Introducción a la estabilidad de sistemas eléctricos de potencia

Descubre el fascinante mundo detrás de los sistemas eléctricos de potencia, auténticas maravillas tecnológicas que abarcan países enteros con miles de componentes interconectados. La compleja dinámica de estos sistemas implica el uso de herramientas matemáticas y de modelizado que permitan garantiza...

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Autores:
Garcés Ruiz, Alejandro
Gil González, Walter Julián
Montoya Giraldo, Oscar Danilo
Tipo de recurso:
Book
Fecha de publicación:
2023
Institución:
Universidad Tecnológica de Pereira
Repositorio:
Repositorio Institucional UTP
Idioma:
spa
OAI Identifier:
oai:repositorio.utp.edu.co:11059/14905
Acceso en línea:
https://hdl.handle.net/11059/14905
https://doi.org/10.22517/9789587228960
https://repositorio.utp.edu.co/home
Palabra clave:
620 - Ingeniería y operaciones afines::621 - Física aplicada
Control automático
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
Circuitos magnéticos
Sistemas de potencia
Control automático
Circuitos magnéticos
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
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openAccess
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Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
id UTP2_16868641bae7d59d5edacd9c9f19a974
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network_acronym_str UTP2
network_name_str Repositorio Institucional UTP
repository_id_str
dc.title.spa.fl_str_mv Introducción a la estabilidad de sistemas eléctricos de potencia
title Introducción a la estabilidad de sistemas eléctricos de potencia
spellingShingle Introducción a la estabilidad de sistemas eléctricos de potencia
620 - Ingeniería y operaciones afines::621 - Física aplicada
Control automático
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
Circuitos magnéticos
Sistemas de potencia
Control automático
Circuitos magnéticos
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
title_short Introducción a la estabilidad de sistemas eléctricos de potencia
title_full Introducción a la estabilidad de sistemas eléctricos de potencia
title_fullStr Introducción a la estabilidad de sistemas eléctricos de potencia
title_full_unstemmed Introducción a la estabilidad de sistemas eléctricos de potencia
title_sort Introducción a la estabilidad de sistemas eléctricos de potencia
dc.creator.fl_str_mv Garcés Ruiz, Alejandro
Gil González, Walter Julián
Montoya Giraldo, Oscar Danilo
dc.contributor.author.none.fl_str_mv Garcés Ruiz, Alejandro
Gil González, Walter Julián
Montoya Giraldo, Oscar Danilo
dc.subject.ddc.none.fl_str_mv 620 - Ingeniería y operaciones afines::621 - Física aplicada
topic 620 - Ingeniería y operaciones afines::621 - Física aplicada
Control automático
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
Circuitos magnéticos
Sistemas de potencia
Control automático
Circuitos magnéticos
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
dc.subject.lemb.none.fl_str_mv Control automático
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
Circuitos magnéticos
dc.subject.proposal.spa.fl_str_mv Sistemas de potencia
Control automático
Circuitos magnéticos
Maquinaria eléctrica
Convertidores de corriente eléctrica
Osciladores eléctricos
Recursos energéticos renovables
description Descubre el fascinante mundo detrás de los sistemas eléctricos de potencia, auténticas maravillas tecnológicas que abarcan países enteros con miles de componentes interconectados. La compleja dinámica de estos sistemas implica el uso de herramientas matemáticas y de modelizado que permitan garantizar una operación estable, evitando así posibles apagones. Este libro te invita a explorar esta intrincada red con un enfoque simplificado, especialmente diseñado para estudiantes de ingeniería eléctrica con conocimientos en circuitos eléctricos, análisis de sistemas de potencia y máquinas eléctricas. El libro inicia modelizando la máquina síncrona, como principal componente dinámico de los sistemas clásicos. Igualmente, se presenta el convertidor de potencia, necesario para la integración de recursos renovables. Posteriormente, se presenta las herramientas de análisis de pequeña señal y estabilidad transitoria. El libro recoge más de quince años de experiencia de los autores quienes han orientado este curso en diferentes universidades del país y han realizado investigación en esta área con impacto internacional.
publishDate 2023
dc.date.issued.none.fl_str_mv 2023
dc.date.accessioned.none.fl_str_mv 2024-01-22T13:53:08Z
dc.date.available.none.fl_str_mv 2024-01-22T13:53:08Z
dc.type.spa.fl_str_mv Libro
dc.type.version.none.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.type.content.none.fl_str_mv Text
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/book
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dc.identifier.isbn.none.fl_str_mv 978-958-722-896-0
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/11059/14905
dc.identifier.eisbn.none.fl_str_mv 978-958-722-897-7
dc.identifier.doi.none.fl_str_mv https://doi.org/10.22517/9789587228960
dc.identifier.instname.none.fl_str_mv Universidad Tecnológica de Pereira
dc.identifier.reponame.none.fl_str_mv Repositorio Institucional Universidad Tecnológica de Pereira
dc.identifier.repourl.none.fl_str_mv https://repositorio.utp.edu.co/home
identifier_str_mv 978-958-722-896-0
978-958-722-897-7
Universidad Tecnológica de Pereira
Repositorio Institucional Universidad Tecnológica de Pereira
url https://hdl.handle.net/11059/14905
https://doi.org/10.22517/9789587228960
https://repositorio.utp.edu.co/home
dc.language.iso.none.fl_str_mv spa
language spa
dc.relation.ispartofseries.none.fl_str_mv Textos Academicos
dc.relation.references.none.fl_str_mv Adams, J., Carter, C., and Huang, S.-H. (2012). Ercot experience with sub synchronous control interaction and proposed remediation. In PES T and D 2012, pages 1–5.
