Resilience and stability of power grids using the Kuramoto model

dc.contributor.advisorOsorio Londoño, Gustavo Adolfospa
dc.contributor.advisorAngulo García, Davidspa
dc.contributor.authorGalindo González, Cristian Camilospa
dc.contributor.researchgroupPercepción y Control Inteligente (PCI)spa
dc.date.accessioned2020-11-05T16:02:23Zspa
dc.date.available2020-11-05T16:02:23Zspa
dc.date.issued2020spa
dc.description.abstractIn this document, a methodology is developed to test the non-linear stability of the synchronous state in a power grid as well as its resilience to structural failures by applying a percolation-inspired algorithm based in link and node removal simulations. Vulnerability measures are de ned in terms of either dynamical or topological features of the power grid and both methods are compared. A basic analysis of the Colombian power grid is also included and used to test the proposed algorithm.eng
dc.description.abstractEn este documento, se desarrolla una metodología para estudiar la estabilidad no lineal del estado sincronizado en una red de potencia, así como la resiliencia de la misma ante fallas estructurales aplicando un algoritmo inspirado en la percolación en simulaciones de remoción de conexiones y nodos. Se definen medidas de vulnerabilidad en términos de las características topológicas y dinámicas del sistema de potencia y se comparan ambos métodos. Se presenta además un análisis básico del sistema de transmisión de Colombia y se usa como caso particular de estudio para desarrollar las pruebas del algoritmo propuesto.spa
dc.description.additionalThesis submitted as a partial requirement to receive the grade of: Master in Engineering - Industrial Automation.spa
dc.description.degreelevelMaestríaspa
dc.description.project"Análisis de la eficiencia de convertidores electrónicos de potencia en aplicaciones de generación de energía eléctrica, a partir de fuentes no convencionales" (FP44842 - 052 - 2016) y Convocatoria 775: Jóvenes Investigadores e Innovadores por la paz - 2017. Diseño y construcción de un sistema de generación de energía solar fotovoltaica, autónomo y de alta e ciencia con aplicaciones en la zona rural" (FP44842 - 505 - 2017).spa
dc.description.sponsorshipUniversidad Nacional de Colombia - Manizales, Dirección de Investigación y Extensión (DIMA) y Ministerio de Ciencia, Tecnología e Innovación (Minciencias)spa
dc.format.extent95spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.citationC. C. Galindo-González, "Resilience and stability of power grids using the Kuramoto model", Master's Thesis, Universidad Nacional de Colombia, 2020spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/78588
dc.language.isoengspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Manizalesspa
dc.publisher.departmentDepartamento de Ingeniería Eléctrica y Electrónicaspa
dc.publisher.programManizales - Ingeniería y Arquitectura - Maestría en Ingeniería - Automatización Industrialspa
dc.relation.referencesHypernet Labs, \Galileo." https://hypernetlabs.io/galileo/, 2020.spa
dc.relation.referencesT. Coletta, R. Delabays, I. Adagideli, and P. Jacquod, \Topologically protected loopspa
dc.relation.referencesows in high voltage AC power grids This,"spa
dc.relation.referencesP. Schultz, J. Heitzig, and J. Kurths, \A random growth model for power grids and other spatially embedded infrastructure networks," European Physical Journal: Special Topics, vol. 223, no. 12, pp. 2593{2610, 2014.spa
dc.relation.referencesJ. Nitzbon, P. Schultz, J. Heitzig, J. Kurths, and F. Hellmann, \Deciphering the imprint of topology on nonlinear dynamical network stability," New Journal of Physics, vol. 19, no. 3, 2017.spa
