{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/216346"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/216346","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"Dynamic Aggregation of Grid-tied Inverters","abstract":"Power-electronics inverters are being integrated in large numbers in distribution networks with rapid deployment of renewable resources, energy storage, and flexible loads. Since such distributed energy resources will serve a majority of loads in the next- generation power network, it is critical to develop scalable and accurate modeling tools to study the dynamical behavior of systems with large numbers of inverters. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. To address this issue, a reduced-order aggregated model for parallel-connected grid-tied three-phase inverters is formulated. A necessary and sufficient set of parametric relationships is derived to ensure that the reduced-order models for an arbitrary number of such paralleled inverters have the same model order and structure as any single inverter. The reduced-order model is extended for photovoltaic (PV) inverters, where a PV array, a maximum power point tracking (MPPT) algorithm, and a dc-link capacitor are incorporated into the three-phase inverter model. Furthermore, a network-cognizant aggregation approach for distribution networks comprising grid-tied inverters is developed. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, the reduced-order aggregated model is utilized to replace the inverters in the cluster. The K-means algorithm is leveraged for clustering and a suitable linearization of the power-flow equations reduces computational burden involved in determining terminal voltages for the clusters. Numerical simulation results for a benchmark feeder system demonstrate the accuracy and computational benefits of the aggregation method.","abstract_html":"Power-electronics inverters are being integrated in large numbers in distribution networks with rapid deployment of renewable resources, energy storage, and flexible loads. Since such distributed energy resources will serve a majority of loads in the next- generation power network, it is critical to develop scalable and accurate modeling tools to study the dynamical behavior of systems with large numbers of inverters. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. To address this issue, a reduced-order aggregated model for parallel-connected grid-tied three-phase inverters is formulated. A necessary and sufficient set of parametric relationships is derived to ensure that the reduced-order models for an arbitrary number of such paralleled inverters have the same model order and structure as any single inverter. The reduced-order model is extended for photovoltaic (PV) inverters, where a PV array, a maximum power point tracking (MPPT) algorithm, and a dc-link capacitor are incorporated into the three-phase inverter model. Furthermore, a network-cognizant aggregation approach for distribution networks comprising grid-tied inverters is developed. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, the reduced-order aggregated model is utilized to replace the inverters in the cluster. The K-means algorithm is leveraged for clustering and a suitable linearization of the power-flow equations reduces computational burden involved in determining terminal voltages for the clusters. Numerical simulation results for a benchmark feeder system demonstrate the accuracy and computational benefits of the aggregation method.","abstract_has_math":false,"creators":["Purba, Victor"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-07","date_published":"2020-07","updated_at":"2026-07-24T05:19:48Z","subjects":["grid-tied inverter","model reduction","power systems"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11299/216346","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Purba, Victor"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-09-22T21:02:23Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-09-22T21:02:23Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-07"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["grid-tied inverter","model reduction","power systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11299/216346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Minnesota Ph.D. dissertation. June 2020. Major: Electrical/Computer Engineering. Advisor: Sairaj Dhople. 1 computer file (PDF); viii, 96 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["Power-electronics inverters are being integrated in large numbers in distribution networks with rapid deployment of renewable resources, energy storage, and flexible loads. Since such distributed energy resources will serve a majority of loads in the next- generation power network, it is critical to develop scalable and accurate modeling tools to study the dynamical behavior of systems with large numbers of inverters. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. To address this issue, a reduced-order aggregated model for parallel-connected grid-tied three-phase inverters is formulated. A necessary and sufficient set of parametric relationships is derived to ensure that the reduced-order models for an arbitrary number of such paralleled inverters have the same model order and structure as any single inverter. The reduced-order model is extended for photovoltaic (PV) inverters, where a PV array, a maximum power point tracking (MPPT) algorithm, and a dc-link capacitor are incorporated into the three-phase inverter model. Furthermore, a network-cognizant aggregation approach for distribution networks comprising grid-tied inverters is developed. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, the reduced-order aggregated model is utilized to replace the inverters in the cluster. The K-means algorithm is leveraged for clustering and a suitable linearization of the power-flow equations reduces computational burden involved in determining terminal voltages for the clusters. Numerical simulation results for a benchmark feeder system demonstrate the accuracy and computational benefits of the aggregation method."]},{"key":"dc:title","label":"Title","values":["Dynamic Aggregation of Grid-tied Inverters"]}]}],"canonical_facts":{"dc:creator":["Purba, Victor"],"dc:date.accessioned":["2020-09-22T21:02:23Z"],"dc:date.available":["2020-09-22T21:02:23Z"],"dc:date.issued":["2020-07"],"dc:description":["University of Minnesota Ph.D. dissertation. June 2020. Major: Electrical/Computer Engineering. Advisor: Sairaj Dhople. 1 computer file (PDF); viii, 96 pages."],"dc:description.abstract":["Power-electronics inverters are being integrated in large numbers in distribution networks with rapid deployment of renewable resources, energy storage, and flexible loads. Since such distributed energy resources will serve a majority of loads in the next- generation power network, it is critical to develop scalable and accurate modeling tools to study the dynamical behavior of systems with large numbers of inverters. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. To address this issue, a reduced-order aggregated model for parallel-connected grid-tied three-phase inverters is formulated. A necessary and sufficient set of parametric relationships is derived to ensure that the reduced-order models for an arbitrary number of such paralleled inverters have the same model order and structure as any single inverter. The reduced-order model is extended for photovoltaic (PV) inverters, where a PV array, a maximum power point tracking (MPPT) algorithm, and a dc-link capacitor are incorporated into the three-phase inverter model. Furthermore, a network-cognizant aggregation approach for distribution networks comprising grid-tied inverters is developed. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, the reduced-order aggregated model is utilized to replace the inverters in the cluster. The K-means algorithm is leveraged for clustering and a suitable linearization of the power-flow equations reduces computational burden involved in determining terminal voltages for the clusters. Numerical simulation results for a benchmark feeder system demonstrate the accuracy and computational benefits of the aggregation method."],"dc:identifier.uri":["http://hdl.handle.net/11299/216346"],"dc:language.iso":["en"],"dc:subject":["grid-tied inverter","model reduction","power systems"],"dc:title":["Dynamic Aggregation of Grid-tied Inverters"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:19:48Z"}