Expansión de un sistema de transmisión mediante LOPF-AC

Introducción: En la presente investigación se transforma las ecuaciones que conforman un OPF-AC a un sistema de restricciones lineales mediante series de Taylor, por lo cual se adquiere un modelo LOPF-AC, preciso y aplicable para poder garantizar la minimización de pérdidas en todo el sistema. Objet...

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Autores:
Escudero Delgado, Pablo
Carrión Galarza, Diego
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
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Corporación Universidad de la Costa
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REDICUC - Repositorio CUC
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spa
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https://hdl.handle.net/11323/2391
https://doi.org/10.17981/ingecuc.14.2.2018.11
https://repositorio.cuc.edu.co/
Palabra clave:
Flujos óptimos de potencia
Linealización
Minimización de pérdidas
Planificación de la expansión de la transmisión
Sistemas eléctricos de potencia
Electrical power system
Linearization
Optimal power flow
Transmission expansion planning
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dc.title.spa.fl_str_mv Expansión de un sistema de transmisión mediante LOPF-AC
dc.title.translated.eng.fl_str_mv Expansion of a transmission system using LOPF-AC
title Expansión de un sistema de transmisión mediante LOPF-AC
spellingShingle Expansión de un sistema de transmisión mediante LOPF-AC
Flujos óptimos de potencia
Linealización
Minimización de pérdidas
Planificación de la expansión de la transmisión
Sistemas eléctricos de potencia
Electrical power system
Linearization
Optimal power flow
Transmission expansion planning
title_short Expansión de un sistema de transmisión mediante LOPF-AC
title_full Expansión de un sistema de transmisión mediante LOPF-AC
title_fullStr Expansión de un sistema de transmisión mediante LOPF-AC
title_full_unstemmed Expansión de un sistema de transmisión mediante LOPF-AC
title_sort Expansión de un sistema de transmisión mediante LOPF-AC
dc.creator.fl_str_mv Escudero Delgado, Pablo
Carrión Galarza, Diego
dc.contributor.author.spa.fl_str_mv Escudero Delgado, Pablo
Carrión Galarza, Diego
dc.subject.proposal.spa.fl_str_mv Flujos óptimos de potencia
Linealización
Minimización de pérdidas
Planificación de la expansión de la transmisión
Sistemas eléctricos de potencia
topic Flujos óptimos de potencia
Linealización
Minimización de pérdidas
Planificación de la expansión de la transmisión
Sistemas eléctricos de potencia
Electrical power system
Linearization
Optimal power flow
Transmission expansion planning
dc.subject.proposal.eng.fl_str_mv Electrical power system
Linearization
Optimal power flow
Transmission expansion planning
description Introducción: En la presente investigación se transforma las ecuaciones que conforman un OPF-AC a un sistema de restricciones lineales mediante series de Taylor, por lo cual se adquiere un modelo LOPF-AC, preciso y aplicable para poder garantizar la minimización de pérdidas en todo el sistema. Objetivo: Minimizar las pérdidas en la expansión del sistema de transmisión. Metodología: Se basa en linealizar las ecuaciones del OPF-AC mediante Series de Taylor, para obtener un problema linealizado. Resultados: El modelo determina cuales son las líneas que se deberían implementar y cuales se deberían reforzar, considerando el menor costo y la minimización de las pérdidas. Conclusiones: La demanda total de la red más la proyección de carga de los distintos casos para la expansión del sistema de transmisión es abastecida con normalidad, cumpliendo con los parámetros establecidos de generación y transmisión conjuntamente con las restricciones del algoritmo para obtener un desempeño óptimo en la TEP.