dc.relation.referencesT. Nishikawa and A. E. Motter, \Comparative analysis of existing models for power-grid synchronization," New Journal of Physics, vol. 17, 2015.spa
dc.relation.referencesA. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization, A Universal Concept in Nonlinear Sciences. Cambridge: Cambridge University Press, 2001spa
dc.relation.referencesA. Arenas, A. D az-Guilera, J. Kurths, Y. Moreno, and C. Zhou, \Synchronization in complex networks," Physics Reports, vol. 469, no. 3, pp. 93 { 153, 2008.spa
dc.relation.referencesG. V. Osipov, J. Kurths, and C. Zhou, Synchronization in oscillatory networks. Berlin, Germany: Springer, 2007.spa
dc.relation.referencesF. Dorfler, M. Chertkov, and F. Bullo, \Synchronization in complex oscillator networks and smart grids," Proceedings of the National Academy of Sciences, vol. 110, no. 6, pp. 2005{2010, 2013.spa
dc.relation.referencesA. E. Motter, S. A. Myers, M. Anghel, and T. Nishikawa, \Spontaneous synchrony in power-grid networks," Nature Physics, vol. 9, no. 3, pp. 191{197, 2013.spa
dc.relation.referencesH. Sakaguchi and T. Matsuo, \Cascade Failure in a Phase Model of Power Grids," vol. 81, pp. 1{7, 2012.spa
dc.relation.referencesS. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, \Catastrophic cascade of failures in interdependent networks," Nature, vol. 464, no. 7291, pp. 1025{ 1028, 2010.spa
dc.relation.referencesD. Teather, \Blackout cost New York $36m an hour," The Guardian, 2003.spa
dc.relation.referencesP. Brockway, A. Owen, L. I. Brand Correa, and L. Hardtspa
dc.relation.referencesK. Xi, J. L. A. Dubbeldam, H. X. Lin, and J. H. V. Schuppen, \Power-Imbalance Allocation Control of Power Systems-Secondary Frequency Control," Automatica, vol. 92, pp. 70{72, 2018.spa
dc.relation.referencesS. Tamrakar, M. Conrath, and S. Kettemann, \Propagation of disturbances in AC electricity grids," Scienti c Reports, vol. 8, no. 1, pp. 1{11, 2018.spa
dc.relation.references\La revoluci on renovable que hay en Colombia," Semana, 2019.spa
dc.relation.referencesD. J. Hill and Guanrong Chen, \Power systems as dynamic networks," in 2006 IEEE International Symposium on Circuits and Systems, pp. 4 pp.{725, 2006.spa
dc.relation.referencesC. D. Brummitt, P. D. H. Hines, I. Dobson, C. Moore, and R. M. D'Souza, \Transdisciplinary electric power grid science," Proceedings of the National Academy of Sciences, vol. 110, no. 30, pp. 12159{12159, 2013.spa
dc.relation.referencesG. Filatrella, A. H. Nielsen, and N. F. Pedersen, \Analysis of a power grid using a Kuramoto-like model," European Physical Journal B, vol. 61, no. 4, pp. 485{491, 2008.spa
dc.relation.referencesY. Kuramoto, \Self-entrainment of a population of coupled non-linear oscillators," in International Symposium on Mathematical Problems in Theoretical Physics (H. Araki, ed.), (Berlin, Heidelberg), pp. 420{422, Springer Berlin Heidelberg, 1975.spa
dc.relation.referencesJ. A. Acebr on, L. L. Bonilla, C. J. P erez Vicente, F. Ritort, and R. Spigler, \The kuramoto model: A simple paradigm for synchronization phenomena," Rev. Mod. Phys., vol. 77, pp. 137{185, Apr 2005.spa
dc.relation.referencesF. Dor er and F. Bullo, \On the Critical Coupling for Kuramoto Oscillators," pp. 1{27, 2010.spa
dc.relation.referencesM. Rohden, A. Sorge, D. Witthaut, and M. Timme, \Impact of network topology on synchrony of oscillatory power grids," vol. 013123, pp. 0{8, 2013.spa
dc.relation.referencesM. Rohden, A. Sorge, M. Timme, and D. Witthaut, \Self-organized synchronization in decentralized power grids," Physical Review Letters, vol. 109, no. 6, pp. 1{5, 2012.spa
dc.relation.referencesS. Olmi, A. Navas, S. Boccaletti, and A. Torcini, \Hysteretic transitions in the Kuramoto model with inertia," Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 90, no. 4, pp. 1{16, 2014.spa
