Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva

Introduction— The optimal reactive power dispatch (ORPD) problem consists on finding the optimal settings of several reactive power resources in order to minimize system power losses. The ORPD is a complex combinatorial optimization problem that involves discrete and continuous variables as well as...

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Autores:
Londoño Tamayo, Daniel Camilo
Lopez Lezama, Jesus Maria
Villa Acevedo, Walter Mauricio
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2021
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Corporación Universidad de la Costa
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Palabra clave:
Reactive power
Metaheuristic techniques
Power loss minimization
Constraint handling
Mean-variance mapping optimization
Potencia reactiva
Técnicas metaheurísticas
Minimización de pérdidas
Manejo de restricciones
Optimización de mapeo de media-varianza
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dc.title.spa.fl_str_mv Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
dc.title.translated.none.fl_str_mv Mean-variance mapping optimization algorithm applied to the optimal reactive power dispatch
title Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
spellingShingle Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
Reactive power
Metaheuristic techniques
Power loss minimization
Constraint handling
Mean-variance mapping optimization
Potencia reactiva
Técnicas metaheurísticas
Minimización de pérdidas
Manejo de restricciones
Optimización de mapeo de media-varianza
title_short Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
title_full Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
title_fullStr Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
title_full_unstemmed Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
title_sort Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactiva
dc.creator.fl_str_mv Londoño Tamayo, Daniel Camilo
Lopez Lezama, Jesus Maria
Villa Acevedo, Walter Mauricio
dc.contributor.author.none.fl_str_mv Londoño Tamayo, Daniel Camilo
Lopez Lezama, Jesus Maria
Villa Acevedo, Walter Mauricio
dc.subject.proposal.eng.fl_str_mv Reactive power
Metaheuristic techniques
Power loss minimization
Constraint handling
Mean-variance mapping optimization
topic Reactive power
Metaheuristic techniques
Power loss minimization
Constraint handling
Mean-variance mapping optimization
Potencia reactiva
Técnicas metaheurísticas
Minimización de pérdidas
Manejo de restricciones
Optimización de mapeo de media-varianza
dc.subject.proposal.spa.fl_str_mv Potencia reactiva
Técnicas metaheurísticas
Minimización de pérdidas
Manejo de restricciones
Optimización de mapeo de media-varianza
description Introduction— The optimal reactive power dispatch (ORPD) problem consists on finding the optimal settings of several reactive power resources in order to minimize system power losses. The ORPD is a complex combinatorial optimization problem that involves discrete and continuous variables as well as a nonlinear objective function and nonlinear constraints. Objective— This article seeks to compare the performance of the mean-variance mapping optimization (MVMO) algorithm with other techniques reported in the specialized literature applied to the ORPD solution. Methodology— Two different constraint handling approaches are implemented within the MVMO algorithm: a conventional penalization of deviations from feasible solutions and a penalization by means of a product of subfunctions that serves to identify both when a solution is optimal and feasible. Several tests are carried out in IEEE benchmark power systems of 30 and 57 buses. Conclusions— The MVMO algorithm is effective in solving the ORPD problem. Results evidence that the MVMO algorithm outperforms or matches the quality of solutions reported by several solution techniques reported in the technical literature. The alternative handling constraint proposed for the MVMO reduces the computation time and guarantees both feasibility and optimality of the solutions found.
