Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica

: figuras, tablas

Autores:: Granada Echeverri, Mauricio
Gallego Rendón, Ramón A

Tipo de recurso:: Book

Fecha de publicación:: 2024

Institución:: Universidad Tecnológica de Pereira

Repositorio:: Repositorio Institucional UTP

Idioma:: spa

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dc.title.spa.fl_str_mv	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
title	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
spellingShingle	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica 530 - Física::537 - Electricidad y electrónica Sistemas de interconexión eléctrica Sistemas de energía eléctrica Energía eléctrica Análisis de sistemas eléctricos de potencia Flujo de potencia Confiabilidad (Ingeniería) Programación lineal Sistemas de transmisión de energía
title_short	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
title_full	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
title_fullStr	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
title_full_unstemmed	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
title_sort	Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica
dc.creator.fl_str_mv	Granada Echeverri, Mauricio Gallego Rendón, Ramón A
dc.contributor.author.none.fl_str_mv	Granada Echeverri, Mauricio Gallego Rendón, Ramón A
dc.subject.ddc.none.fl_str_mv	530 - Física::537 - Electricidad y electrónica
topic	530 - Física::537 - Electricidad y electrónica Sistemas de interconexión eléctrica Sistemas de energía eléctrica Energía eléctrica Análisis de sistemas eléctricos de potencia Flujo de potencia Confiabilidad (Ingeniería) Programación lineal Sistemas de transmisión de energía
dc.subject.armarc.none.fl_str_mv	Sistemas de interconexión eléctrica Sistemas de energía eléctrica Energía eléctrica
dc.subject.proposal.spa.fl_str_mv	Análisis de sistemas eléctricos de potencia Flujo de potencia Confiabilidad (Ingeniería) Programación lineal Sistemas de transmisión de energía
description	: figuras, tablas
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-10-03T14:34:15Z
dc.date.available.none.fl_str_mv	2024-10-03T14:34:15Z
dc.date.issued.none.fl_str_mv	2024
dc.type.none.fl_str_mv	Libro
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dc.identifier.isbn.none.fl_str_mv	978-958-722-325-5
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/11059/15332
dc.identifier.eisbn.none.fl_str_mv	978-958-722-682-9
dc.identifier.instname.none.fl_str_mv	Universidad Tecnológica de Pereira
dc.identifier.reponame.none.fl_str_mv	Repositorio Universidad Tecnológica de Pereira
dc.identifier.repourl.none.fl_str_mv	https://repositorio.utp.edu.co/home
identifier_str_mv	978-958-722-325-5 978-958-722-682-9 Universidad Tecnológica de Pereira Repositorio Universidad Tecnológica de Pereira
url	https://hdl.handle.net/11059/15332 https://repositorio.utp.edu.co/home
dc.language.iso.none.fl_str_mv	spa
language	spa
dc.relation.references.none.fl_str_mv	Abadie, J. and Carpentier, J.: 1969, Generalization of the wolf reduced gradient method to the case of nonlinear constraints., Recent Advances in Mathematical Programming. in Optimization, R. Fletcher (ed), New York: Academic Press. pp. 37–47. Bakirtzis, A. and Biskas, P.: 2003, A decentralized solution to the dc-opf of interconnected power systems, IEEE Transactions on Power Systems 18(3), 1007–1013. Baldick, R., Kim, B., Chase, C. and Luo, Y.: 1999, A fast distributed implementation of optimal power flow, IEEE Transactions on Power Systems 14(3), 858–864. Bazaraa, M., Sherali, H. and Shetty, C.: 1993, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons. Biskas, P. and Bakirtzis, A.: 2006, Decentralized opf of large multiarea power system, IEE Proc.