Akagi, H., Watanabe, E. H., and Aredes, M. (2007). Instantaneous Power Theory and Applications to Power Conditioning. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 1 edition.
Anderson, P. and Fouad, A. (2003). Power system control and stability. Piscataway, NJ, Wiley-Interscience, NY, 2 edition.
Arrillaga, J. andWatson, N. (2003). Power System Harmonics. John Wiley and Sons, NY, 3 edition
Bravo, M., Garces, A., Montoya, O. D., and Baier, C. R. (2018). Nonlinear analysis for the three-phase PLL: A new look for a classical problem. In 2018 IEEE 19thWorkshop on Control and Modeling for Power Electronics (COMPEL). IEEE.
Chang-Chien, L.-R. and Yin, Y.-C. (2009). Strategies for operating wind power in a similar manner of conventional power plant. IEEE Transactions on Energy Conversion, 24(4):926–934
Chen, L., Liu, Y., Arsoy, A., Ribeiro, P., Steurer, M., and Iravani, M. (2006). Detailed modeling of superconducting magnetic energy storage (smes) system. IEEE Transactions on Power Delivery, 21(2):699–710. CIGRE A1/C4 working group (2022). Guide on the Assessment, Specification and Design of Synchronous Condenser for Power System with Predominance of Low or Zero Inertia Generators. CIGRE.
Conejo, A. and Baringo, L. (2018). Power system operations. Springer
Damas, R. N., Son, Y., Yoon, M., Kim, S.-Y., and Choi, S. (2020). Subsynchronous oscillation and advanced analysis: A review. IEEE Access, 8:224020–224032.
D’Arco, S. and Suul, J. A. (2014). Equivalence of virtual synchronous machines and frequency-droops for converter-based microgrids. IEEE Transactions on Smart Grid, 5(1):394–395.
Dario Jaramillo, R. and Garces, A. (2015). Wave energy: Modeling and analysis of power grid integration. IEEE Latin America Transactions, 13(12):3863–3872.
Davy, R. and Hiskens, I. (1997). Lyapunov functions for multimachine power systems with dynamic loads. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44(9):796–812.
D’Arco, S., Suul, J. A., and Fosso, O. B. (2015). A virtual synchronous machine implementation for distributed control of power converters in smartgrids. Electric Power Systems Research, 122:180–197.
ENTSO-E (2022). Stability management in power electronics dominated systems: a prerequisite to the success of the energy transition. European Network of Transmission System Operators for Electricity.
Farrokhabadi, M., Cañizares, C. A., Simpson-Porco, J.W., Nasr, E., Fan, L., Mendoza-Araya, P. A., Tonkoski, R., Tamrakar, U., Hatziargyriou, N., Lagos, D., Wies, R. W., Paolone, M., Liserre, M., Meegahapola, L., Kabalan, M., Hajimiragha, A. H., Peralta, D., Elizondo, M. A., Schneider, K. P., Tuffner, F. K., and Reilly, J. (2020). Microgrid stability de nitions, analysis, and examples. IEEE Transactions on Power Systems, 35(1):13– 29.
Feynman, R., Leighton, R., and Sands, M. (2015). The Feynman Lectures on Physics, Vol. I. Hachette UK, NY, 1 edition.
Garces, A. (2022). Economic dispatch of thermal units, pages 125–144
Garcés, A. and Galvis, J.-C. (2004). Flujo de carga armónico en sistemas de distribucion radiales. Trabajo de grado.
Garces, A. and Gil-Gonzalez, W. (2021). Stability analysis for a grid forming converter with inverse droop connected to an in nite bus. In 2021 IEEE 5th Colombian Conference on Automatic Control (CCAC), pages 286–290.
Gil-González, W., Garces, A., and Escobar, A. (2019a). Passivity-based control and stability analysis for hydro-turbine governing systems. Applied Mathematical Modelling, 68:471–486.
Gil-González,W. J., Garces, A., Fosso,O. B., and Escobar-Mejía, A. (2019b). Passivity-based control of power systems considering hydro turbine with surge tank. IEEE Transactions on Power Systems, 35(3):2002– 2011.
Gil-González, W., Montoya, O. D., Garces, A., et al. (2019). Direct power control of electrical energy storage systems: A passivity-based pi approach. Electric Power Systems Research, 175:105885.
Gless, G. E. (1966). Direct method of liapunov applied to transient power system stability. IEEE Transactions on Power Apparatus and Systems, PAS-85(2):159–168.
Haddad, W. and Chellaboina, V. (2008). Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press, NY, 2 edition.
Hale, J. K. (1980). Ordinary di erential equations. John Wiley and sons, Malabar, Florida, 2 edition.
Hatziargyriou, N., Milanovic, J., Rahmann, C., Ajjarapu, V., Cañizares, C., Erlich, I., Hill, D., Hiskens, I., Kamwa, I., Pal, B., et al. (2020). Stability de nitions and characterization of dynamic behavior in systems with high penetration of power electronic interfaced technologies.
He, J., Li, Y., Liang, B., and Wang, C. (2017). Inverse power factor droop control for decentralized power sharing in series-connected microconverters-based islanding microgrids. IEEE Transactions on Industrial Electronics, 64(9):7444–7454.
He ron, W. G. and Phillips, R. A. (1952). E ect of a modern amplidyne voltage regulator on underexcited operation of large turbine generators [includes discussion]. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems, 71(3):692–697
Hill, D. (1993). Nonlinear dynamic load models with recovery for voltage stability studies. IEEE Transactions on Power Systems, 8(1):166–176.