publishDate 2018
dc.date.issued.none.fl_str_mv 2018-12-18
dc.date.accessioned.none.fl_str_mv 2019-02-11T23:06:37Z
dc.date.available.none.fl_str_mv 2019-02-11T23:06:37Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.citation.spa.fl_str_mv P. Escudero-Delgado y D. Carrión-Galarza, “Expansión de un sistema de transmisión mediante LOPF-AC,” INGE CUC, vol. 14, no. 2, pp.116-125, 2018. DOI: http://doi.org/10.17981/ingecuc.14.2.2018.11
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/2391
dc.identifier.url.spa.fl_str_mv https://doi.org/10.17981/ingecuc.14.2.2018.11
dc.identifier.doi.spa.fl_str_mv 10.17981/ingecuc.14.2.2018.11
dc.identifier.eissn.spa.fl_str_mv 2382-4700
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.pissn.spa.fl_str_mv 0122-6517
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv P. Escudero-Delgado y D. Carrión-Galarza, “Expansión de un sistema de transmisión mediante LOPF-AC,” INGE CUC, vol. 14, no. 2, pp.116-125, 2018. DOI: http://doi.org/10.17981/ingecuc.14.2.2018.11
10.17981/ingecuc.14.2.2018.11
2382-4700
Corporación Universidad de la Costa
0122-6517
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/2391
https://doi.org/10.17981/ingecuc.14.2.2018.11
https://repositorio.cuc.edu.co/
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language spa
dc.relation.ispartofseries.spa.fl_str_mv INGE CUC; Vol. 14, Núm. 2 (2018)
dc.relation.ispartofjournal.spa.fl_str_mv INGE CUC
INGE CUC
dc.relation.references.spa.fl_str_mv S. S. Taheri, J. Kazempour and S. Seyedshenava, “Transmission expansion in an oligopoly considering generation investment equilibrium,” Energy Econ., vol. 64, pp. 55–62, 2017. https://doi.org/10.1016/j.eneco.2017.03.003
T. Akbari, A. Rahimi-kian and M. Heidarizadeh, “Security-Constrained Transmission Expansion Planning : A Multi-Objective Approach,” lectrical Eng. (ICEE), 2011 19th Iran. Conf., p. 6, 2011.
D . Sainju, R. Sinha and B. R. Pokhrel, “Static Expansion Planning of Transmission Line Using Mixed Integer Linear Programming Method,” in Power Systems (ICPS), 2016 IEEE 6th International Conference on, 2016, pp. 1–6. https://doi.org/10.1109/ICPES.2016.7584141
P. V. Escudero and D. F. Carrión, “Modelo de Expansión de un sistema de transmisión basado en linealización de flujos de potencia óptimos AC.,” p. 34, 2018.
D . Carrión, E. Inga, J. W. Gonzalez and R. Hincapié, “Optimal Geographical Placement of Phasor Measurement Units based on Clustering Techniques,” in 51st International Universities’ Power Engineering Conference, 2016, p. 6. https://doi.org/10.1109/UPEC.2016.8114003
W. H. Caisapanta and D. F. Carrión, “Expansión de sistemas de transmisión eléctrica usando criterios de óptima potencia AC,” 2016.
D. Carrión, J. W. González, I. A. Isaac and G. J. López, “Optimal Fault Location in Transmission Lines Using Hybrid Method,” in 2017 IEEE PES Innovative Smart Grid Technologies Conference, 2017, p. 6. https://doi.org/10.1109/ISGT-LA.2017.8126757
G. Yaguana and D. Carrión, “Optimización de la expansión de los sistemas de transmisión usando gams.pdf.” Quito, p. 21, 2016.