publishDate 2021
dc.date.issued.none.fl_str_mv 2021
dc.date.accessioned.none.fl_str_mv 2023-07-10T16:43:59Z
dc.date.available.none.fl_str_mv 2023-07-10T16:43:59Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.citation.spa.fl_str_mv D. Londoño Tamayo, J. López Lezama & W. Villa Acevedo, “ Mean-Variance Mapping Optimization Algorithm Applied to the Optimal Reactive Power Dispatch”, INGECUC, vol. 17. no. 1, pp. 239–255. DOI: http://doi.org/10.17981/ingecuc.17.1.2021.19
dc.identifier.issn.spa.fl_str_mv 0122-6517
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/11323/10314
dc.identifier.doi.none.fl_str_mv 10.17981/ingecuc.17.1.2021.19
dc.identifier.eissn.spa.fl_str_mv 2382-4700
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
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 D. Londoño Tamayo, J. López Lezama & W. Villa Acevedo, “ Mean-Variance Mapping Optimization Algorithm Applied to the Optimal Reactive Power Dispatch”, INGECUC, vol. 17. no. 1, pp. 239–255. DOI: http://doi.org/10.17981/ingecuc.17.1.2021.19
0122-6517
10.17981/ingecuc.17.1.2021.19
2382-4700
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/10314
https://repositorio.cuc.edu.co/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartofjournal.spa.fl_str_mv INGE CUC
dc.relation.references.spa.fl_str_mv [1] S. M. Mohseni-Bonab & A. Rabiee, “Optimal reactive power dispatch: a review, and a new stochastic voltage stability constrained multi-objective model at the presence of uncertain wind power generation,” IET Gener Transm Distrib, vol. 11, no. 4, pp. 815–829, Mar. 2017. https://doi.org/10.1049/ietgtd.2016.1545
[2] R. Mota-Palomino & V. H. Quintana, “Sparse Reactive Power Scheduling by a Penalty Function - Linear Programming Technique,” IEEE Trans Power Syst, vol. 1, no. 3, pp. 31–39, Ago. 1986. https://doi. org/10.1109/TPWRS.1986.4334951
[3] K. Aoki, M. Fan, & A. Nishikori, “Optimal VAr planning by approximation method for recursive mixedinteger linear programming,” IEEE Trans Power Syst, vol. 3, no. 4, pp. 1741–1747, Nov. 1988. https:// doi.org/10.1109/59.192990
[4] V. H. Quintana & M. Santos-Nieto, “Reactive-power dispatch by successive quadratic programming,” IEEE Trans Energy Convers, vol. 4, no. 3, pp. 425–435, Sep. 1989. https://doi.org/10.1109/60.43245
[5] F. C. Lu & Y. Y. Hsu, “Reactive power/voltage control in a distribution substation using dynamic programming,” Transm Distrib IEE Proc - Gener, vol. 142, no. 6, pp. 639–645, Nov. 1995. https://doi. org/10.1049/ip-gtd:19952210
[6] S. Granville, “Optimal reactive dispatch through interior point methods,” IEEE Trans Power Syst, vol. 9, no. 1, pp. 136–146, Feb. 1994. https://doi.org/10.1109/59.317548
[7] A. A. A. E. Ela, M. A. Abido, & S. R. Spea, “Differential evolution algorithm for optimal reactive power dispatch,” Electr Power Syst Res, vol. 81, no. 2, pp. 458–464, Feb. 2011. https://doi.org/10.1016/j. epsr.2010.10.005
[8] A. Mukherjee & V. Mukherjee, “Solution of optimal reactive power dispatch by chaotic krill herd algorithm,” Transm Distrib IET Gener, vol. 9, no. 15, pp. 2351–2362, 2015. https://doi.org/10.1049/ietgtd.2015.0077
[9] A. H. Gandomi & A. H. Alavi, “Krill herd: A new bio-inspired optimization algorithm,” Commun Nonlinear Sci Numer Simul, vol. 17, no. 12, pp. 4831–4845, Dic. 2012. https://doi.org/10.1016/j.cnsns.2012.05.010
[10] H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama & Y. Nakanishi, “A particle swarm optimization for reactive power and voltage control considering voltage security assessment,” presented at IEEE Power Engineering Society Winter Meeting. Conference Proceedings, Cat. No.01CH37194, COLO, USA, 2001. https://doi.org/10.1109/PESW.2001.916897
