., y Sousa Santos, V. (2018). Unbalanced voltages impacts on the energy performance of induction motors. International Journal of Electrical and Computer Engineering (IJECE). 8(3), 1412~1422. DOI: 10.11591/ijece.v8i3
dc.relation.ispartofjournal.eng.fl_str_mv International Journal of Electrical and Computer Engineering (IJECE)
dc.relation.references.none.fl_str_mv [1] M. Sulaiman, Z. Salleh, and R. Omar, “Effects of parameters variation in fuzzy based induction motor drives”, Indonesian Journal of Electrical Engineering and Computer Science, vol. 16, No. 2, pp. 272-280, Nov. 2015.
[2] V. Sousa, P. R. Viego, J. R. Gómez, E. C. Quispe and M. Balbis, "Estimating induction motor efficiency under no-controlled conditions in the presences of unbalanced and harmonics voltages," in Proceedings CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), 2015, pp. 567-572.
[3] V. S. Santos, P. V Felipe and J. G. Sarduy, ”Bacterial foraging algorithm application for induction motor field efficiency estimation under unbalanced voltages” Measurement, vol. 46, no.7, pp. 2232-2237, Aug. 2013.
[4] S. M. Ahmed, H. Abu-Rub, S. S. Refaat and A. Iqbal, “Diagnosis of stator turn-to-turn fault and stator voltage unbalance fault using ANFIS,” International Journal of Electrical and Computer Engineering, vol. 3, No. 1, pp. 129-135, Feb. 2015.
[5] M. Al-Badri, P. Pillay and P. Angers, "A novel in situ efficiency estimation algorithm for three-phase induction motors operating with distorted unbalanced voltages," IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5338-5347, 2017.
[6] G. J. Retter, “Matrix and Space-Phasor Theory of Electrical Machines”, Académiai Kiadó, 1987, p. 411.
[7] A. Siddique, G.S. Yadava and B. Singh, “Effect of voltage unbalance on induction motors”, in Proceedings IEEE International Symposium on Electrical Insulation, 2004, pp. 26-29.
[8] J. R. Linders, “Effect of power supply variations on ac motor characteristics,” IEEE Transactions on Industry Applications, vol. IA-8, no. 4, pp. 383-400, July/August 1972.
[9] “IEC Rotating Electrical Machines - Part 26: Effects on unbalanced voltages on the performance of induction motors”, IEC Standard 60034-26, Geneva, Switzerland, 2006.
[10] M.A. de Armas, J. Gomez, “Análisis generalizado de los motores asíncronos con alimentación desbalanceada o no mediante la teoría de los campos rotatorios,” Energética, no. 39, pp. 5-11, 2008.
[11] Y. J. Wang, “Analysis of effects of three-phase voltage unbalance on induction motors with emphasis on the angle of the complex voltage unbalance factor,” IEEE Transactions on Energy Conversion, vol. 16, no. 3, pp. 270-275, Sept. 2001.
[12] J. Faiz, H. Ebrahimpour, and P. Pillay, “Influence of unbalanced voltage on the steady-state performance of a three-phase squirrel-cage induction motor,” IEEE Transactions on Energy Conversion, vol. 19, no. 4, pp. 657-662, 2004.
[13] A. Costa, and X. M. Lopez Fernandez, “Effects of unbalanced power supply on efficient performance of three
phase induction motors”, in Proceedings XL International Symposium on Electrical Machines SME’2004, 2004, pp. 15-18.
[14] “NEMA Motors and Generators”, Standard Publication ANSI/NEMA MG1-2003, Revision 1-2004, Publishing by NEMA, Rosslyn, USA, 2003.
[15] A. M. S. Mendes, E. C. Quispe, X. M. López-Fernández, and A. J. Marques Cardoso, “Influence of the positive sequence voltage on the temperature of three-phase induction motors,” in Proceedings XIX International Conference on Electrical Machines - ICEM 2010, 2010, pp. 1-6.
[16] E. C. Quispe, X. M. López-Fernández, A. M. S. Mendes, A. J. Marques Cardoso and J. A. Palacios, “Experimental Study of the effect of positive sequence voltage on the derating of three-phase induction motors under voltaje unbalance”, in Proceedings 2011 IEEE International Electric Machines & Drives Conference (IEMDC), 2011, pp. 908-912.
[17] M. Jannati, T. Sutikno, N. R. N. Idris and M. J. A. Aziz, “Modeling of balanced and unbalanced three-phase induction motor under balanced and unbalanced supply based on winding function method,” International Journal of Electrical and Computer Engineering, vol. 5, No. 4, pp. 644-655, Aug. 2015.