IEEE (1969). Proposed excitation system de nitions for synchronous machines. IEEE Transactions on Power Apparatus and Systems, PAS 88(8):1248–1258.
IEEE (1994). Working group on prime mover and energy supply models for system dynamic performance studies dynamic models for combined cycle plants in power system studies. IEEE Transactions on Power Systems, 9(3):1698–1708.
IEEE-PES (2012). Ieee guide for control of small (100 kva to 5 mva) hydroelectric power plants. IEEE Std 1020-2011 (Revision of IEEE Std 1020-1988), pages 1–56.
IEEE TASK FORCE (1977). First benchmark model for computer simulation of subsynchronous resonance. IEEE Transactions on Power Apparatus and Systems, 96(5):1565–1572.
Kassakian, J. G., Perreault, D. J., Verghese, G. C., and Schlecht, M. F. (2023). Principles of power electronics. Cambridge University Press.
Khalil, H. (2002). Nonlinear Systems. Prentice Hall, NY, 3 edition.
Koritarov, V., Guzowski, L., Feltes, J., Kazachkov, Y., Gong, B., Trouille, B., Donalek, P., and Gevorgian, V. (2013a). Modeling Ternary Pumped Storage Units. Argonne National Laboratory
Koritarov, V., Guzowski, L., Feltes, J., Kazachkov, Y., Lam, B., Carlos Grande-Moran, G. T., Eng, L., Trouille, B., and Donalek, P. (2013b). Review of Existing Hydroelectric Turbine-Governor Simulation Models. Argonne National Laboratory
Krause, P., Wasynczuk, O., and Sudho , S. (2002). Analysis of electric machinery and drive systems. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 2 edition.
Kron, G. (1942). Tensors for circuits. Dover Publications.
Kundur, P. (1994). Power systems stability and control. EPRI: power systems engineering series, NY, 3 edition.
Li, H., Wang, J., and Meng, J. (2021). Nonlinear control. In Learning Control, pages 93–102. Elsevier.
Luo, X., Wang, J., Dooner, M., and Clarke, J. (2015). Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied Energy, 137:511 – 536.
Machowski, J., Lubosny, Z., Bialek, J. W., and Bumby, J. R. (2020). Power system dynamics: stability and control. John Wiley and Sons, 3 edition.
Montoya, O. D., Garcés, A., and Espinosa-Pérez, G. (2018). A generalized passivity-based control approach for power compensation in distribution systems using electrical energy storage systems. Journal of Energy Storage, 16:259–268
Morison, K. and Glavic, M. (2007). Review of on-line dynamic security assessment tools and techniques. Technical report.
Narasimhamurthi, N. (1984). On the existence of energy function for power systems with transmission losses. IEEE Transactions on Circuits and Systems, 31(2):199–203.
Nikravesh, S. K. Y. (2018). Nonlinear Systems Stability Analysis. CRC Press.
Ortega, A. and Milano, F. (2016). Generalized model of vsc-based energy storage systems for transient stability analysis. IEEE Transactions on Power Systems, 31(5):3369–3380.
Ortega, R., Espinosa-Pérez, G., and Astol , A. (2013). Passivity-based control of ac drives: theory for the user and application examples. International Journal of Control, 86(4):625–635.
Ortega, R. and Garcia-Canseco, E. (2004). Interconnection and damping assignment passivity-based control: A survey. European Journal of Control, 10(5):432–450.
Padiyar, K. (2012). Analysis of Subsynchronous Resonance in Power Systems. Springer Science and Business Media, NY, US, 1 edition.
Patarroyo-Montenegro, J. F., Vasquez-Plaza, J. D., Andrade, F., and Fan, L. (2020). An Optimal Power Control Strategy for Grid-Following Inverters in a Synchronous Frame. Applied Sciences, 10(19):6730.
Patterson, B. (2012). Dc, come home: Dc microgrids and the birth of the enernet. Power and Energy Magazine, IEEE, 10(6):60–69.
Pearre, N. S. and Ribberink, H. (2019). Review of research on v2x technologies, strategies, and operations. Renewable and Sustainable Energy Reviews, 105:61 – 70.
Perez, M. A., Ceballos, S., Konstantinou, G., Pou, J., and Aguilera, R. P. (2021). Modular multilevel converters: Recent achievements and challenges. IEEE Open Journal of the Industrial Electronics Society, 2:224–239.
Perez Londono, S. M., Rodriguez Garcia, L. F., and Mora Florez, J. J. (2015). Obtencion de modelos de carga compuestos en sistemas de potencia para analisis dinamico: revision y aplicacion. Tecnura, 19:171–189.
Perko, L. (2001). Differential Equations and Dynamical Systems. Springer Verlag, New York, 1 edition.
Perko, L. (2013). Differential equations and dynamical systems, volume 7. Springer Science & Business Media.
Pulgar-Painemal, H. (2019). Enforcement of current limits in d g-based wind turbine dynamic models through capability curve. IEEE Transactions on Sustainable Energy, 10(1):318–320.
Rabie, D., Senjyu, T., Alkhalaf, S., Mohamed, Y. S., and Shehata, E. (2021). Study and analysis of voltage source converter control stability for HVDC system using di erent control techniques. Ain Shams Engineering Journal, 12(3):2763–2779.
Sami, I., Ullah, N., Muyeen, S. M., Techato, K., Chowdhury, M. S., and Ro, J.-S. (2020). Control methods for standalone and grid connected micro-hydro power plants with synthetic inertia frequency support: A comprehensive review. IEEE Access, 8:176313–176329.