R. Hemmati, R.-A. Hooshmand and A. Khodabakhshian, “Comprehensive review of generation and transmission expansion planning,” IET Gener. Transm. Distrib., vol. 7, no. 9, pp. 955–964, Sep. 2013. https://doi.org/10.1049/iet-gtd.2013.0031
A. K. Ferdavani, M. Salem, I. Alhamrouni and A. Khairuddin, “Transmission expansion planning using AC-based differential evolution algorithm,” IET Gener.Transm. Distrib., vol. 8, no. 10, pp. 1637–1644, Oct. 2014. https://doi.org/10.1049/iet-gtd.2014.0001
G. Latorre, R. Dario Cruz, J. M. Areiza and A. Villegas, “Classification of publications and models on transmission expansion planning,” IEEE Trans. Power Syst., vol. 18, no. 2, pp. 938–946, 2003. https://doi.org/10.1109/TPWRS.2003.811168
T. Akbari, A. Rahimi-Kian and M. Tavakoli Bina, “Security- constrained transmission expansion planning: A stochastic multi-objective approach,” Int. J. Electr.Power Energy Syst., vol. 43, no. 1, pp. 444–453, 2012. https://doi.org/10.1016/j.ijepes.2012.05.058
J. Marecek, M. Mevissen and J. C. Villumsen, “MINLP in transmission expansion planning,” in Power Systems Computation Conference (PSCC), 2016, pp. 1–8. https://doi.org/10.1109/PSCC.2016.7540906
A. Capasso, A. Cervone, R. Lamedica and L. Palagi, “A LP and MILP methodology to support the planning of transmission power systems,” Electr. Power Syst. Res., vol. 140, pp. 699–707, 2016. https://doi.org/10.1016/j.epsr.2016.04.024
M. Jadidoleslam, A. Ebrahimi and M. A. Latify, “Probabilistic transmission expansion planning to maximize the integration of wind power,” Renew. Energy, vol. 114, pp. 866–878, 2017. https://doi.org/10.1016/j.renene.2017.07.063
D . Carrión, E. Inga, J. W. Gonzalez, and R. Hincapié, “Optimal Geographical Placement of Phasor Measurement Units based on Clustering Techniques,” in 2016 51st International Universities Power Engineering Conference, 2016, pp. 6–11. https://doi.org/10.1109/UPEC.2016.8114003
L. Garver, “Transmission Network Estimation Using Linear Programming,” IEEE Trans. Power Appar. Syst., vol. PAS-89, no. 7, pp. 1688–1697, 1970. https://doi.org/10.1109/TPAS.1970.292825
H. Zhang, V. Vittal, G. T. Heydt and J. Quintero, “A relaxed AC optimal power flow model based on a Taylor series,” 2013 IEEE Innov. Smart Grid Technol. (ISGT Asia), pp. 1–5, 2013.
D. Carrion, J. W. Gonzalez, I. A. Isaac, G. J. Lopez and H. A. Cardona, “Load Characterization Based on Voltage and Current Phasorial Measurements in Micro-Grids,” 2017 Int. Conf. Inf. Syst. Comput. Sci., pp. 1–6, 2017. https://doi.org/10.1109/INCISCOS.2017.23
D . Z. Fitiwi, L. Olmos, M. Rivier, F. de Cuadra and I. J. Pérez-Arriaga, “Finding a representative network losses model for large-scale transmission expansión planning with renewable energy sources,” Energy, vol. 101, pp. 343–358, 2016. https://doi.org/10.1016/j.energy.2016.02.015
S. de la Torre, A. J. Conejo and J. Contreras, “Transmission expansion planning in electricity markets,” IEEE Trans. Power Syst., vol. 23, no. 1, pp. 238–248, 2008. https://doi.org/10.1109/TPWRS.2007.913717
C. A. Sima, G. C. Lazaroiu and V. Dumbrava, “Transmission expansion planning optimization for improving RES integration on electricity market,” in 2017 10th International Symposium on Advanced Topics in Electrical Engineering (ATEE), 2017, pp. 855–859. https://doi.org/10.1109/ATEE.2017.7905085
M. Tavakoli Bina and T. Akbari, “Approximated MILP model for AC transmission expansion planning: global solutions versus local solutions,” IET Gener. Transm. Distrib., vol. 10, no. 7, pp. 1563–1569, 2016. https://doi.org/10.1049/iet-gtd.2015.0723
L. P. Garcés, A. J. Conejo, R. García-Bertrand and R. Romero, “A bilevel approach to transmission expansión planning within a market environment,” IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1513–1522, 2009. https://doi.org/10.1109/TPWRS.2009.2021230