[18] E. C. Quispe, “Efectos del desequilibrio de tensiones sobre la operación del motor de inducción trifásico. Énfasis en la caracterización del desequilibrio de tensiones y el efecto sobre la potencia nominal,” Ph.D. Dissertation, School of Electrical and Electronic Engineering, Univ. Del Valle, Colombia, 2012.
[19] S.E.M. de Oliveira, “Operation of three-phase induction connected to one-phase supply,” IEEE Transaction on Energy Conversion, vol. 5, no. 4, pp. 713-718, Dec. 1990. [20] P.C. Cochran, “Polyphase induction motors: analysis, desing and application”, Copyright 1989 by Marcel Dekker, Inc., Print in USA, New York, 1989. p. 678.
[21] M. Kostic, and A. Nicolic, “Negative consequence of motor voltage asymmetry and its influence to the unefficient energy usage,” WSEAS Transactions on Circuits and Systems, vol. 9, no. 8, pp. 547-552, Aug. 2010.
[22] E. C. Quispe, X. M. Lopez-Fernandez, A. M. S. Mendes, A. J. Marquez-Cardoso and J. A. Palacios. “Influence of the positive sequence voltage on the derating of three-phase induction motors under voltage unbalance”, in Proceedings 2013 IEEE International Electric Machines & Drives Conference (IEMDC), 2013, pp. 100-105.
[23] E. C. Quispe, “Una visión integral para el uso racional de la energía en la aplicación de los motores eléctricos de inducción,” Revista El Hombre y la Maquina, No. 20-21, pp. 52-59, Jul/Dic 2003.
[24] A. Eltom, and M.A. Aziz, “The economics of energy efficient motors during unbalanced voltage condition”, in Proceedings of the Inaugural IEEE Power Engineering Society PES Conference and Exposition in Africa, 2005, pp. 378-384.
[25] J. Faiz, H. Ebrahimpour, and P. Pillay, “Influence of unbalanced voltage supply of three phase squirrel cage induction motor and economic analysis,” Energy Conversion and Management, vol. 47, no. 3, pp. 289-302, Feb, 2006.
dc.rights.spa.fl_str_mv Derechos Reservados - Universidad Autónoma de Occidente
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.eng.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.eng.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.creativecommons.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
rights_invalid_str_mv Derechos Reservados - Universidad Autónoma de Occidente
https://creativecommons.org/licenses/by-nc-nd/4.0/
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.eng.fl_str_mv application/pdf
dc.format.extent.spa.fl_str_mv 11 páginas
dc.coverage.spatial.none.fl_str_mv Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí
dc.publisher.eng.fl_str_mv Institute of Advanced Engineering and Science
institution Universidad Autónoma de Occidente
bitstream.url.fl_str_mv https://red.uao.edu.co/bitstreams/d4b5675d-7e8d-4ea3-a4f9-f927e131630a/download
https://red.uao.edu.co/bitstreams/5a785c19-f55f-4f50-94bc-67735a6d2a4a/download
https://red.uao.edu.co/bitstreams/3e6f9d95-1713-4688-81f6-b54590a0df4b/download
https://red.uao.edu.co/bitstreams/1b33a55b-4596-4649-af84-c57dc5d79cd7/download
https://red.uao.edu.co/bitstreams/b91f5718-69ff-4806-9f5a-dcdc9ec12f48/download
bitstream.checksum.fl_str_mv 4460e5956bc1d1639be9ae6146a50347
20b5ba22b1117f71589c7318baa2c560
ca1da4ebb29ed4308ca88ecf99bd2891
002827d3fba042f7e6741d382cc30048
d8b5e30d4f7d60c8b59c2d03f186a475
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Digital Universidad Autonoma de Occidente
repository.mail.fl_str_mv repositorio@uao.edu.co
_version_ 1814260215050141696
spelling Quispe Oqueña, Enrique Ciro5d812e79c25beafd495677bd503541a4Ferreria, Fernandoe627366357566716795ea43fa73eb2f1Sousa Santos, Vladimir7d49f4c6dc5688b53999d936638b4426López, Iván D.4f4787a84f5a79d2335308935bb831e5Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-06T14:37:00Z2019-11-06T14:37:00Z2018-05-072088-8708http://hdl.handle.net/10614/11408DOI: 10.11591/ijece.v8i3This paper presents the results of a study about the effects of unbalanced voltages on the energy performance of three-phase induction motors. The principal contribution of this paper is that presents a detailed analysis of the influence of positive and negative sequence voltage components and the angle between them on several characteristics such as: line currents, losses, efficiency and power factor under