{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21599"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21599","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Waveform relaxation methods for the simulation of systems of differential algebraic equations with applications to electric power systems","abstract":"This thesis reports the continuing effort towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large power system dynamics. Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the waveform relaxation algorithm. One of the main contributions in this area includes a method for determining a fault-dependent partitioning of the power system for parallel implementation. Simulation results for small, medium, and large test systems are included.","abstract_html":"This thesis reports the continuing effort towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large power system dynamics. Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the waveform relaxation algorithm. One of the main contributions in this area includes a method for determining a fault-dependent partitioning of the power system for parallel implementation. Simulation results for small, medium, and large test systems are included.","abstract_has_math":false,"creators":["Crow, Mariesa Louise"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Pai, M.A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:13:28Z","date_published":"2011-05-07T13:13:28Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1990 Crow, Mariesa Louise"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9021667","(UMI)AAI9021667"],"render_values":[{"text":"AAI9021667","href":null,"code":true},{"text":"(UMI)AAI9021667","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21599","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pai, M.A."]},{"key":"dc:creator","label":"Author","values":["Crow, Mariesa Louise"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:13:28Z","10000-01-01","1990"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1990 Crow, Mariesa Louise"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9021667","(UMI)AAI9021667","http://hdl.handle.net/2142/21599"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis reports the continuing effort towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large power system dynamics. Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. 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Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the waveform relaxation algorithm. One of the main contributions in this area includes a method for determining a fault-dependent partitioning of the power system for parallel implementation. Simulation results for small, medium, and large test systems are included.","Made available in DSpace on 2011-05-07T13:13:28Z (GMT). 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