[11] A. A. A. Esmin, G. Lambert-Torres & A. C. Zambroni de Souza, “A hybrid particle swarm optimization applied to loss power minimization,” IEEE Trans Power Syst, vol. 20, no. 2, pp. 859–866, May. 2005. https://doi.org/10.1109/TPWRS.2005.846049
[12] D. Gutiérrez, W. M. Villa, & J. M. López-Lezama, “Flujo Óptimo Reactivo mediante Optimización por Enjambre de Partículas,” Inf Tecnol, vol. 28, no. 5, pp. 215–224, 2017. https://doi.org/10.4067/S0718- 07642017000500020
[13] K. Mahadevan & P. S. Kannan, “Comprehensive learning particle swarm optimization for reactive power dispatch,” Appl Soft Comput, vol. 10, no. 2, pp. 641–652, Mar. 2010. https://doi.org/10.1016/j. asoc.2009.08.038
[14] R. P. Singh, V. Mukherjee & S. P. Ghoshal, “Optimal reactive power dispatch by particle swarm optimization with an aging leader and challengers,” Appl Soft Comput, vol. 29, pp. 298–309, Apr. 2015. https://doi.org/10.1016/j.asoc.2015.01.006
[15] S. Duman, Y. Sönmez, U. Güvenç & N. Yörükeren, “Optimal reactive power dispatch using a gravitational search algorithm,” Transm Distrib IET Gener, vol. 6, no. 6, pp. 563–576, Jun. 2012. https://doi. org/10.1049/iet-gtd.2011.0681
[16] E. Rashedi, H. Nezamabadi-pour & S. Saryazdi, “GSA: A Gravitational Search Algorithm,” Inf Sci, vol. 179, no. 13, pp. 2232–2248, Jun. 2009. https://doi.org/10.1016/j.ins.2009.03.004
[17] G. Chen, L. Liu, Z. Zhang, & S. Huang, “Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints,” Appl Soft Comput, vol. 50, pp. 58–70, Jan. 2017. https://doi.org/10.1016/j.asoc.2016.11.008
[18] B. Shaw, V. Mukherjee & S. P. Ghoshal, “Solution of reactive power dispatch of power systems by an opposition-based gravitational search algorithm,” Int J Electr Power Energy Syst, vol. 55, pp. 29–40, Feb. 2014. https://doi.org/10.1016/j.ijepes.2013.08.010
[19] A. Rajan & T. Malakar, “Optimal reactive power dispatch using hybrid Nelder–Mead simplex based firefly algorithm,” Int J Electr Power Energy Syst, vol. 66, pp. 9–24, Mar. 2015. https://doi.org/10.1016/j. ijepes.2014.10.041
[20] M. Ettappan, V. Vimala, S. Ramesh & V. T. Kesavan, “Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm,” Microprocess Microsyst, vol. 76, Jul. 2020. https://doi.org/10.1016/j.micpro.2020.103085
[21] C. Dai, W. Chen, Y. Zhu, & X. Zhang, “Seeker Optimization Algorithm for Optimal Reactive Power Dispatch,” IEEE Trans Power Syst, vol. 24, no. 3, pp. 1218–1231, Aug. 2009. https://doi.org/10.1109/ TPWRS.2009.2021226
[22] A. Bhattacharya & P. K. Chattopadhyay, “Biogeography-Based Optimization for solution of Optimal Power Flow problem,” ECTI, ECTI-CON2010, CNX, pp. 435–439, May. 2010. Available: https://ieeexplore.ieee.org/document/5491454
[23] R. Ng Shin Mei, M. H. Sulaiman, Z. Mustaffa & H. Daniyal, “Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique,” Appl Soft Comput, vol. 59, pp. 210–222, Oct. 2017. https://doi.org/10.1016/j.asoc.2017.05.057
[24] A. A. Heidari, R. Ali Abbaspour & A. Rezaee Jordehi, “Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems,” Appl Soft Comput, vol. 57, pp. 657–671, Aug. 2017. https://doi.org/10.1016/j.asoc.2017.04.048
[25] D. Gutierrez Rojas, J. Lopez Lezama & W. Villa, “Metaheuristic Techniques Applied to the Optimal Reactive Power Dispatch: a Review,” IEEE Lat Am Trans, vol. 14, no. 5, pp. 2253–2263, May. 2016. https://doi.org/10.1109/TLA.2016.7530421