Shih, M.-H. and Tan, K.-K. (2023). Covering theorems of convex sets related to xed-point theorems. In Nonlinear and convex analysis, pages 235–244. CRC Press.
Slootweg, J., de Haan, S., Polinder, H., and Kling, W. (2003). General model for representing variable speed wind turbines in power system dynamics simulations. IEEE Transactions on Power Systems, 18(1):144– 151.
Stagg, G. and El-Abiad, A. (1988). Computer methods in power systems analysis. McGraw-Hill.
Teodorescu, R., Liserre, M., and Rodriguez, P. (2011). Grid Converters for Photovoltaic and Wind Power Systems. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 1 edition.
Van Der Schaft, A., Jeltsema, D., et al. (2014). Port-hamiltonian systems theory: An introductory overview. Foundations and Trends® in Systems and Control, 1(2-3):173–378.
Vega-Herrera, J., Rahmann, C. A., Valencia, F., and Strunz, K. (2020). Analysis and application of quasi-static and dynamic phasor calculus for stability assessment of integrated power electric and electronic systems. IEEE Transactions on Power Systems.
Venkataramana, A. (2007). Computational Techniques for Voltage Stability Assessment and Control. Springer, NY, 1 edition.
Villegas Pico, H., McCalley, J. D., Angel, A., Leon, R., and Castrillon, N. J. (2012). Analysis of very low frequency oscillations in hydro-dominant power systems using multi-unit modeling. IEEE Transactions on Power Systems, 27(4):1906–1915.
Walker, D., Bowler, C., Jackson, R., and Hodges, D. (1975). Results of subsynchronous resonance test at mohave. IEEE Transactions on Power Apparatus and Systems, 94(5):1878–1889.
Willems, J. L. and Willems, J. C. (1970). The application of lyapunov methods to the computation of transient stability regions for multimachine power systems. IEEE Transactions on Power Apparatus and Systems, PAS-89(5):795–801.
Wu, D., Tang, F., Vasquez, J. C., and Guerrero, J. M. (2014). Control and analysis of droop and reverse droop controllers for distributed generations. In 2014 IEEE 11th International Multi-Conference on Systems, Signals & Devices (SSD14), pages 1–5. IEEE.
Zografos, D. and Ghandhari, M. (2016). Estimation of power system inertia. In 2016 IEEE Power and Energy Society General Meeting (PESGM), pages 1–5.
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spelling Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 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 dehttps://creativecommons.org/licenses/by-nc-nd/4.0/http://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessGarcés Ruiz, AlejandroGil González, Walter JuliánMontoya Giraldo, Oscar Danilo2024-01-22T13:53:08Z2024-01-22T13:53:08Z2023978-958-722-896-0https://hdl.handle.net/11059/14905978-958-722-897-7https://doi.org/10.22517/9789587228960Universidad Tecnológica de PereiraRepositorio Institucional Universidad Tecnológica de Pereirahttps://repositorio.utp.edu.co/homeDescubre el fascinante mundo detrás de los sistemas eléctricos de potencia, auténticas maravillas tecnológicas que abarcan países enteros con miles de componentes interconectados. La compleja dinámica de estos sistemas implica el uso de herramientas matemáticas y de modelizado que permitan garantizar una operación estable, evitando así posibles apagones. Este libro te invita a explorar esta intrincada red con un enfoque simplificado, especialmente diseñado para estudiantes de ingeniería eléctrica con conocimientos en circuitos eléctricos, análisis de sistemas de potencia y máquinas eléctricas. El libro inicia modelizando la máquina síncrona, como principal componente dinámico de los sistemas clásicos. Igualmente, se presenta el convertidor de potencia, necesario para la integración de recursos renovables. Posteriormente, se presenta las herramientas de análisis de pequeña señal y estabilidad transitoria. El libro recoge más de quince años de experiencia de los autores quienes han orientado este curso en diferentes universidades del país y han realizado investigación en esta área con impacto internacional.Contenido Primera Parte Modelizado de componentes ...............................................................................................21 CAPÍTULO 1 Dinámica del sistema eléctrico............................................................................................23 1.1. Dinámica y estabilidad de sistemas eléctricos .........................................................25 1.2. Un poco de historia ..................................................................................................28 1.3. El sistema eléctrico moderno ...................................................................................29 1.4. Control automático de la generación........................................................................32 1.5. Efecto de las energías renovables.............................................................................33 1.6. Dispositivos FACTs y almacenamiento de energía..................................................36 1.7. Redes en corriente continua .....................................................................................37 1.8. Confiabilidad, seguridad y resiliencia ......................................................................38 1.9. Estudios de estabilidad de sistemas eléctricos .........................................................39 1.10. Escalas de tiempo de los fenómenos dinámicos en los sistemas de potencia ........40 1.11. Clasificación de tipos de estabilidad en los sistemas de potencia. .........................41 1.12. Actividades.............................................................................................................44 CAPÍTULO 2 La máquina síncrona ...........................................................................................................47 2.1. Estructura de la máquina síncrona trifásica..............................................................49 2.2. Campo magnético giratorio......................................................................................51 2.3. Modelo eléctrico de la máquina síncrona.................................................................53 2.3.1. Circuitos magnéticos......................................................................................54 2.3.2. Inductancias en la máquina síncrona ..............................................................58 2.4. Modelo dinámico del eje ..........................................................................................65 2.5. Energía y coenergía ..................................................................................................66 2.6. Actividades...............................................................................................................72 CAPÍTULO 3 Las transformadas de Clarke y Park.................................................................................77 3.1. Dificultades del modelo