dc.relation.referencesF. A. Rodrigues, T. K. Peron, P. Ji, and J. Kurths, \The Kuramoto model in complex networks," Physics Reports, vol. 610, pp. 1{98, 2016.spa
dc.relation.referencesH. . Chiang, F. F.Wu, and P. P. Varaiya, \Foundations of the potential energy boundary surface method for power system transient stability analysis," IEEE Transactions on Circuits and Systems, vol. 35, no. 6, pp. 712{728, 1988.spa
dc.relation.referencesH. Kwatny, L. Bahar, and A. Pasrija, \Energy-like lyapunov functions for power system stability analysis," IEEE Transactions on Circuits and Systems, vol. 32, no. 11, pp. 1140{1149, 1985.spa
dc.relation.referencesK. Xi, J. L. Dubbeldam, and H. X. Lin, \Synchronization of cyclic power grids: Equilibria and stability of the synchronous state," Chaos, vol. 27, no. 1, 2017.spa
dc.relation.referencesP. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, \How basin stability complements the linear-stability paradigm," Nature Physics, vol. 9, no. 2, pp. 89{92, 2013.spa
dc.relation.referencesP. J. Menck, J. Heitzig, J. Kurths, and H. J. Schellnhuber, \How dead ends undermine power grid stability," Nature Communications, vol. 5, pp. 1{8, 2014.spa
dc.relation.referencesC. Mitra, A. Choudhary, S. Sinha, J. Kurths, and R. V. Donner, \Multiple-node basin stability in complex dynamical networks," Physical Review E, vol. 95, no. 3, pp. 1{9, 2017.spa
dc.relation.referencesC. Mitra, T. Kittel, A. Choudhary, J. Kurths, and R. V. Donner, \Recovery time after localized perturbations in complex dynamical networks Recovery time after localized perturbations in complex dynamical networks," 2017.spa
dc.relation.referencesM. F. Wol , P. G. Lind, and P. Maass, \Power grid stability under perturbation of single nodes: E ects of heterogeneity and internal nodes," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 28, no. 10, p. 103120, 2018.spa
dc.relation.referencesP. Schultz, J. Heitzig, and J. Kurths, \Detours around basin stability in power networks," New Journal of Physics, vol. 16, 2014.spa
dc.relation.referencesA. Plietzsch, P. Schultz, J. Heitzig, and J. Kurths, \Local vs. global redundancy { tradeo s between resilience against cascading failures and frequency stability," European Physical Journal: Special Topics, vol. 225, no. 3, pp. 551{568, 2016.spa
dc.relation.referencesA. N. Montanari, E. I. Moreira, and L. A. Aguirre, \E ects of network heterogeneity and tripping time on the basin stability of power systems," Communications in Nonlinear Science and Numerical Simulation, vol. 89, p. 105296, 2020.spa
dc.relation.referencesM. Tyloo, L. Pagnier, and P. Jacquod, \The key player problem in complex oscillator networks and electric power grids: Resistance centralities identify local vulnerabilities," Science Advances, vol. 5, no. 11, 2019.spa
dc.relation.referencesM. Tyloo and P. Jacquod, \Global robustness versus local vulnerabilities in complex synchronous networks," Phys. Rev. E, vol. 100, p. 032303, Sep 2019.spa
dc.relation.referencesF. Hellmann, P. Schultz, P. Jaros, R. Levchenko, T. Kapitaniak, J. Kurths, and Y. Maistrenko, \Network-induced multistability through lossy coupling and exotic solitary states," Nature Communications, vol. 11, p. 592, Jan 2020.spa
dc.relation.referencesM. Tyloo, R. Delabays, and P. Jacquod, \Noise-induced desynchronization and stochastic escape from equilibrium in complex networks," Phys. Rev. E, vol. 99, p. 062213, Jun 2019.spa
dc.relation.referencesI. Simonsen, L. Buzna, K. Peters, S. Bornholdt, and D. Helbing, \Transient dynamics increasing network vulnerability to cascading failures," Physical Review Letters, vol. 100, no. 21, pp. 1{4, 2008.spa