-Gener. Transm. Distrib. 153(1), 99–105. Biswas, P. P., Suganthan, P., Mallipeddi, R. and Amaratunga, G. A.: 2018, Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques, Engineering Applications of Artificial Intelligence 68, 81–100. Burchett, R. C., Happ, H. H. and Wirgau, K. A.: 1982, Large scale optimal power flow, IEEE Transactions on Power Apparatus and Systems 101(10), 3722–3732. Carpentier, J.: 1986, Cric, a new active reactive decoupling prcess in load flows, optimal power flows and system control., Proc. IFAC conference on power systems and power plan control pp. 65–70. Carroll, C.: 1959, An operations research approach to the economic optimization of a kraft pulping process, Ph.D. Dissertation, Institute of Paper Chemistry, Appleton, WI, . Carvalho, M., Soares, S. and Ohishi, T.: 1988, Optimal active power dispatch by network flow approach., IEEE Transactions on Power Systems 3(3), 1640–1647. Castillo, E., Conejo, A. J., Pedregal, P., Garcia, R. and Alguacil, N.: 2002, Building and Solving Mathematical Programming Models in Engineering and Science, John Wiley & Sons. Cohen, G.: 1980, Auxiliary problem principle and decomposition of optimization problems, Journal of Optimization Theory and Applications 32(3), 277–305. Conejo, A. and Aguado, J.: 1998, Multi-area coordinated decentralized dc optimal power flow, IEEE Transactions on Power Systems 13. Conejo, A. J. and Baringo, L.: 2018, Optimal power flow, Power System Operations, Springer, pp. 165–196. Conejo, P., Nogales, F. and Prieto, F.: 2002, A decomposition procedure based on approximate newton directions, in Mathematical programming. Springer-Verlag. . Cooper, L. and Drebes, C.: 1967, An approximate solution method for the fixed charge problem, Naval research logistics quarterly pp. 101–111. Dommel, H. and Tinney, W.: 1968, Optimal power flow solutions, IEEE Trans. Power Apparat. Syst. 87, 1866–1876. Fiacco, A. and McCormick, G.: 1968, Nonlinear programming: Sequential unconstrained minimization techniques, Wiley, New York, reissued by SIAM in 1995 . Frisch, K.: 1954, Principles of linear programming - with particular reference to the double gradient form of the logarithmic potential method., Memorandum on October 18. University Institute of Economics, Oslo . Garcia, A. and Mantovani, J.: 1988, Alocac¸ao de reativos em ˜ sistemas de energia eletrica utilizando um modelo implicitamente ´ acoplado, VII Congresso brasileiro de automatica, anais da ´ sociedade brasilera de automatica, S ´ ao Jos ˜ e dos Campos ´ 7, 861–866. Geoffrion, A. M. and Marsten, R.: 1972, Integer programming algorithms: A frame-woork and state of art survey., Management science 18, 565–481. Granada Echeverri, M., Lopez Lezama, J. M. and ´ Sanchez Mantovani, J. R.: 2010, Decentralized ac power flow for ´ multi-area power systems using a decomposition approach based on lagrangian relaxation Granada, M., Rider, M. J., Mantovani, J. R. and Shahidehpour, M.: 2008, Multi-areas optimal reactive power flow, Transmission and Distribution Conference and Exposition: Latin America, 2008 IEEE/PES, IEEE, pp. 1–6. Granada, M., Rider, M. J., Mantovani, J. and Shahidehpour, M.: 2012, A