different voltage unbalanced conditions. A three-phase induction motor of 3 HP was used as a case study. The results of the investigation show that the positive sequence voltage must be considered together with the voltage unbalance factor (VUF) or percent voltage unbalance (PVU) index to evaluate the performance of the induction motor. It is also shown that the behavior of the motor load influences on the positive sequence parameters next to the voltage, while in the case of negative sequence only influences the negative sequence voltagehttp://repositorio.cuc.edu.co/handle/11323/4624application/pdf11 páginasengInstitute of Advanced Engineering and ScienceDerechos 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_abf2Unbalanced voltages impacts on the energy performance of induction motorsArtículo 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_970fb48d4fbd8a85Motores eléctricos de inducciónElectric motors, InductionEfficiencyEnergy performanceInduction motorsLossesPower factorVoltage unbalance1422314128Quispe, E. C., López, I. D., Ferreira, F. J., y Sousa Santos, V. (2018). Unbalanced voltages impacts on the energy performance of induction motors. International Journal of Electrical and Computer Engineering (IJECE). 8(3), 1412~1422. DOI: 10.11591/ijece.v8i3International Journal of Electrical and Computer Engineering (IJECE)[1] M. Sulaiman, Z. Salleh, and R. Omar, “Effects of parameters variation in fuzzy based induction motor drives”, Indonesian Journal of Electrical Engineering and Computer Science, vol. 16, No. 2, pp. 272-280, Nov. 2015.[2] V. Sousa, P. R. Viego, J. R. Gómez, E. C. Quispe and M. Balbis, "Estimating induction motor efficiency under no-controlled conditions in the presences of unbalanced and harmonics voltages," in Proceedings CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), 2015, pp. 567-572.[3] V. S. Santos, P. V Felipe and J. G. Sarduy, ”Bacterial foraging algorithm application for induction motor field efficiency estimation under unbalanced voltages” Measurement, vol. 46, no.7, pp. 2232-2237, Aug. 2013.[4] S. M. Ahmed, H. Abu-Rub, S. S. Refaat and A. Iqbal, “Diagnosis of stator turn-to-turn fault and stator voltage unbalance fault using ANFIS,” International Journal of Electrical and Computer Engineering, vol. 3, No. 1, pp. 129-135, Feb. 2015.[5] M. Al-Badri, P. Pillay and P. Angers, "A novel in situ efficiency estimation algorithm for three-phase induction motors operating with distorted unbalanced voltages," IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5338-5347, 2017.[6] G. J. Retter, “Matrix and Space-Phasor Theory of Electrical Machines”, Académiai Kiadó, 1987, p. 411.[7] A. Siddique, G.S. Yadava and B. Singh, “Effect of voltage unbalance on induction motors”, in Proceedings IEEE International Symposium on Electrical Insulation, 2004, pp. 26-29.[8] J. R. Linders, “Effect of power supply variations on ac motor characteristics,” IEEE Transactions on Industry Applications, vol. IA-8, no. 4, pp. 383-400, July/August 1972.[9] “IEC Rotating Electrical Machines - Part 26: Effects on unbalanced voltages on the performance of induction motors”, IEC Standard 60034-26, Geneva, Switzerland, 2006.[10] M.A. de Armas, J. Gomez, “Análisis generalizado de los motores asíncronos con alimentación desbalanceada o no mediante la teoría de los campos rotatorios,” Energética, no. 39, pp. 5-11, 2008.[11] Y. J. Wang, “Analysis of effects of three-phase voltage unbalance on induction motors with emphasis on the angle of the complex voltage unbalance factor,” IEEE Transactions on Energy Conversion, vol. 16, no. 3, pp. 270-275, Sept. 2001.[12] J. Faiz, H. Ebrahimpour, and P. Pillay, “Influence of unbalanced voltage on the steady-state performance of a three-phase squirrel-cage induction motor,” IEEE Transactions on Energy Conversion, vol. 19, no. 4, pp. 657-662, 2004.[13] A. Costa, and X. M. Lopez Fernandez, “Effects of unbalanced power supply on efficient performance of threephase induction motors”, in Proceedings XL International Symposium on Electrical Machines SME’2004, 2004, pp. 15-18.[14] “NEMA Motors and Generators”, Standard Publication ANSI/NEMA MG1-2003, Revision 1-2004, Publishing by NEMA, Rosslyn, USA, 2003.