dc.relation.referencesM. Rohden, D. Jung, S. Tamrakar, and S. Kettemann, \Cascading failures in ac electricity grids," Physical Review E, vol. 94, no. 3, pp. 1{8, 2016.spa
dc.relation.referencesB. Sch afer, D. Witthaut, M. Timme, and V. Latora, \Dynamically induced cascading failures in power grids," Nature Communications, vol. 9, no. 1, 2018.spa
dc.relation.referencesM. Fazlyab, F. D or er, and V. M. Preciado, \Optimal network design for synchronization of coupled oscillators," Automatica, vol. 84, pp. 181 { 189, 2017.spa
dc.relation.referencesH. Taher, S. Olmi, and E. Sch oll, \Enhancing power grid synchronization and stability through time-delayed feedback control," Phys. Rev. E, vol. 100, p. 062306, Dec 2019.spa
dc.relation.referencesS. Dietrich and A. Amnon, \Introduction to percolation theory," 1994.spa
dc.relation.referencesW. Chen, Z. Zheng, and R. M. D'Souza, \Deriving an underlying mechanism for discontinuous percolation," Epl, vol. 100, no. 6, pp. 1{6, 2012.spa
dc.relation.referencesR. M. D'Souza and M. Mitzenmacher, \Local cluster aggregation models of explosive percolation," Physical Review Letters, vol. 104, no. 19, pp. 10{13, 2010.spa
dc.relation.referencesZ. Kong and E. M. Yeh, \Correlated and cascading node failures in random geometric networks: A percolation view," ICUFN 2012 - 4th International Conference on Ubiquitous and Future Networks, Final Program, vol. 56, no. 11, pp. 520{525, 2012.spa
dc.relation.referencesH. Xiao and E. M. Yeh, \Cascading link failure in the power grid: A percolation-based analysis," IEEE International Conference on Communications, 2011.spa
dc.relation.referencesL. A. Machuca Moreno, \An alisis de estabilidad transitoria basado en teor a de redes complejas y el fen omeno de percolaci on," 2017.spa
dc.relation.referencesM. Mureddu, G. Caldarelli, A. Damiano, A. Scala, and H. Meyer-Ortmanns, \Islanding the power grid on the transmission level: less connections for more security," Scienti c Reports, vol. 6, p. 34797, Oct 2016.spa
dc.relation.referencesJ. Gao, X. Liu, D. Li, and S. Havlin, \Recent progress on the resilience of complex networks," Energies, vol. 8, no. 10, pp. 12187{12210, 2015.spa
dc.relation.referencesD. H. Kim, D. A. Eisenberg, Y. H. Chun, and J. Park, \Network topology and resilience analysis of south korean power grid," Physica A: Statistical Mechanics and its Applications, vol. 465, pp. 13 { 24, 2017.spa
dc.relation.referencesC. Fu, Y. Gao, S. Cai, H. Yang, and C. Yang, \Center of mass in complex networks," Scienti c Reports, vol. 7, no. December 2016, pp. 1{7, 2017.spa
dc.relation.referencesR. V. Sol e, M. Rosas-Casals, B. Corominas-Murtra, and S. Valverde, \Robustness of the european power grids under intentional attack," Phys. Rev. E, vol. 77, p. 026102, Feb 2008.spa
dc.relation.referencesD. Li, Q. Zhang, E. Zio, S. Havlin, and R. Kang, \Network reliability analysis based on percolation theory," Reliability Engineering and System Safety, vol. 142, pp. 556{562, 2015.spa
dc.relation.referencesL. Chen, P. Ji, D. Waxman, W. Lin, and J. Kurths, \E ects of dynamical and structural modi cations on synchronization," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 8, p. 083131, 2019.spa
dc.relation.referencesZ. Huang, C.Wang, S. Ruj, M. Stojmenovic, and A. Nayak, \Modeling cascading failures in smart power grid using interdependent complex networks and percolation theory," Proceedings of the 2013 IEEE 8th Conference on Industrial Electronics and Applications, ICIEA 2013, pp. 1023{1028, 2013.spa
dc.relation.referencesY. Yang and A. E. Motter, \Cascading failures as continuous phase-space transitions," Phys. Rev. Lett., vol. 119, p. 248302, Dec 2017.spa