decentralized approach for optimal reactive power dispatch using a lagrangian decomposition method, Electric Power Systems Research 89, 148–156. Granville, S.: 1994, Optimal reactive dispatch through interior point methods, IEEE Transactions on Power Systems 9(1), 136–146. Granville, S., Pereira, M. and Monticelli, A.: 1988, An integrated methodology for var source planning, IEEE transactions on PAS 3, 549–557. Hertog, D. D.: 1994, Interior point approach to linear, quadratic and convex programming, algorithms, and complexity, Kluwer Publishers, Dordrecht, The Netherlands . Huard, P.: 1964, Resolution des p.m. ´ a contraintes non-lin ` eaires par ´ la methode des centres, ´ Note A.D.F. HR 5.690 . Hur, D., Park, J. and Kim, B.: 2002, Evaluation of convergence rate in the auxiliary problem principle for distributed optimal power flow, IEE Proceedings - Generation, Transmission and Distribution, Piscataway 149(5), 525–532. Iwamoto, S. and Tamura, Y.: 1981, A load flow calculation method for ill-conditioned power systems, IEEE Trans. Power App. Syst. 100(4), 1736–1743. Karmarkar, N.: 1984, A new polynomial-time algorithm for linear programming, Combinatorica 4 pp. 373–395. Khachiyan, L.: 1979, A polynomial-time algorithm in linear programming; english translation in: Soviet mathematics doklady 20 (1979) 191-194., Doklady Akademii Nauk SSSR 244, 1093–1096. Kim, B. and Baldick, R.: 1997, Coarse-grained distributed optimal power flow, IEEE Transactions on Power Systems 12(2), 932–939. Kindermann, G.: 2003, Curto-Circuito, Florianopolis: Edic¸ ´ ao do ˜ Autor. UFSCEEL-LABPLAN Kojima, M., Mizuno, S. and Yoshise, A.: 1989, Progress in mathematical programming: Interior point and related methods, Springer Verlag, New York pp. 29–47. Lebow, W. M., Mehra, R. K., Nadira, R., Rouhani, R. and Usoro, P.: 1984, Optimization of reactive volt-amperes (var) sources in system planning, EPRI Report El-3729, Project 2109-1 1. Lopez, J. C., Granada, M. and Mantovani, J.: 2010, Multi-area ´ decentralized optimal var planning using the dantzig-wolfe decomposition principle, Transmission and Distribution Conference and Exposition: Latin America (T&D-LA), 2010 IEEE/PES, IEEE, pp. 92–98. Losi, A. and Russo, M.: 2003, A note on the application of the auxiliary problem principle, Journal of Optimization Theory and Applications, New York 117(2), 377–396. Lu, W., Liu, M., Lin, S. and Li, L.: 2018, Fully decentralized optimal power flow of multi-area interconnected power systems based on distributed interior point method, IEEE Transactions on Power Systems 33(1), 901–910. Mantovani, J.: 1987, Planejamento de reativos em sistemas de energia eletrica: soluc¸ ´ ao via programac¸ ˜ ao linear sucessiva ˜ utilizando um modelo implicitamente acoplado, Tese de mestrado, UNICAMP . Mantovani, J. R. S. and Garcia, A. V.: 1996, A heuristic method for reactive power planning, IEEE Transactions on Power Systems 11(1), 68–74. Mantovani, J. R. S., Garcia, A. V. and Modesto, S. A. G.: 2001, Var planning using genetic algorithm and linear programming, Proc. Inst. Elect.Eng., Gen., Transm. Dist. 148(3), 257–262. Meggido, N.: 1989, Progress in mathematical programming: Interior point and related methods, Springer Verlag, New York pp. 131–158 Mehrotra, S.: 1992, On the implementation of a primal-dual interior point., SIAM Journal on Optimization 2, 575–601. Monteiro, R. D. C., Adler, I. and Resende, M. G. C.: 