G. Srinivasulu, “Multi- Objective Transmission Expansion Planning for IEEE 24 Bus RTS,” pp. 144–149, 2015. https://doi.org/10.1109/PCCCTSG.2015.7503895
T. Akbari and M. Tavakoli Bina, “A linearized formulation of AC multi-year transmission expansion planning: A mixed-integer linear programming approach,” Electr. Power Syst. Res., vol. 114, pp. 93–100, Sep. 2014. https://doi.org/10.1016/j.epsr.2014.04.013
M. Olofsson, G. Andersson and L. Soder, “Linear programming based optimal power flow using second order sensitivities,” IEEE Trans. Power Syst., vol. 10, no. 3, pp. 1691–1697, 1995. https://doi.org/10.1109/59.466472
H. Zhang, V. Vittal, G. T. Heydt and J. Quintero, “A Mixed-Integer Linear Programming Approach for Multi-Stage Security-Constrained Transmission Expansion Planning,” Power Syst. IEEE Trans., vol. 27, no. 2, pp. 1125–1133, 2012. https://doi.org/10.1109/TPWRS.2011.2178000
A. Lotfjou, Y. Fu and M. Shahidehpour, “Hybrid AC/DC Transmission Expansion Planning,” IEEE Trans. Power Deliv., vol. 27, no. 3, pp. 1620–1628, Jul. 2012. https://doi.org/10.1109/TPWRD.2012.2194515
N. Alguacil, A. L. Motto, and A. J. Conejo, “Transmission expansion planning: A mixed-integer LP approach,” IEEE Trans. Power Syst., vol. 18, no. 3, pp. 1070–1077, 2003. https://doi.org/10.1109/TPWRS.2003.814891
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spelling Escudero Delgado, PabloCarrión Galarza, Diego2019-02-11T23:06:37Z2019-02-11T23:06:37Z2018-12-18P. Escudero-Delgado y D. Carrión-Galarza, “Expansión de un sistema de transmisión mediante LOPF-AC,” INGE CUC, vol. 14, no. 2, pp.116-125, 2018. DOI: http://doi.org/10.17981/ingecuc.14.2.2018.11https://hdl.handle.net/11323/2391https://doi.org/10.17981/ingecuc.14.2.2018.1110.17981/ingecuc.14.2.2018.112382-4700Corporación Universidad de la Costa0122-6517REDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Introducción: En la presente investigación se transforma las ecuaciones que conforman un OPF-AC a un sistema de restricciones lineales mediante series de Taylor, por lo cual se adquiere un modelo LOPF-AC, preciso y aplicable para poder garantizar la minimización de pérdidas en todo el sistema. Objetivo: Minimizar las pérdidas en la expansión del sistema de transmisión. Metodología: Se basa en linealizar las ecuaciones del OPF-AC mediante Series de Taylor, para obtener un problema linealizado. Resultados: El modelo determina cuales son las líneas que se deberían implementar y cuales se deberían reforzar, considerando el menor costo y la minimización de las pérdidas. Conclusiones: La demanda total de la red más la proyección de carga de los distintos casos para la expansión del sistema de transmisión es abastecida con normalidad, cumpliendo con los parámetros establecidos de generación y transmisión conjuntamente con las restricciones del algoritmo para obtener un desempeño óptimo en la TEP.Introduction− In this document we transform the OPF-AC equations into a system of linear constraints using Taylor series, for which a LOPF-AC model is acquired, accurate and applicable to guarantee the minimization of losses in the whole system.Objective−To minimize the electrical losses in the ex-pansion of the transmission system.Methodology−It is based on linearizing OPF-AC equa-tions by Taylor series, to obtain a linear problem.Results− The model determines which lines should be implemented and which ones should be reinforced, con-sidering the lower cost and the minimization of losses.Conclusions−The total demand of the network plus the loading projection of the different cases for the ex-pansion of the transmission system is supplied normally, complying with the established parameters of generation and transmission together with the constraints of the algorithm to obtain an optimal performance in the TEP.Escudero