eléctrico de la máquina .....................................................79 3.2. Transformadas de Clarke y Park ..............................................................................80 3.2.1. Interpretación física de las transformadas......................................................83 3.2.2. Transformación de elementos pasivos............................................................84 3.3. Derivadas en el marco de referencia 0dq .................................................................86 3.4. Modelo eléctrico de la máquina en el marco 0dq.....................................................87 3.5. Actividades...............................................................................................................93 CAPÍTULO 4 Sistemas electromecánicos...................................................................................................97 4.1. Turbina hidroeléctrica ..............................................................................................99 4.2. Modelo de una turbina hidroeléctrica.......................................................................103 4.3. Turbina termoeléctrica..............................................................................................106 4.4. Turbina eólica...........................................................................................................109 4.5. Sistemas de fase no-mínima.....................................................................................113 4.6. Gobernador de velocidad y control primario ...........................................................114 4.7. Sistema de excitación y AVR ...................................................................................115 4.8. Actividades...............................................................................................................118 CAPÍTULO 5 Modelos simplificados de la máquina síncrona .................................................................121 5.1. Modelo promediado .................................................................................................123 5.2. Transitorio, subtransitorio y estado estacionario......................................................125 5.3. Modelo clásico .........................................................................................................125 5.4. Modelo transitorio....................................................................................................130 5.5. Modelo de Heffron-Phillips......................................................................................136 5.6. Actividades...............................................................................................................140 CAPÍTULO 6 El convertidor de potencia ..................................................................................................143 6.1. Integración de fuentes renovables............................................................................145 6.2. Control vectorial clásico...........................................................................................147 6.3. El PLL ......................................................................................................................149 6.4. Modulación por ancho de pulsos..............................................................................150 6.5. Modelo promediado .................................................................................................151 6.6. Control interno de corrientes....................................................................................154 6.7. Control externo de potencia .....................................................................................157 6.8. Otras formas de control............................................................................................158 6.9. Convertidores formadores de red .............................................................................159 6.10. Control en redes altamente resistivas.....................................................................161 6.11. Convertidor modular multi-nivel............................................................................162 6.12. Actividades.............................................................................................................164 Segunda Parte Estabilidad en estado estacionario .....................................................................................167 CAPÍTULO 7 Estabilidad de pequeña señal para una única máquina conectada a una barra infinita.....169 7.1. Estabilidad en sistemas linealizados ........................................................................171 7.1.1. Valores y vectores propios..............................................................................174 7.2. El operador exponencial..........................................................................................178 7.2.1. Análisis en el plano.........................................................................................182 7.3. Análisis de un generador conectado a una barra infinita..........................................184 7.3.1. Modelo clásico................................................................................................184 7.3.2. Modelo transitorio ..........................................................................................186 7.4. Actividades...............................................................................................................189 CAPÍTULO 8 Análisis de sensibilidad........................................................................................................191 8.0.1. Equilibrios hiperbólicos...............................................................................................193 8.1. Bifurcaciones ..................................................................................................................195 8.2. Tasa de amortiguamiento ................................................................................................198 8.3. Factores de participación ................................................................................................199 8.4. Funciones de sensibilidad ...............................................................................................202 8.5. Actividades......................................................................................................................205 CAPÍTULO 9 Análisis de redes...................................................................................................................209 9.1. Representación matricial de la red..................................................................................211 9.2. El flujo de potencia .........................................................................................................215 9.2.1. Flujo