1990, A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension, Math. Oper. Res. 15(2), 191-214. Monticelli, A.: 1999, State Estimation in Electric Power Systems a Generalized Approach, Kluwer Academic Publishers. Massachusetts, USA. Monticelli, A. J.: 1983, Fluxo de Carga em Redes de Energia Eletrica ´ , Editora Edgard Blucher LTDA Nemirovsky, A. and Yudin, D.: 1983, informational complexity and efficient methods for solution of convex extremal problems, Wiley, New York . Ness, J. E. V.: 1959, Iteration methods for digital load flow studies, IEEE Transactions on Power Apparatus and Systems 78, 583–588. Nogales, F., Prieto, F. and Conejo, A.: 2003, A decomposition methodology applied to the multi-area optimal power flow problem, Annals of operations research (120), 99–116. Oliveira, A. and Filho, S.: 2003, Metodo de pontos interiores para ´ o problema de fluxo de potencia ˆ otimo dc., ´ REvista controle & automac¸ao 14(3), 278–285. Palacios-Gomez, F., Lasdon, L. and Engquist, M.: 1982, Nonlinear ´ optimization by successive linear programming, Management science 28, 1106–1120. Parisot, G.: 1961, Resolution num ´ erique approch ´ ee du probl ´ eme ` de programmation lineaire par application de la programmation ´ logarithmique, Ph.D. Dissertation. University of Lille, France . Renegar, J.: 1988, A polynomial-time algorithm, based on newton method, for linear programming, Math. Program 40, 59–93. Rosenbrock, H.: 1960, Automatic method for finding the greatest or least value of a function, Computer J pp. 175–184. Sasson, A.: 1969, Nonlinear programming solutions for the load-flow, minimum-loss, and economic dispatching problems, IEEE Trans. Power App. Syst. 88, 399–409 Sasson, A., Trevino, C. and Aboytes, F.: 1971, Improved newton’s load flow through a minimization technique, IEEE Trans. Power App. Syst. 90, 1974–1981. Stott, B. and Alsac, O.: 1983, Experience with successive linear programming for optimal rescheduling of active and reactive power., CIGRE/IFAC symposium on control applications to power system security . Sun, D., Ashley, B., Beuler, B., Hughes, A. and Tinney, W.: 1984, Optimal power flow by newton approach, IEEE Transactions on Power Apparatus and Systems 103(10), 2864–2880. Sun, D. I., Demaree, K. D. and Brewer, B.: 1990, Application and adaptation of newton for optimal power flow., In Application of Optimization Methods for Economy/Security Functions in Power System Operations. An IEEE Tutorial pp. 14–90. Tang, Y., Dvijotham, K. and Low, S.: 2017, Real-time optimal power flow, IEEE Transactions on Smart Grid 8(6), 2963–2973. Tinney, W. and Hart, C.: 1967, Power flow solution by newton’s method, IEEE Transactions on Power Apparatus and Systems 86, 1449–1456. Torres, G. and Quintana, V.: 1998, An interior-point methods for nonlinear optimal power flow using voltage rectangular coordinates, IEEE Trans. Power Syst. 13(4), 1211-1218. Wallach, Y.: 1968, Gradient methods for load flow-problems, IEEE Transactions on Power Apparatus and Systems 87, 1314–1318. Ward, J. and Hale, W.: 1956, Digital computer solution of power flow problems, AIEE Transactions Power App. Syst. 75, 398–404. Wolfe, P.: 1963, Methods of nonlinear programming, Recent Advances in Mathematical Programming. in R.L. Graves and P. Wolfe (eds), McGraw-Hill . Zollenkopf, K.: 1971, Bi-factorization-basic computation algorithm and programming techniques, Large sparse sets of linear equations, edited by Reid, J.K., N. York, Academic Press pp. 75–97.