[26] W. M. Villa-Acevedo, J. M. López-Lezama, & J. A. Valencia-Velásquez, “A Novel Constraint Handling Approach for the Optimal Reactive Power Dispatch Problem,” Energies, vol. 11, no. 9, pp. 1–23, 2018. https://doi.org/10.3390/en11092352
[27] I. Erlich, G. K. Venayagamoorthy & N. Worawat, “A Mean-Variance Optimization algorithm,” presented at IEEE CEC, CEC, BCN, pp. 1–6, 18-23 Jul. 2010. https://doi.org/10.1109/CEC.2010.5586027
[28] I. Erlich, “Mean-variance mapping optimization algorithm home page,” UDE, 2018. Available: https:// www.uni-due.de/mvmo/
[29] J. L. Rueda & I. Erlich, “Optimal dispatch of reactive power sources by using MVMOs optimization,” presented at IEEE CIASG, CIASG, SG, 16-19 Apr. 2013. https://doi.org/10.1109/CIASG.2013.6611495
[30] J. C. Cepeda, J. L. Rueda & I. Erlich, “Identification of dynamic equivalents based on heuristic optimization for smart grid applications,” IEEE CEC, CEC, Bris, QLD, AU, 10-15 Jun. 2012. https://doi. org/10.1109/CEC.2012.6256493
[31] J. L. Rueda & I. Erlich, “Evaluation of the mean-variance mapping optimization for solving multimodal problems,” IEEE SIS, SIS, SG, 16-19 Apr. 2013. https://doi.org/10.1109/SIS.2013.6615153
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spelling Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)Derechos de autor 2021 INGE CUChttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Londoño Tamayo, Daniel CamiloLopez Lezama, Jesus MariaVilla Acevedo, Walter Mauricio2023-07-10T16:43:59Z2023-07-10T16:43:59Z2021D. Londoño Tamayo, J. López Lezama & W. Villa Acevedo, “ Mean-Variance Mapping Optimization Algorithm Applied to the Optimal Reactive Power Dispatch”, INGECUC, vol. 17. no. 1, pp. 239–255. DOI: http://doi.org/10.17981/ingecuc.17.1.2021.190122-6517https://hdl.handle.net/11323/1031410.17981/ingecuc.17.1.2021.192382-4700Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Introduction— The optimal reactive power dispatch (ORPD) problem consists on finding the optimal settings of several reactive power resources in order to minimize system power losses. The ORPD is a complex combinatorial optimization problem that involves discrete and continuous variables as well as a nonlinear objective function and nonlinear constraints. Objective— This article seeks to compare the performance of the mean-variance mapping optimization (MVMO) algorithm with other techniques reported in the specialized literature applied to the ORPD solution. Methodology— Two different constraint handling approaches are implemented within the MVMO algorithm: a conventional penalization of deviations from feasible solutions and a penalization by means of a product of subfunctions that serves to identify both when a solution is optimal and feasible. Several tests are carried out in IEEE benchmark power systems of 30 and 57 buses. Conclusions— The MVMO algorithm is effective in solving the ORPD problem. Results evidence that the MVMO algorithm outperforms or matches the quality of solutions reported by several solution techniques reported in the technical literature. The alternative handling constraint proposed for the MVMO reduces the computation time and guarantees both feasibility and optimality of the solutions found.Introducción— El problema del despacho óptimo de potencia reactiva (DOPR) consiste en encontrar la configuración óptima de diferentes recursos de potencia reactiva para minimizar las pérdidas de potencia del sistema. El DOPR es un problema complejo de optimización combinatorial que involucra