de potencia lineal .....................................................................................220 9.3. Eliminación de nodos de Kron........................................................................................222 9.4. Actividades......................................................................................................................226 CAPÍTULO 10 Estabilidad de pequeña señal en el caso multi-máquina ..................................................229 10.1. Modelo clásico multi-máquina .....................................................................................231 10.2. Modelo con respecto al centro de inercia .....................................................................237 10.3. Modelo general multi-máquina.....................................................................................238 10.4. El fenómeno de resonancia subsíncrona .......................................................................239 10.5. Estudios de estabilidad de pequeña señal .....................................................................242 10.6. Actividades....................................................................................................................244 CAPÍTULO 11 Estabilidad de tensión..........................................................................................................247 11.1. Colapso de tensión ........................................................................................................249 11.2. Análisis de un generador conectado a una carga...........................................................250 11.3. Curvas en nariz..............................................................................................................253 11.4. Modelo de la carga ........................................................................................................254 11.5. Efecto de los sistemas de compensación.......................................................................255 11.6. Efecto de los controles en los transformadores.............................................................256 11.7. Análisis de sensibilidad.................................................................................................257 11.8. Formas de mejorar la estabilidad de tensión.................................................................260 11.9. Actividades....................................................................................................................260 Parte 3 Estabilidad transitoria.........................................................................................................263 CAPÍTULO 12 Método de áreas iguales.......................................................................................................265 12.1. Estabilidad transitoria ...................................................................................................267 12.2. Análisis en el plano de fases .........................................................................................269 12.3. Método de áreas iguales................................................................................................271 12.4. Formas de mejorar la estabilidad transitoria.................................................................281 12.4.1. Aumento de la tensión del sistema del sistema ...............................................281 12.4.2. Desconexión de un generador .........................................................................282 12.4.3. Compensación serie.........................................................................................283 12.4.4. Compensación paralelo ...................................................................................284 12.4.5. Resistencia transitoria .....................................................................................284 12.4.6. Recierres..........................................................................................................285 12.4.7. Control en el gobernador de velocidad ...........................................................286 12.5. Actividades....................................................................................................................287 CAPÍTULO 13 Estabilidad transitoria en el caso multi-máquina.............................................................289 13.1. Método de áreas iguales para dos máquinas síncronas.................................................291 13.1.1. Solución numérica de ecuaciones diferenciales.........................................................297 13.2. Modelo clásico para un sistema multi-máquina............................................................299 13.3. Dinámica con respecto al centro de inercia ..................................................................305 13.4. Actividades....................................................................................................................307 CAPÍTULO 14 Pasividad, disipatividad y funciones de energía................................................................309 14.1. Funciones de Lyapunov ................................................................................................311 14.2. Pasividad y disipatividad ..............................................................................................320 14.3. Conexión de sistemas pasivos.......................................................................................323 14.4. Sistemas hamiltonianos controlados por puertos..........................................................325 14.5. Actividades....................................................................................................................333 Referencias.............................................................................................................................335351application/pdfspaUniversidad Tecnológica de PereiraTextos AcademicosAdams, J., Carter, C., and Huang, S.-H. (2012). Ercot experience with sub synchronous control interaction and proposed remediation. In PES T and D 2012, pages 1–5.Akagi, H., Watanabe, E. H., and Aredes, M. (2007). Instantaneous Power Theory and Applications to Power Conditioning. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 1 edition.Anderson, P. and Fouad, A. (2003). Power system control and stability. Piscataway, NJ, Wiley-Interscience, NY, 2 edition.Arrillaga, J. andWatson, N. (2003). Power System Harmonics. John Wiley and Sons, NY, 3 editionBravo, M., Garces, A., Montoya, O. D., and Baier, C. R. (2018). Nonlinear analysis for the three-phase PLL: A new look for a classical problem. In 2018 IEEE 19thWorkshop on Control and Modeling for Power Electronics (COMPEL). IEEE.Chang-Chien, L.-R. and Yin, Y.