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spelling	Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)Manifiesto (Manifestamos) en este documento la voluntad de autorizar a la Biblioteca Jorge Roa Martínez de la Universidad Tecnológica de Pereira la publicación en el Repositorio institucional (http://biblioteca.utp.edu.co), la versión electrónica de la OBRA titulada: La Universidad Tecnológica de Pereira, entidad académica sin ánimo de lucro, queda por lo tanto facultada para ejercer plenamente la autorización anteriormente descrita en su actividad ordinaria de investigación, docencia y publicación. La autorización otorgada se ajusta a lo que establece la Ley 23 de 1982. Con todo, en mi (nuestra) condición de autor (es) me (nos) reservo (reservamos) los derechos morales de la OBRA antes citada con arreglo al artículo 30 de la Ley 23 de 1982. En concordancia suscribo (suscribimos) este documento en el momento mismo que hago (hacemos) entrega de mi (nuestra) OBRA a la Biblioteca “Jorge Roa Martínez” de la Universidad Tecnológica de Pereira. Manifiesto (manifestamos) que la OBRA objeto de la presente autorizacióhttps://creativecommons.org/licenses/by-nc-sa/4.0/http://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessGranada Echeverri, MauricioGallego Rendón, Ramón A2024-10-03T14:34:15Z2024-10-03T14:34:15Z2024978-958-722-325-5https://hdl.handle.net/11059/15332978-958-722-682-9Universidad Tecnológica de PereiraRepositorio Universidad Tecnológica de Pereirahttps://repositorio.utp.edu.co/home: figuras, tablasEl problema de flujo de carga es el aspecto central del análisis de sistemas eléctricos de potencia y su formulación y solución es una tarea obligatoria en los estudios de planeamiento a largo plazo de sistemas eléctricos, en los estudios de seguridad (confiabilidad, ´ contingencias, cortocircuito, estabilidad) y en los estudios que se realizan de manera permanente para la programación de la operación´ diaria de un sistema eléctrico y para su control. La idea del problema de flujo de potencia optimo (FPO) fue introducida a principios de la década de los 60 como una extensión del problema de despacho económico convencional (DEC). Con la llegada del FPO se marcó el fin del periodo clásico de DEC, el cual se desarrolló a lo largo de treinta a nos usando el método de igual ´ costo incremental. Aunque realmente el DEC y el FPO son ambos problemas de optimización, el primero sólo considera la generación de potencia activa y representa la red eléctrica a través de simples restricciones de igualdad. En el FPO ciertas variables controlables (controles activos y/o reactivos) son ajustadas para minimizar una función objetivo predefinida mientras se satisfacen límites operativos (restricciones de desigualdad) y físicos (restricciones de igualdad) de un sistema eléctrico de potencia (SEP) bajo condiciones de operación estática.1 Introducción--2 Conceptos generales--2 1 Programación matemática--Programación lineal--MPI para PL--Programación no-Lineal--Optimilidad de KKT de primer orden--P-PNL irrestricta--P-PNL con restricciones--MPI para P-PNL--Formulación del problema--FPO-FP-AC como problema de PNL--FPO-FP-AC como problema de PNL--FPO-Minimización de costos de combustible--FPO-Minimización de perdidas activas--Planeamiento de reactivos--Modelo lineal -FPOR-PL sucesiva--Ejemplo-Sistema de tres barras--Gradiente descendiente para FPO--FPO únicamente con restricciones de igualdad--Restricciones funcionales de desigualdad--Cálculo del paso exploratorio--Método de Newton para cálculo de FPO--Restricciones de desigualdad del FPO--Penalidades cuadráticas--Límites sobre funciones especiales--Restricciones de desigualdad no-lineales--Formulación acoplada del FPO--Versión desacoplada del FPO--MPI para FPO-DC--Modelo de FPO-DC--FPOR usando MPI Predictor-Corrector--Algoritmo Predictor-Corrector--FPO Multi-Areas--Esquema de descomposición regional--Esquema de descomposición--Descomposición matemática--Descomposición