variables discretas y continuas, así como una función objetivo no lineal y restricciones no lineales. Objetivo— En este artículo se busca comparar el desempeño del algoritmo de optimización de mapeo de media varianza (MVMO, por sus siglas en inglés) con otras técnicas reportadas en la literatura especializada aplicadas a la solución del DOPR. Metodología— En el algoritmo MVMO se aplican dos enfoques diferentes de manejo de restricciones: penalización convencional de las desviaciones de las soluciones factibles y penalización por medio del producto de subfunciones que sirve para identificar cuándo una solución es óptima y factible. Se realizan simulaciones en sistemas de prueba IEEE de 30 y 57 barras. Conclusiones— El algoritmo MVMO es efectivo para solucionar el DOPR. Los resultados evidencian que el algoritmo MVMO supera o iguala a varias técnicas reportadas en la literatura técnica en la calidad de soluciones. El manejo alternativo de restricciones propuesto para el MVMO reduce el tiempo de cálculo y garantiza tanto factibilidad como optimalidad de las soluciones encontradas.17 páginasapplication/pdfspaCorporación Universidad de la CostaColombiahttps://revistascientificas.cuc.edu.co/ingecuc/article/view/3109Algoritmo de optimización de mapeo de media varianza aplicado al despacho óptimo de potencia reactivaMean-variance mapping optimization algorithm applied to the optimal reactive power dispatchArtículo 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/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85INGE CUC[1] S. M. Mohseni-Bonab & A. Rabiee, “Optimal reactive power dispatch: a review, and a new stochastic voltage stability constrained multi-objective model at the presence of uncertain wind power generation,” IET Gener Transm Distrib, vol. 11, no. 4, pp. 815–829, Mar. 2017. https://doi.org/10.1049/ietgtd.2016.1545[2] R. Mota-Palomino & V. H. Quintana, “Sparse Reactive Power Scheduling by a Penalty Function - Linear Programming Technique,” IEEE Trans Power Syst, vol. 1, no. 3, pp. 31–39, Ago. 1986. https://doi. org/10.1109/TPWRS.1986.4334951[3] K. Aoki, M. Fan, & A. Nishikori, “Optimal VAr planning by approximation method for recursive mixedinteger linear programming,” IEEE Trans Power Syst, vol. 3, no. 4, pp. 1741–1747, Nov. 1988. https:// doi.org/10.1109/59.192990[4] V. H. Quintana & M. Santos-Nieto, “Reactive-power dispatch by successive quadratic programming,” IEEE Trans Energy Convers, vol. 4, no. 3, pp. 425–435, Sep. 1989. https://doi.org/10.1109/60.43245[5] F. C. Lu & Y. Y. Hsu, “Reactive power/voltage control in a distribution substation using dynamic programming,” Transm Distrib IEE Proc - Gener, vol. 142, no. 6, pp. 639–645, Nov. 1995. https://doi. org/10.1049/ip-gtd:19952210[6] S. Granville, “Optimal reactive dispatch through interior point methods,” IEEE Trans Power Syst, vol. 9, no. 1, pp. 136–146, Feb. 1994. https://doi.org/10.1109/59.317548[7] A. A. A. E. Ela, M. A. Abido, & S. R. Spea, “Differential evolution algorithm for optimal reactive power dispatch,” Electr Power Syst Res, vol. 81, no. 2, pp. 458–464, Feb. 2011. https://doi.org/10.1016/j. epsr.2010.10.005[8] A. Mukherjee & V. Mukherjee, “Solution of optimal reactive power dispatch by chaotic krill herd algorithm,” Transm Distrib IET Gener, vol. 9, no. 15, pp. 2351–2362, 2015. https://doi.org/10.1049/ietgtd.2015.0077[9] A. H. Gandomi & A. H. Alavi, “Krill herd: A new bio-inspired optimization algorithm,” Commun Nonlinear Sci Numer Simul, vol. 17, no. 12, pp. 4831–4845, Dic. 