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Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems

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dc.contributor.authorHarb, Ahmad M.en
dc.contributor.committeechairNayfeh, Ali H.en
dc.contributor.committeecochairMili, Lamine M.en
dc.contributor.committeememberVanLandingham, Hugh F.en
dc.contributor.committeememberPhadke, Arun G.en
dc.contributor.committeememberMook, Dean T.en
dc.contributor.departmentElectrical and Computer Engineeringen
dc.date.accessioned2014-03-14T20:21:51Zen
dc.date.adate1996-12-16en
dc.date.available2014-03-14T20:21:51Zen
dc.date.issued1996-12-16en
dc.date.rdate1996-12-16en
dc.date.sdate1998-07-13en
dc.description.abstractA bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical compensation values, while in the CHOLLA#4 system, we show that there is only one Hopf bifurcation. The results show that as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability via a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. When a damper winding is placed either along the q-axis, or d-axis, or both axes of the BOARDMAN system and the machine saturation is considered in the CHOLLA#4 system, the study shows that, there is only one Hopf bifurcation and it occurs at a much lower level of compensation, indicating that the damper windings and the machine saturation destabilize the system by inducing subsynchronous resonance. Finally, we investigate the effect of linear and nonlinear controllers on mitigating subsynchronous resonance in the CHOLLA#4 system . The study shows that the linear controller increases the compensation level at which subsynchronous resonance occurs and the nonlinear controller does not affect the location and type of the Hopf bifurcation, but it reduces the amplitude of the limit cycle born as a result of the Hopf bifurcation.en
dc.description.degreePh. D.en
dc.format.extentxii, 107 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-35541228119663620en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-35541228119663620/en
dc.identifier.urihttp://hdl.handle.net/10919/30487en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartharb.pdfen
dc.relation.haspartetd.pdfen
dc.relation.isformatofOCLC# 38741016en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectsubsynchronous resonanceen
dc.subjectbifurcation theoryen
dc.subjectpower systemsen
dc.subjectmethods of multiple scalesen
dc.subject.lccLD5655.V856 1996.H373en
dc.titleApplication of Bifurcation Theory to Subsynchronous Resonance in Power Systemsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineElectrical and Computer Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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