[15] A. M. S. Mendes, E. C. Quispe, X. M. López-Fernández, and A. J. Marques Cardoso, “Influence of the positive sequence voltage on the temperature of three-phase induction motors,” in Proceedings XIX International Conference on Electrical Machines - ICEM 2010, 2010, pp. 1-6.[16] E. C. Quispe, X. M. López-Fernández, A. M. S. Mendes, A. J. Marques Cardoso and J. A. Palacios, “Experimental Study of the effect of positive sequence voltage on the derating of three-phase induction motors under voltaje unbalance”, in Proceedings 2011 IEEE International Electric Machines & Drives Conference (IEMDC), 2011, pp. 908-912.[17] M. Jannati, T. Sutikno, N. R. N. Idris and M. J. A. Aziz, “Modeling of balanced and unbalanced three-phase induction motor under balanced and unbalanced supply based on winding function method,” International Journal of Electrical and Computer Engineering, vol. 5, No. 4, pp. 644-655, Aug. 2015.[18] E. C. Quispe, “Efectos del desequilibrio de tensiones sobre la operación del motor de inducción trifásico. Énfasis en la caracterización del desequilibrio de tensiones y el efecto sobre la potencia nominal,” Ph.D. Dissertation, School of Electrical and Electronic Engineering, Univ. Del Valle, Colombia, 2012.[19] S.E.M. de Oliveira, “Operation of three-phase induction connected to one-phase supply,” IEEE Transaction on Energy Conversion, vol. 5, no. 4, pp. 713-718, Dec. 1990. [20] P.C. Cochran, “Polyphase induction motors: analysis, desing and application”, Copyright 1989 by Marcel Dekker, Inc., Print in USA, New York, 1989. p. 678.[21] M. Kostic, and A. Nicolic, “Negative consequence of motor voltage asymmetry and its influence to the unefficient energy usage,” WSEAS Transactions on Circuits and Systems, vol. 9, no. 8, pp. 547-552, Aug. 2010.[22] E. C. Quispe, X. M. Lopez-Fernandez, A. M. S. Mendes, A. J. Marquez-Cardoso and J. A. Palacios. “Influence of the positive sequence voltage on the derating of three-phase induction motors under voltage unbalance”, in Proceedings 2013 IEEE International Electric Machines & Drives Conference (IEMDC), 2013, pp. 100-105.[23] E. C. Quispe, “Una visión integral para el uso racional de la energía en la aplicación de los motores eléctricos de inducción,” Revista El Hombre y la Maquina, No. 20-21, pp. 52-59, Jul/Dic 2003.[24] A. Eltom, and M.A. Aziz, “The economics of energy efficient motors during unbalanced voltage condition”, in Proceedings of the Inaugural IEEE Power Engineering Society PES Conference and Exposition in Africa, 2005, pp. 378-384.[25] J. Faiz, H. Ebrahimpour, and P. Pillay, “Influence of unbalanced voltage supply of three phase squirrel cage induction motor and economic analysis,” Energy Conversion and Management, vol. 47, no. 3, pp. 289-302, Feb, 2006.PublicationCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/d4b5675d-7e8d-4ea3-a4f9-f927e131630a/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/5a785c19-f55f-4f50-94bc-67735a6d2a4a/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALUnbalanced voltages impacts on the energy performance of induction motors.pdfUnbalanced voltages impacts on the energy performance of induction motors.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf302510https://red.uao.edu.co/bitstreams/3e6f9d95-1713-4688-81f6-b54590a0df4b/downloadca1da4ebb29ed4308ca88ecf99bd2891MD54TEXTUnbalanced voltages impacts on the energy performance of induction motors.pdf.txtUnbalanced voltages impacts on the energy performance of induction motors.pdf.txtExtracted texttext/plain35496https://red.uao.edu.co/bitstreams/1b33a55b-4596-4649-af84-c57dc5d79cd7/download002827d3fba042f7e6741d382cc30048MD55THUMBNAILUnbalanced voltages impacts on the energy performance of induction motors.pdf.jpgUnbalanced voltages impacts on the energy performance of induction motors.pdf.jpgGenerated Thumbnailimage/jpeg13571https://red.uao.edu.co/bitstreams/b91f5718-69ff-4806-9f5a-dcdc9ec12f48/downloadd8b5e30d4f7d60c8b59c2d03f186a475MD5610614/11408oai:red.uao.edu.co:10614/114082024-01-25 14:49:05.11https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidenteopen.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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