Delgado, Pablo-6407514b-f0ca-45d4-8291-aba9efe21fd3-0Carrión Galarza, Diego-0df80214-7244-4ec5-bc9f-d43c696a8466-010 páginasapplication/pdfspaCorporación Universidad de la CostaINGE CUC; Vol. 14, Núm. 2 (2018)INGE CUCINGE CUCS. S. Taheri, J. Kazempour and S. Seyedshenava, “Transmission expansion in an oligopoly considering generation investment equilibrium,” Energy Econ., vol. 64, pp. 55–62, 2017. https://doi.org/10.1016/j.eneco.2017.03.003T. Akbari, A. Rahimi-kian and M. Heidarizadeh, “Security-Constrained Transmission Expansion Planning : A Multi-Objective Approach,” lectrical Eng. (ICEE), 2011 19th Iran. Conf., p. 6, 2011.D . Sainju, R. Sinha and B. R. Pokhrel, “Static Expansion Planning of Transmission Line Using Mixed Integer Linear Programming Method,” in Power Systems (ICPS), 2016 IEEE 6th International Conference on, 2016, pp. 1–6. https://doi.org/10.1109/ICPES.2016.7584141P. V. Escudero and D. F. Carrión, “Modelo de Expansión de un sistema de transmisión basado en linealización de flujos de potencia óptimos AC.,” p. 34, 2018.D . Carrión, E. Inga, J. W. Gonzalez and R. Hincapié, “Optimal Geographical Placement of Phasor Measurement Units based on Clustering Techniques,” in 51st International Universities’ Power Engineering Conference, 2016, p. 6. https://doi.org/10.1109/UPEC.2016.8114003W. H. Caisapanta and D. F. Carrión, “Expansión de sistemas de transmisión eléctrica usando criterios de óptima potencia AC,” 2016.D. Carrión, J. W. González, I. A. Isaac and G. J. López, “Optimal Fault Location in Transmission Lines Using Hybrid Method,” in 2017 IEEE PES Innovative Smart Grid Technologies Conference, 2017, p. 6. https://doi.org/10.1109/ISGT-LA.2017.8126757G. Yaguana and D. Carrión, “Optimización de la expansión de los sistemas de transmisión usando gams.pdf.” Quito, p. 21, 2016.R. Hemmati, R.-A. Hooshmand and A. Khodabakhshian, “Comprehensive review of generation and transmission expansion planning,” IET Gener. Transm. Distrib., vol. 7, no. 9, pp. 955–964, Sep. 2013. https://doi.org/10.1049/iet-gtd.2013.0031A. K. Ferdavani, M. Salem, I. Alhamrouni and A. Khairuddin, “Transmission expansion planning using AC-based differential evolution algorithm,” IET Gener.Transm. Distrib., vol. 8, no. 10, pp. 1637–1644, Oct. 2014. https://doi.org/10.1049/iet-gtd.2014.0001G. Latorre, R. Dario Cruz, J. M. Areiza and A. Villegas, “Classification of publications and models on transmission expansion planning,” IEEE Trans. Power Syst., vol. 18, no. 2, pp. 938–946, 2003. https://doi.org/10.1109/TPWRS.2003.811168T. Akbari, A. Rahimi-Kian and M. Tavakoli Bina, “Security- constrained transmission expansion planning: A stochastic multi-objective approach,” Int. J. Electr.Power Energy Syst., vol. 43, no. 1, pp. 444–453, 2012. https://doi.org/10.1016/j.ijepes.2012.05.058J. Marecek, M. Mevissen and J. C. Villumsen, “MINLP in transmission expansion planning,” in Power Systems Computation Conference (PSCC), 2016, pp. 1–8. https://doi.org/10.1109/PSCC.2016.7540906A. Capasso, A. Cervone, R. Lamedica and L. Palagi, “A LP and MILP methodology to support the planning of transmission power systems,” Electr. Power Syst. Res., vol. 140, pp. 699–707, 2016. https://doi.org/10.1016/j.epsr.2016.04.024M. Jadidoleslam, A. Ebrahimi and M. A. Latify, “Probabilistic transmission expansion planning to maximize the integration of wind power,” Renew. Energy, vol. 114, pp. 866–878, 2017. https://doi.org/10.1016/j.renene.2017.07.063D . Carrión, E. Inga, J. W. Gonzalez, and R. Hincapié, “Optimal Geographical Placement of Phasor Measurement Units based on Clustering Techniques,” in 2016 51st International Universities Power Engineering Conference, 2016, pp. 6–11. https://doi.org/10.1109/UPEC.2016.8114003L. Garver, “Transmission Network Estimation Using Linear Programming,” IEEE Trans. Power Appar. Syst., vol. PAS-89, no. 