dc.relation.referencesC. Caro-Ruiz, J. Ma, D. Hill, A. Pavas, and E. Mojica-Nava, \A minimum cut-set vulnerability analysis of power networks," Sustainable Energy, Grids and Networks, vol. 21, p. 100302, 2020.spa
dc.relation.referencesJ. Saram aki, M. Kivel a, J. P. Onnela, K. Kaski, and J. Kert esz, \Generalizations of the clustering coe cient to weighted complex networks," Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 75, no. 2, pp. 1{4, 2007.spa
dc.relation.referencesU. Brandes, \A faster algorithm for betweenness centrality," The Journal of Mathematical Sociology, vol. 25, no. 2, pp. 163{177, 2001.spa
dc.relation.referencesP. M. Anderson and A. A. Fouad, Power system control and stability. 2002.spa
dc.relation.referencesK. Schmietendorf, J. Peinke, R. Friedrich, and O. Kamps, \Self-organized synchronization and voltage stability in networks of synchronous machines," European Physical Journal: Special Topics, vol. 223, no. 12, pp. 2577{2592, 2014.spa
dc.relation.referencesY. Kuramoto, Chemical oscillations, waves, and turbulence. 2003.spa
dc.relation.referencesS. H. Strogatz, \From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Physica D: Nonlinear Phenomena, vol. 143, no. 1-4, pp. 1{20, 2000.spa
dc.relation.referencesS. Strogatz, SYNC: The emerging science of spontaneous order. 2003.spa
dc.relation.referencesP. Ji, T. K. D. M. Peron, F. A. Rodrigues, and J. Kurths, \Low-dimensional behavior of Kuramoto model with inertia in complex networks," Scienti c Reports, vol. 4, pp. 1{6, 2014.spa
dc.relation.referencesB. Sonnenschein, T. K. Peron, F. A. Rodrigues, J. Kurths, and L. Schimansky-Geier, \Collective dynamics in two populations of noisy oscillators with asymmetric interactions," Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 91, no. 6, pp. 1{7, 2015.spa
dc.relation.referencesM. Rohden, D. Witthaut, M. Timme, and H. Meyer-Ortmanns, \Curing critical links in oscillator networks as power grid models," Submitted, no. December, pp. 0{10, 2015.spa
dc.relation.referencesH. Kim, S. H. Lee, and P. Holme, \Building blocks of the basin stability of power grids," Physical Review E, vol. 93, no. 6, pp. 1{8, 2016.spa
dc.relation.referencesL. Cao, C. Tian, Z. Wang, X. Zhang, and Z. Liu, \In uence of stochastic perturbations on the cluster explosive synchronization of second-order Kuramoto oscillators on networks," Physical Review E, vol. 022220, pp. 1{7, 2018spa
dc.relation.referencesJ. M. Grzybowski, E. E. Macau, and T. Yoneyama, \On synchronization in power-grids modelled as networks of second-order Kuramoto oscillators," Chaos, vol. 26, 2016.spa
dc.relation.referencesA. B. Birch eld, E. Schweitzer, M. H. Athari, T. Xu, T. J. Overbye, A. Scaglione, and Z. Wang, \A metric-based validation process to assess the realism of synthetic power grids," Energies, vol. 10, no. 8, 2017.spa
dc.relation.referencesA. S. Eran Schweitzer and R. Thomas, \The validation of synthetic power system cases," IREP'2017 Symposium, 2017.spa
dc.relation.referencesZ. Liu, Y. Zhang, Y. Wang, N. Wei, and C. Gu, \Development of the interconnected power grid in europe and suggestions for the energy internet in china," Global Energy Interconnection, vol. 3, no. 2, pp. 111 { 119, 2020.spa
dc.relation.referencesS. H. Yook and H. Meyer-Ortmanns, \Synchronization of R ossler oscillators on scalefree topologies," Physica A: Statistical Mechanics and its Applications, vol. 371, no. 2, pp. 781{789, 2006.spa
dc.relation.referencesT. Nishikawa, A. E. Motter, Y. C. Lai, and F. C. Hoppensteadt, \Heterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize?," Physical Review Letters, vol. 91, no. 1, pp. 2{5, 2003.spa
dc.relation.referencesA. G. H. (auth.), Percolation Theory For Flow In Porous Media. Lecture Notes in Physics 674, Springer Berlin Heidelberg, 1 ed., 2005.spa