Langrangiana--Flujo de potencia optimo reactivo--ORPF: esquema centralizado--Descomposición regional: esquema descentralizado--ORPF-MA: principio de problema auxiliar--ORPF-MA: DCPO--Bibliografía--Indice general270 páginasapplication/pdfspaUniversidad Tecnológica de PereiraPereira530 - Física::537 - Electricidad y electrónicaSistemas de interconexión eléctricaSistemas de energía eléctricaEnergía eléctricaAnálisis de sistemas eléctricos de potenciaFlujo de potenciaConfiabilidad (Ingeniería)Programación linealSistemas de transmisión de energíaFlujo de potencia óptimo en sistemas de transmisión de energía eléctricaLibroinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_2f33Textinfo:eu-repo/semantics/bookAbadie, J. and Carpentier, J.: 1969, Generalization of the wolf reduced gradient method to the case of nonlinear constraints., Recent Advances in Mathematical Programming. in Optimization, R. Fletcher (ed), New York: Academic Press. pp. 37–47.Bakirtzis, A. and Biskas, P.: 2003, A decentralized solution to the dc-opf of interconnected power systems, IEEE Transactions on Power Systems 18(3), 1007–1013.Baldick, R., Kim, B., Chase, C. and Luo, Y.: 1999, A fast distributed implementation of optimal power flow, IEEE Transactions on Power Systems 14(3), 858–864.Bazaraa, M., Sherali, H. and Shetty, C.: 1993, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons.Biskas, P. and Bakirtzis, A.: 2006, Decentralized opf of large multiarea power system, IEE Proc.-Gener. Transm. Distrib. 153(1), 99–105.Biswas, P. P., Suganthan, P., Mallipeddi, R. and Amaratunga, G. A.: 2018, Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques, Engineering Applications of Artificial Intelligence 68, 81–100.Burchett, R. C., Happ, H. H. and Wirgau, K. A.: 1982, Large scale optimal power flow, IEEE Transactions on Power Apparatus and Systems 101(10), 3722–3732.Carpentier, J.: 1986, Cric, a new active reactive decoupling prcess in load flows, optimal power flows and system control., Proc. IFAC conference on power systems and power plan control pp. 65–70.Carroll, C.: 1959, An operations research approach to the economic optimization of a kraft pulping process, Ph.D. Dissertation, Institute of Paper Chemistry, Appleton, WI, .Carvalho, M., Soares, S. and Ohishi, T.: 1988, Optimal active power dispatch by network flow approach., IEEE Transactions on Power Systems 3(3), 1640–1647.Castillo, E., Conejo, A. J., Pedregal, P., Garcia, R. and Alguacil, N.: 2002, Building and Solving Mathematical Programming Models in Engineering and Science, John Wiley & Sons.Cohen, G.: 1980, Auxiliary problem principle and decomposition of optimization problems, Journal of Optimization Theory and Applications 32(3), 277–305.Conejo, A. and Aguado, J.: 1998, Multi-area coordinated decentralized dc optimal power flow, IEEE Transactions on Power Systems 13.Conejo, A. J. and Baringo, L.: 2018, Optimal power flow, Power System Operations, Springer, pp. 165–196.Conejo, P., Nogales, F. and Prieto, F.: 2002, A decomposition procedure based on approximate newton directions, in Mathematical programming. Springer-Verlag. .Cooper, L. and Drebes, C.: 1967, An approximate solution method for the fixed charge problem, Naval research logistics quarterly pp. 101–111.Dommel, H. and Tinney, W.: 1968, Optimal power flow solutions, IEEE Trans. Power Apparat. Syst. 87, 1866–1876.Fiacco, A. and McCormick, G.: 1968, Nonlinear programming: Sequential unconstrained minimization techniques, Wiley, New York, reissued by SIAM in 1995 .Frisch, K.: 1954, Principles of linear programming - with particular reference to the double gradient form of the logarithmic potential method., Memorandum on October 18. University Institute of Economics, Oslo .Garcia, A. and Mantovani, J.: 1988, Alocac¸ao de reativos em ˜ sistemas de energia eletrica utilizando um modelo implicitamente ´ acoplado, VII Congresso brasileiro de automatica, anais da ´ sociedade brasilera de automatica, S ´ ao Jos ˜ e dos Campos ´ 7, 