2012. https://doi.org/10.1016/j.cnsns.2012.05.010[10] H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama & Y. Nakanishi, “A particle swarm optimization for reactive power and voltage control considering voltage security assessment,” presented at IEEE Power Engineering Society Winter Meeting. Conference Proceedings, Cat. No.01CH37194, COLO, USA, 2001. https://doi.org/10.1109/PESW.2001.916897[11] A. A. A. Esmin, G. Lambert-Torres & A. C. Zambroni de Souza, “A hybrid particle swarm optimization applied to loss power minimization,” IEEE Trans Power Syst, vol. 20, no. 2, pp. 859–866, May. 2005. https://doi.org/10.1109/TPWRS.2005.846049[12] D. Gutiérrez, W. M. Villa, & J. M. López-Lezama, “Flujo Óptimo Reactivo mediante Optimización por Enjambre de Partículas,” Inf Tecnol, vol. 28, no. 5, pp. 215–224, 2017. https://doi.org/10.4067/S0718- 07642017000500020[13] K. Mahadevan & P. S. Kannan, “Comprehensive learning particle swarm optimization for reactive power dispatch,” Appl Soft Comput, vol. 10, no. 2, pp. 641–652, Mar. 2010. https://doi.org/10.1016/j. asoc.2009.08.038[14] R. P. Singh, V. Mukherjee & S. P. Ghoshal, “Optimal reactive power dispatch by particle swarm optimization with an aging leader and challengers,” Appl Soft Comput, vol. 29, pp. 298–309, Apr. 2015. https://doi.org/10.1016/j.asoc.2015.01.006[15] S. Duman, Y. Sönmez, U. Güvenç & N. Yörükeren, “Optimal reactive power dispatch using a gravitational search algorithm,” Transm Distrib IET Gener, vol. 6, no. 6, pp. 563–576, Jun. 2012. https://doi. org/10.1049/iet-gtd.2011.0681[16] E. Rashedi, H. Nezamabadi-pour & S. 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Erlich, “Evaluation of the mean-variance mapping optimization for solving multimodal problems,” IEEE SIS, SIS, SG, 16-19 Apr. 2013. https://doi.org/10.1109/SIS.2013.6615153255239117Reactive powerMetaheuristic techniquesPower loss minimizationConstraint handlingMean-variance mapping optimizationPotencia reactivaTécnicas metaheurísticasMinimización de pérdidasManejo de restriccionesOptimización de mapeo de media-varianzaPublicationORIGINALAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdfAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdfArtículoapplication/pdf1032292https://repositorio.cuc.edu.co/bitstreams/fb569666-b13e-43fb-b28f-72b2dd9c26e3/download8c4351dc059046ffb5c77543214b0c3aMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://repositorio.cuc.edu.co/bitstreams/67d6ead8-76ee-4e7b-be15-2a77eec4a0b8/download2f9959eaf5b71fae44bbf9ec84150c7aMD52TEXTAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdf.txtAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdf.txtExtracted texttext/plain42124https://repositorio.cuc.edu.co/bitstreams/df47b801-4c42-42d9-9866-abdbcb9b5ade/downloadd0748aa9450726a10744a64dd3de81aaMD53THUMBNAILAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdf.jpgAlgoritmo de Optimización de Mapeo de Media Varianza Aplicado al Despacho Óptimo de Potencia Reactiva.pdf.jpgGenerated Thumbnailimage/jpeg12348https://repositorio.cuc.edu.co/bitstreams/3af29b09-d631-46f3-88d6-6bac28918571/download941a8cf2b60613657470c12d6d3721e6MD5411323/10314oai:repositorio.cuc.edu.co:11323/103142024-09-17 14:16:20.751https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos de autor 2021 INGE CUCopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa 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ada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.


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