{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/66236"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/66236","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Time Scales, Coherency, and Weak Coupling","abstract":"In this thesis we study a relation between time scales and structural properties of a class of systems represented by power systems. First, the time scale decomposition of linear time invariant systems is studied. The properties of the time scale decomposition are shown to be defined by properties of solutions of a generalized matrix Riccati equation. Use of the Riccati equation formulation and a particular method for finding its solution led to the result which shows that the singular perturbation method and modal method for reduced order modeling are two extreme points of an iterative method for the time scale decomposition: singular perturbation is its first point and modal method is the limiting point. Convergence properties of a known class of iterative methods for the time scale decomposition are characterized. A method for the time scale decomposition of weakly nonlinear systems is proposed as an extension of linear system analysis to nonlinear systems. Then, for electromechanical model of power systems a connection between its time scales and structural properties is established by showing that the so-called slow coherency can be expressed in terms of the same Riccati equation used for the time scale decomposition. It is shown analytically and then conformed experimentally on a few realistic size systems, that in the case of slow coherency, the coherent areas are weakly coupled, and hence relatively independent on the fault location. By using the Riccati formulation of coherency, an efficient numerical algorithm for identifying coherent areas is obtained. Finally, a possibility of extending this study to the direct transient stability analysis of power systems is briefly discussed.","abstract_html":"In this thesis we study a relation between time scales and structural properties of a class of systems represented by power systems. First, the time scale decomposition of linear time invariant systems is studied. The properties of the time scale decomposition are shown to be defined by properties of solutions of a generalized matrix Riccati equation. Use of the Riccati equation formulation and a particular method for finding its solution led to the result which shows that the singular perturbation method and modal method for reduced order modeling are two extreme points of an iterative method for the time scale decomposition: singular perturbation is its first point and modal method is the limiting point. Convergence properties of a known class of iterative methods for the time scale decomposition are characterized. A method for the time scale decomposition of weakly nonlinear systems is proposed as an extension of linear system analysis to nonlinear systems. Then, for electromechanical model of power systems a connection between its time scales and structural properties is established by showing that the so-called slow coherency can be expressed in terms of the same Riccati equation used for the time scale decomposition. It is shown analytically and then conformed experimentally on a few realistic size systems, that in the case of slow coherency, the coherent areas are weakly coupled, and hence relatively independent on the fault location. By using the Riccati formulation of coherency, an efficient numerical algorithm for identifying coherent areas is obtained. Finally, a possibility of extending this study to the direct transient stability analysis of power systems is briefly discussed.","abstract_has_math":false,"creators":["Avramovic, Bozidar"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-12T20:55:16Z","date_published":"2014-12-12T20:55:16Z","updated_at":"2026-07-22T22:25:55Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8108445"],"render_values":[{"text":"(UMI)AAI8108445","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/66236","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Avramovic, Bozidar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-12T20:55:16Z","10000-01-01","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/66236","(UMI)AAI8108445"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we study a relation between time scales and structural properties of a class of systems represented by power systems. First, the time scale decomposition of linear time invariant systems is studied. The properties of the time scale decomposition are shown to be defined by properties of solutions of a generalized matrix Riccati equation. Use of the Riccati equation formulation and a particular method for finding its solution led to the result which shows that the singular perturbation method and modal method for reduced order modeling are two extreme points of an iterative method for the time scale decomposition: singular perturbation is its first point and modal method is the limiting point. Convergence properties of a known class of iterative methods for the time scale decomposition are characterized. A method for the time scale decomposition of weakly nonlinear systems is proposed as an extension of linear system analysis to nonlinear systems. Then, for electromechanical model of power systems a connection between its time scales and structural properties is established by showing that the so-called slow coherency can be expressed in terms of the same Riccati equation used for the time scale decomposition. It is shown analytically and then conformed experimentally on a few realistic size systems, that in the case of slow coherency, the coherent areas are weakly coupled, and hence relatively independent on the fault location. By using the Riccati formulation of coherency, an efficient numerical algorithm for identifying coherent areas is obtained. Finally, a possibility of extending this study to the direct transient stability analysis of power systems is briefly discussed.","Made available in DSpace on 2014-12-12T20:55:16Z (GMT). No. of bitstreams: 1 8108445.pdf: 4688089 bytes, checksum: e5ee334ecf6467b265214f93eb441dee (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 66415 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","148 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Time Scales, Coherency, and Weak Coupling"]}]}],"canonical_facts":{"dc:creator":["Avramovic, Bozidar"],"dc:date":["2014-12-12T20:55:16Z","10000-01-01","1980"],"dc:description":["In this thesis we study a relation between time scales and structural properties of a class of systems represented by power systems. First, the time scale decomposition of linear time invariant systems is studied. The properties of the time scale decomposition are shown to be defined by properties of solutions of a generalized matrix Riccati equation. Use of the Riccati equation formulation and a particular method for finding its solution led to the result which shows that the singular perturbation method and modal method for reduced order modeling are two extreme points of an iterative method for the time scale decomposition: singular perturbation is its first point and modal method is the limiting point. Convergence properties of a known class of iterative methods for the time scale decomposition are characterized. A method for the time scale decomposition of weakly nonlinear systems is proposed as an extension of linear system analysis to nonlinear systems. Then, for electromechanical model of power systems a connection between its time scales and structural properties is established by showing that the so-called slow coherency can be expressed in terms of the same Riccati equation used for the time scale decomposition. It is shown analytically and then conformed experimentally on a few realistic size systems, that in the case of slow coherency, the coherent areas are weakly coupled, and hence relatively independent on the fault location. By using the Riccati formulation of coherency, an efficient numerical algorithm for identifying coherent areas is obtained. Finally, a possibility of extending this study to the direct transient stability analysis of power systems is briefly discussed.","Made available in DSpace on 2014-12-12T20:55:16Z (GMT). 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