-C. (2009). Strategies for operating wind power in a similar manner of conventional power plant. IEEE Transactions on Energy Conversion, 24(4):926–934Chen, L., Liu, Y., Arsoy, A., Ribeiro, P., Steurer, M., and Iravani, M. (2006). Detailed modeling of superconducting magnetic energy storage (smes) system. IEEE Transactions on Power Delivery, 21(2):699–710. CIGRE A1/C4 working group (2022). Guide on the Assessment, Specification and Design of Synchronous Condenser for Power System with Predominance of Low or Zero Inertia Generators. CIGRE.Conejo, A. and Baringo, L. (2018). Power system operations. SpringerDamas, R. N., Son, Y., Yoon, M., Kim, S.-Y., and Choi, S. (2020). Subsynchronous oscillation and advanced analysis: A review. IEEE Access, 8:224020–224032.D’Arco, S. and Suul, J. A. (2014). Equivalence of virtual synchronous machines and frequency-droops for converter-based microgrids. IEEE Transactions on Smart Grid, 5(1):394–395.Dario Jaramillo, R. and Garces, A. (2015). Wave energy: Modeling and analysis of power grid integration. IEEE Latin America Transactions, 13(12):3863–3872.Davy, R. and Hiskens, I. (1997). Lyapunov functions for multimachine power systems with dynamic loads. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44(9):796–812.D’Arco, S., Suul, J. A., and Fosso, O. B. (2015). A virtual synchronous machine implementation for distributed control of power converters in smartgrids. Electric Power Systems Research, 122:180–197.ENTSO-E (2022). Stability management in power electronics dominated systems: a prerequisite to the success of the energy transition. European Network of Transmission System Operators for Electricity.Farrokhabadi, M., Cañizares, C. A., Simpson-Porco, J.W., Nasr, E., Fan, L., Mendoza-Araya, P. A., Tonkoski, R., Tamrakar, U., Hatziargyriou, N., Lagos, D., Wies, R. W., Paolone, M., Liserre, M., Meegahapola, L., Kabalan, M., Hajimiragha, A. H., Peralta, D., Elizondo, M. A., Schneider, K. P., Tuffner, F. K., and Reilly, J. (2020). Microgrid stability de nitions, analysis, and examples. IEEE Transactions on Power Systems, 35(1):13– 29.Feynman, R., Leighton, R., and Sands, M. (2015). The Feynman Lectures on Physics, Vol. I. Hachette UK, NY, 1 edition.Garces, A. (2022). Economic dispatch of thermal units, pages 125–144Garcés, A. and Galvis, J.-C. (2004). Flujo de carga armónico en sistemas de distribucion radiales. Trabajo de grado.Garces, A. and Gil-Gonzalez, W. (2021). Stability analysis for a grid forming converter with inverse droop connected to an in nite bus. In 2021 IEEE 5th Colombian Conference on Automatic Control (CCAC), pages 286–290.Gil-González, W., Garces, A., and Escobar, A. (2019a). Passivity-based control and stability analysis for hydro-turbine governing systems. Applied Mathematical Modelling, 68:471–486.Gil-González,W. J., Garces, A., Fosso,O. B., and Escobar-Mejía, A. (2019b). Passivity-based control of power systems considering hydro turbine with surge tank. IEEE Transactions on Power Systems, 35(3):2002– 2011.Gil-González, W., Montoya, O. D., Garces, A., et al. (2019). Direct power control of electrical energy storage systems: A passivity-based pi approach. Electric Power Systems Research, 175:105885.Gless, G. E. (1966). Direct method of liapunov applied to transient power system stability. IEEE Transactions on Power Apparatus and Systems, PAS-85(2):159–168.Haddad, W. and Chellaboina, V. (2008). Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press, NY, 2 edition.Hale, J. K. (1980). Ordinary di erential equations. John Wiley and sons, Malabar, Florida, 2 edition.Hatziargyriou, N., Milanovic, J., Rahmann, C., Ajjarapu, V., Cañizares, C., Erlich, I., Hill, D., Hiskens, I., Kamwa, I., Pal, B., et al. (2020). Stability de nitions and characterization of dynamic behavior in systems with high penetration of power electronic interfaced technologies.He, J., Li, Y., Liang, B., and Wang, C. (2017). Inverse power factor droop control for decentralized power sharing in series-connected microconverters-based islanding microgrids. IEEE Transactions on Industrial Electronics, 64(9):7444–7454.He ron, W. G. and Phillips, R. A. (1952). E ect of a modern amplidyne voltage regulator on underexcited operation of large turbine generators [includes discussion]. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems, 71(3):692–697Hill, D. (1993). Nonlinear dynamic load models with recovery for voltage stability studies. IEEE Transactions on Power Systems, 8(1):166–176.IEEE (1969). Proposed excitation system de nitions for synchronous machines. IEEE Transactions on Power Apparatus and Systems, PAS 88(8):1248–1258.IEEE (1994). Working group on prime mover and energy supply models for system dynamic performance studies dynamic models for combined cycle plants in power system studies. IEEE Transactions on Power Systems, 9(3):1698–1708.IEEE-PES (2012). Ieee guide for control of small (100 kva to 5 mva) hydroelectric power plants. IEEE Std 1020-2011 (Revision of IEEE Std 1020-1988), pages 1–56.IEEE TASK FORCE (1977). First benchmark model for computer simulation of subsynchronous resonance. IEEE Transactions on Power Apparatus and Systems, 96(5):1565–1572.Kassakian, J. G., Perreault, D. J., Verghese, G. C., and Schlecht, M. F. (2023). Principles of power electronics. Cambridge University Press.Khalil, H. (2002). Nonlinear Systems. Prentice Hall, NY, 3 edition.Koritarov, V., Guzowski, L., Feltes, J., Kazachkov, Y., Gong, B., Trouille, B., Donalek, P., and Gevorgian, V. (2013a). Modeling Ternary Pumped Storage Units. Argonne National LaboratoryKoritarov, V., Guzowski, L., Feltes, J., Kazachkov, Y., Lam, B., Carlos Grande-Moran, G. T., Eng, L., Trouille, B., and Donalek, P. (2013b). Review of Existing Hydroelectric Turbine-Governor Simulation Models. Argonne National LaboratoryKrause, P., Wasynczuk, O., and Sudho , S. (2002). Analysis of electric machinery and drive systems. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 2 edition.Kron, G. (1942). Tensors for circuits. Dover Publications.Kundur, P. (1994). Power systems stability and control. EPRI: power systems engineering series, NY, 3 edition.Li, H., Wang, J., and Meng, J. (2021). Nonlinear control. In Learning Control, pages 93–102. Elsevier.Luo, X., Wang, J., Dooner, M., and Clarke, J. (2015). Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied Energy, 137:511 – 536.Machowski, J., Lubosny, Z., Bialek, J. W., and Bumby, J. R. (2020). Power system dynamics: stability and control. John Wiley and Sons, 3 edition.Montoya, O. D., Garcés, A., and Espinosa-Pérez, G. (2018). A generalized passivity-based control approach for power compensation in distribution systems using electrical energy storage systems. Journal of Energy Storage, 16:259–268Morison, K. and Glavic, M. (2007). Review of on-line dynamic security assessment tools and techniques. Technical report.Narasimhamurthi, N. (1984). On the existence of energy function for power systems with transmission losses. IEEE Transactions on Circuits and Systems, 31(2):199–203.Nikravesh, S. K. Y. (2018). Nonlinear Systems Stability Analysis. CRC Press.Ortega, A. and Milano, F. (2016). Generalized model of vsc-based energy storage systems for transient stability analysis. IEEE Transactions on Power Systems, 31(5):3369–3380.Ortega, R., Espinosa-Pérez, G., and Astol , A. (2013). Passivity-based control of ac drives: theory for the user and application examples. International Journal of Control, 86(4):625–635.Ortega, R. and Garcia-Canseco, E. (2004). Interconnection and damping assignment passivity-based control: A survey. European Journal of Control, 10(5):432–450.Padiyar, K. (2012). Analysis of Subsynchronous Resonance in Power Systems. Springer Science and Business Media, NY, US, 1 edition.Patarroyo-Montenegro, J. F., Vasquez-Plaza, J. D., Andrade, F., and Fan, L. (2020). An Optimal Power Control Strategy for Grid-Following Inverters in a Synchronous Frame. Applied Sciences, 10(19):6730.Patterson, B. (2012). Dc, come home: Dc microgrids and the birth of the enernet. Power and Energy Magazine, IEEE, 10(6):60–69.Pearre, N. S. and Ribberink, H. (2019). Review of research on v2x technologies, strategies, and operations. Renewable and Sustainable Energy Reviews, 105:61 – 70.Perez, M. A., Ceballos, S., Konstantinou, G., Pou, J., and Aguilera, R. P. (2021). Modular multilevel converters: Recent achievements and challenges. IEEE Open Journal of the Industrial Electronics Society, 2:224–239.Perez Londono, S. M., Rodriguez Garcia, L. F., and Mora Florez, J. J. (2015). Obtencion de modelos de carga compuestos en sistemas de potencia para analisis dinamico: revision y aplicacion. Tecnura, 19:171–189.Perko, L. (2001). Differential Equations and Dynamical Systems. Springer Verlag, New York, 1 edition.Perko, L. (2013). Differential equations and dynamical systems, volume 7. Springer Science & Business Media.Pulgar-Painemal, H. (2019). Enforcement of current limits in d g-based wind turbine dynamic models through capability curve. IEEE Transactions on Sustainable Energy, 10(1):318–320.Rabie, D., Senjyu, T., Alkhalaf, S., Mohamed, Y. S., and Shehata, E. (2021). Study and analysis of voltage source converter control stability for HVDC system using di erent control techniques. Ain Shams Engineering Journal, 12(3):2763–2779.Sami, I., Ullah, N., Muyeen, S. M., Techato, K., Chowdhury, M. S., and Ro, J.-S. (2020). Control methods for standalone and grid connected micro-hydro power plants with synthetic inertia frequency support: A comprehensive review. IEEE Access, 8:176313–176329.Shih, M.-H. and Tan, K.-K. (2023). Covering theorems of convex sets related to xed-point theorems. In Nonlinear and convex analysis, pages 235–244. CRC Press.Slootweg, J., de Haan, S., Polinder, H., and Kling, W. (2003). General model for representing variable speed wind turbines in power system dynamics simulations. IEEE Transactions on Power Systems, 18(1):144– 151.Stagg, G. and El-Abiad, A. (1988). Computer methods in power systems analysis. McGraw-Hill.Teodorescu, R., Liserre, M., and Rodriguez, P. (2011). Grid Converters for Photovoltaic and Wind Power Systems. IEEE Power Engineering Society, NJ, Wiley-Interscience, NY, 1 edition.Van Der Schaft, A., Jeltsema, D., et al. (2014). Port-hamiltonian systems theory: An introductory overview. Foundations and Trends® in Systems and Control, 1(2-3):173–378.Vega-Herrera, J., Rahmann, C. A., Valencia, F., and Strunz, K. (2020). Analysis and application of quasi-static and dynamic phasor calculus for stability assessment of integrated power electric and electronic systems. IEEE Transactions on Power Systems.Venkataramana, A. (2007). Computational Techniques for Voltage Stability Assessment and Control. Springer, NY, 1 edition.Villegas Pico, H., McCalley, J. D., Angel, A., Leon, R., and Castrillon, N. J. (2012). Analysis of very low frequency oscillations in hydro-dominant power systems using multi-unit modeling. IEEE Transactions on Power Systems, 27(4):1906–1915.Walker, D., Bowler, C., Jackson, R., and Hodges, D. (1975). Results of subsynchronous resonance test at mohave. IEEE Transactions on Power Apparatus and Systems, 94(5):1878–1889.Willems, J. L. and Willems, J. C. (1970). The application of lyapunov methods to the computation of transient stability regions for multimachine power systems. IEEE Transactions on Power Apparatus and Systems, PAS-89(5):795–801.Wu, D., Tang, F., Vasquez, J. C., and Guerrero, J. M. (2014). Control and analysis of droop and reverse droop controllers for distributed generations. In 2014 IEEE 11th International Multi-Conference on Systems, Signals & Devices (SSD14), pages 1–5. IEEE.Zografos, D. and Ghandhari, M. (2016). Estimation of power system inertia. In 2016 IEEE Power and Energy Society General Meeting (PESGM), pages 1–5.620 - Ingeniería y operaciones afines::621 - Física aplicadaControl automáticoMaquinaria eléctricaConvertidores de corriente eléctricaOsciladores eléctricosRecursos energéticos renovablesCircuitos magnéticosSistemas de potenciaControl automáticoCircuitos magnéticosMaquinaria eléctricaConvertidores de corriente eléctricaOsciladores eléctricosRecursos energéticos renovablesIntroducción a la estabilidad de sistemas eléctricos de potenciaLibroinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_2f33Textinfo:eu-repo/semantics/bookPublicationORIGINALIntroducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdfIntroducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdfapplication/pdf6828221https://dspace7-utp.metabuscador.org/bitstreams/300b7265-4e73-4bb8-91b6-c4eadae5ca01/downloaddb97122e1e43263b1ad0e4027a7731aeMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://dspace7-utp.metabuscador.org/bitstreams/7f558228-b900-4410-98b2-0a5d7331c1c7/download2f9959eaf5b71fae44bbf9ec84150c7aMD52TEXTIntroducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdf.txtIntroducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdf.txtExtracted texttext/plain1103543https://dspace7-utp.metabuscador.org/bitstreams/75973a2f-2686-4ac7-9c0c-15564594aefd/downloaded3026c69d8f38c00c54f3479598e252MD53THUMBNAILInstriducción a la estabilidad de sistemas.PNGimage/png597573https://dspace7-utp.metabuscador.org/bitstreams/2fdc18ce-4288-4cba-8fcc-43b6d424e48a/download29e0167b10fe52a7f5c5d43d54118b33MD54Introducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdf.jpgIntroducción a la Estabilidad de Sistemas Eléctricos de Potencia.pdf.jpgGenerated Thumbnailimage/jpeg6290https://dspace7-utp.metabuscador.org/bitstreams/8f392f41-4efc-4056-a6e8-ed32e5ef0ade/downloadde9396c039d1000f6ad1ef1004252513MD5511059/14905oai:dspace7-utp.metabuscador.org:11059/149052024-09-05 17:08:04.473https://creativecommons.org/licenses/by-nc-nd/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 deopen.accesshttps://dspace7-utp.metabuscador.orgRepositorio de la Universidad Tecnológica de 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