Mathematical Modeling and Dynamic Recovery of Power Systems

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dc.contributor.authorGarcia Hilares, Nilton Alanen
dc.contributor.committeechairEmbree, Mark P.en
dc.contributor.committeememberKekatos, Vasileiosen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.departmentMathematicsen
dc.date.accessioned2023-05-20T08:00:48Zen
dc.date.available2023-05-20T08:00:48Zen
dc.date.issued2023-05-19en
dc.description.abstractPower networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study the swing equation for networks and its linearization (LSEN) as a tool for modeling power systems. Nowadays, phasor measurement units (PMUs) are used across power networks to measure the magnitude and phase angle of electric signals. Given the abundant data that PMUs can produce, we study applications of the dynamic mode decomposition (DMD) and Loewner framework to power systems. The matrices that define the LSEN model have a particular structure that is not recovered by DMD. We thus propose a novel variant of DMD, called structure-preserving DMD (SPDMD), that imposes the LSEN structure upon the recovered system. Since the solution of the LSEN can potentially exhibit interesting transient dynamics, we study the transient growth for the exponential matrix related to the LSEN. We follow Godunov's approach to get upper bounds for the transient growth and also analyze the relationship of such bounds with classical bounds based on the spectrum, numerical range, and pseudospectra. We show how Godunov's bounds can be optimized to bound the solution operator at a given time. The Loewner framework provides a tool for identifying a dynamical system from tangential measurements. The singular values of Loewner matrices guide the discovery of the true order of the underlying system. However, these singular values can exhibit rapid decay when the interpolation points are far from the poles of the system. We establish a range of bounds for this decay of singular values and apply this analysis to power systems.en
dc.description.abstractgeneralPower networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study a mathematical model called the LSEN to understand and recover the dynamics of power networks. The LSEN model defines some matrices that have special structures dictated by the application. We propose a novel method to recover matrices with this desired structure from data. We also study some properties of the solution of the LSEN model related to the exponential of a matrix, connecting classical results with the particular approach that we follow. In the system identification context, we also study bounds on the singular values of Loewner matrices to understand the interplay between the data (measurements of the system) and mathematical artifacts (poles of the system).en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:37531en
dc.identifier.urihttp://hdl.handle.net/10919/115130en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution-ShareAlike 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-sa/4.0/en
dc.subjectpower systems modelingen
dc.subjecttransient growthen
dc.subjectLyapunov upper boundsen
dc.subjectZolotarev numberen
dc.subjectSylvester upper boundsen
dc.subjectdynamical mode decomposition.en
dc.titleMathematical Modeling and Dynamic Recovery of Power Systemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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