861–866.Geoffrion, A. M. and Marsten, R.: 1972, Integer programming algorithms: A frame-woork and state of art survey., Management science 18, 565–481.Granada Echeverri, M., Lopez Lezama, J. M. and ´ Sanchez Mantovani, J. R.: 2010, Decentralized ac power flow for ´ multi-area power systems using a decomposition approach based on lagrangian relaxationGranada, M., Rider, M. J., Mantovani, J. R. and Shahidehpour, M.: 2008, Multi-areas optimal reactive power flow, Transmission and Distribution Conference and Exposition: Latin America, 2008 IEEE/PES, IEEE, pp. 1–6.Granada, M., Rider, M. J., Mantovani, J. and Shahidehpour, M.: 2012, A decentralized approach for optimal reactive power dispatch using a lagrangian decomposition method, Electric Power Systems Research 89, 148–156.Granville, S.: 1994, Optimal reactive dispatch through interior point methods, IEEE Transactions on Power Systems 9(1), 136–146.Granville, S., Pereira, M. and Monticelli, A.: 1988, An integrated methodology for var source planning, IEEE transactions on PAS 3, 549–557.Hertog, D. D.: 1994, Interior point approach to linear, quadratic and convex programming, algorithms, and complexity, Kluwer Publishers, Dordrecht, The Netherlands .Huard, P.: 1964, Resolution des p.m. ´ a contraintes non-lin ` eaires par ´ la methode des centres, ´ Note A.D.F. HR 5.690 .Hur, D., Park, J. and Kim, B.: 2002, Evaluation of convergence rate in the auxiliary problem principle for distributed optimal power flow, IEE Proceedings - Generation, Transmission and Distribution, Piscataway 149(5), 525–532.Iwamoto, S. and Tamura, Y.: 1981, A load flow calculation method for ill-conditioned power systems, IEEE Trans. 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York, Academic Press pp. 75–97.PublicationORIGINALFlujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdfFlujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdfapplication/pdf6963757https://repositorio.utp.edu.co/bitstreams/0466a148-1f40-47db-93b5-d78526fd833c/downloadea2e1f409e2e035d55b85f21178f2753MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-815543https://repositorio.utp.edu.co/bitstreams/fb87847c-8d14-4a4b-bde1-02a567298eb8/download73a5432e0b76442b22b026844140d683MD52THUMBNAILImagen3.pngimage/png332756https://repositorio.utp.edu.co/bitstreams/d811ca24-381b-43e4-b681-88b041e1939d/downloadb9f921c240d093034de897f9e9e7eb87MD53Flujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdf.jpgFlujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdf.jpgGenerated Thumbnailimage/jpeg11564https://repositorio.utp.edu.co/bitstreams/3c42891e-ede2-4f46-b8fd-afe985defba0/downloada82c7b80f464b87661a82466555bc7ccMD55TEXTFlujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdf.txtFlujo de potencia óptimo en sistemas de transmisión de energía Eléctrica.pdf.txtExtracted texttext/plain102192https://repositorio.utp.edu.co/bitstreams/bf16c9aa-b0a5-492a-821d-5aec372e3ba2/download4a7429650a50073742a55996de0bb55bMD5411059/15332oai:repositorio.utp.edu.co:11059/153322024-10-04 04:01:38.387https://creativecommons.org/licenses/by-nc-sa/4.0/Manifiesto (Manifestamos) en este documento la voluntad de autorizar a la Biblioteca Jorge Roa Martínez de la Universidad Tecnológica de Pereira la publicación en el Repositorio institucional (http://biblioteca.utp.edu.co), la versión electrónica de la OBRA titulada: La Universidad Tecnológica de Pereira, entidad académica sin ánimo de lucro, queda por lo tanto facultada para ejercer plenamente la autorización anteriormente descrita en su actividad ordinaria de investigación, docencia y publicación. 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Manifiesto (manifestamos) que la OBRA objeto de la presente autorizacióopen.accesshttps://repositorio.utp.edu.coRepositorio de la Universidad Tecnológica de 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

Flujo de potencia óptimo en sistemas de transmisión de energía eléctrica

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