7, pp. 1688–1697, 1970. https://doi.org/10.1109/TPAS.1970.292825H. Zhang, V. Vittal, G. T. Heydt and J. Quintero, “A relaxed AC optimal power flow model based on a Taylor series,” 2013 IEEE Innov. Smart Grid Technol. (ISGT Asia), pp. 1–5, 2013.D. Carrion, J. W. Gonzalez, I. A. Isaac, G. J. Lopez and H. A. Cardona, “Load Characterization Based on Voltage and Current Phasorial Measurements in Micro-Grids,” 2017 Int. Conf. Inf. Syst. Comput. Sci., pp. 1–6, 2017. https://doi.org/10.1109/INCISCOS.2017.23D . Z. Fitiwi, L. Olmos, M. Rivier, F. de Cuadra and I. J. Pérez-Arriaga, “Finding a representative network losses model for large-scale transmission expansión planning with renewable energy sources,” Energy, vol. 101, pp. 343–358, 2016. https://doi.org/10.1016/j.energy.2016.02.015S. de la Torre, A. J. Conejo and J. Contreras, “Transmission expansion planning in electricity markets,” IEEE Trans. Power Syst., vol. 23, no. 1, pp. 238–248, 2008. https://doi.org/10.1109/TPWRS.2007.913717C. A. Sima, G. C. Lazaroiu and V. Dumbrava, “Transmission expansion planning optimization for improving RES integration on electricity market,” in 2017 10th International Symposium on Advanced Topics in Electrical Engineering (ATEE), 2017, pp. 855–859. https://doi.org/10.1109/ATEE.2017.7905085M. Tavakoli Bina and T. Akbari, “Approximated MILP model for AC transmission expansion planning: global solutions versus local solutions,” IET Gener. Transm. Distrib., vol. 10, no. 7, pp. 1563–1569, 2016. https://doi.org/10.1049/iet-gtd.2015.0723L. P. Garcés, A. J. Conejo, R. García-Bertrand and R. Romero, “A bilevel approach to transmission expansión planning within a market environment,” IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1513–1522, 2009. https://doi.org/10.1109/TPWRS.2009.2021230G. Srinivasulu, “Multi- Objective Transmission Expansion Planning for IEEE 24 Bus RTS,” pp. 144–149, 2015. https://doi.org/10.1109/PCCCTSG.2015.7503895T. Akbari and M. 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Power Syst., vol. 18, no. 3, pp. 1070–1077, 2003. https://doi.org/10.1109/TPWRS.2003.814891125116214INGE CUCINGE CUChttps://revistascientificas.cuc.edu.co/ingecuc/article/view/1835Expansión de un sistema de transmisión mediante LOPF-ACExpansion of a transmission system using LOPF-ACArtículo 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/ARTinfo:eu-repo/semantics/acceptedVersioninfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Flujos óptimos de potenciaLinealizaciónMinimización de pérdidasPlanificación de la expansión de la transmisiónSistemas eléctricos de potenciaElectrical power systemLinearizationOptimal power flowTransmission expansion planningPublicationORIGINALExpansión de un sistema de transmisión mediante LOPF-AC.pdfExpansión de un sistema de transmisión mediante LOPF-AC.pdfapplication/pdf815502https://repositorio.cuc.edu.co/bitstreams/caef71e7-d3a4-448b-8045-260f79fe91a7/download4877c774c48155766b2681944faab4baMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/d7f883ad-7dbd-4ab3-a9e8-4d335ffda6da/download8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILExpansión de un sistema de transmisión mediante LOPF-AC.pdf.jpgExpansión de un sistema de transmisión mediante LOPF-AC.pdf.jpgimage/jpeg45510https://repositorio.cuc.edu.co/bitstreams/fc9d71b4-91d3-4287-9b4c-c761f108a612/download88b329cc1bf9a2773d3018fc2107597aMD54TEXTExpansión de un sistema de transmisión mediante LOPF-AC.pdf.txtExpansión de un sistema de transmisión mediante LOPF-AC.pdf.txttext/plain35968https://repositorio.cuc.edu.co/bitstreams/1aa11e67-f999-41e5-8cff-8d94cc32ca68/download8438a2a0d73fde6e24d2f30d6ccc96c1MD5511323/2391oai:repositorio.cuc.edu.co:11323/23912024-09-17 14:12:04.496open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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