dc.relation.referencesR. Carareto, M. S. Baptista, and C. Grebogi, \Natural synchronization in power-grids with anti-correlated units," Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 4, pp. 1035{1046, 2013.spa
dc.relation.referencesD. Witthaut and M. Timme, \Braess's paradox in oscillator networks, desynchronization and power outage," New Journal of Physics, vol. 14, pp. 1{17, 2012.spa
dc.relation.referencesE. B. T. Tchuisseu, D. Gomila, P. Colet, D. Witthaut, M. Timme, and B. Sch afer, \Curing braess' paradox by secondary control in power grids," New Journal of Physics, vol. 20, no. 8, pp. 1{11, 2018.spa
dc.relation.referencesJ. P. Pade and T. Pereira, \Improving Network Structure can lead to Functional Failures," Nature Publishing Group, pp. 1{6, 2015.spa
dc.relation.referencesR. S. Pinto and A. Saa, \Synchrony-optimized networks of Kuramoto oscillators with inertia," Physica A: Statistical Mechanics and its Applications, vol. 463, pp. 77{87, 2016.spa
dc.relation.referencesM. Fazlyab, F. D or er, and V. M. Preciado, \Optimal network design for synchronization of coupled oscillators," Automatica, vol. 84, pp. 181{189, 2017.spa
dc.relation.referencesH. Kim, S. H. Lee, J. Davidsen, and S.-w. Son, \Multistability and variations in basin of attraction in power-grid systems," 2018.spa
dc.relation.referencesWei Wu and Chikong Wong, \Facts applications in preventing loop ows in interconnected systems," in 2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491), vol. 1, pp. 170{174 Vol. 1, 2003.spa
dc.relation.referencesP. Schultz, P. J. Menck, J. Heitzig, and J. Kurths, \Potentials and limits to basin stability estimation," New Journal of Physics, vol. 19, p. 023005, feb 2017.spa
dc.relation.referencesM. Khedkar, G. Dhole, and V. Neve, \Transient stability analysis by transient energy function method: Closest and controlling unstable equilibrium point approach," Journal of the Institution of Engineers (India): Electrical Engineering Division, vol. 85, pp. 83{ 88, 09 2004spa
dc.relation.referencesH.-D. Chang, C.-C. Chu, and G. Cauley, \Direct stability analysis of electric power systems using energy functions: Theory, applications, and perspective," Proceedings of the IEEE, vol. 83, pp. 1497 { 1529, 12 1995.spa
dc.relation.referencesF. Hellmann, P. Schultz, C. Grabow, J. Heitzig, and J. Kurths, \Survivability of Deterministic Dynamical Systems," Scienti c Reports, vol. 6, no. March, pp. 1{12, 2016.spa
dc.relation.referencesUPME, STN - Sistema de Transmisi on Nacional de Energ a El ectrica, Colombia, http://sig.simec.gov.co/GeoPortal/Mapas/Mapas, 2016.spa
dc.rightsDerechos reservados - Universidad Nacional de Colombiaspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial 4.0 Internacionalspa
dc.rights.spaAcceso abiertospa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/spa
dc.subject.ddc000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computaciónspa
dc.subject.ddc620 - Ingeniería y operaciones afines::621 - Física aplicadaspa
dc.subject.proposalModelo de Kuramotospa
dc.subject.proposalKuramoto modeleng
dc.subject.proposalpower grideng
dc.subject.proposalred de potenciaspa
dc.subject.proposalsynchronizationeng
dc.subject.proposalsincronizaciónspa
dc.subject.proposaldinámica no linealspa
dc.subject.proposalnon-linear dynamicseng
dc.subject.proposalbasin stabilityeng
dc.subject.proposalestabilidad del dominio de atracciónspa
dc.subject.proposalredes complejasspa
dc.subject.proposalcomplex networkeng
dc.titleResilience and stability of power grids using the Kuramoto modelspa
dc.title.alternativeResilience and stability of power grids using the Kuramoto modelspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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