{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/132541"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/132541","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Phase control of delta-connected single-phase grid-forming inverters for auxiliary signal injection","abstract":"This thesis presents a strategy for controlling the phase differences of a three-phase voltage source made up of single-phase droop-controlled grid forming inverters arranged in a delta configuration. We begin by deriving the simplified $dq$ model of a three-phase ($3\\phi$) grid-forming inverter and discuss proper selection of inner-current loop and outer-voltage loop gains for stability. We then analyze dynamic behavior of $3\\phi$ inverters with different types of primary control (namely droop, virtual synchronous machine, and virtual oscillator control). Using this analysis, we motivate control and modeling methods for single-phase ($1\\phi$) inverters and highlight the similarities and differences. From here we develop a high-fidelity model describing a system of three single-phase delta-connected grid-forming inverters. With this model, we simulate and analyze the phase balancing dynamics of systems with single-phase grid-forming inverters with different types of primary control. We derive a linearized model of the inverter phase dynamics for a system with three droop-controlled grid-forming inverters, and use it to formulate a Linear Quadratic Integral (LQI) controller capable of phase angle reference tracking. The proposed controller enables the system to be operated as a three-phase balanced source. A similar, but much more simple, methodology is used to develop a Proportional-Integral (PI) controller which is used to benchmark the behavior of the LQI controller. Unbalanced operation is also desirable when supplying an unbalanced load or injecting auxiliary signals for fault detection. Both MATLAB and Controller Hardware in-the-loop (C-HIL) are used to validate the proposed controllers and demonstrate performance under both nominal and unbalanced conditions. The LQI and PI controllers ensure minimal overshoot, zero steady-state error, and robust reference tracking in both the linearized and nonlinear model used to derive them. The results exemplify the flexibility of controller tuning for precise shaping of system response, which is essential for adapting inverter-based resources (IBRs) to grid protection requirements. The controller types are compared rigorously.","abstract_html":"This thesis presents a strategy for controlling the phase differences of a three-phase voltage source made up of single-phase droop-controlled grid forming inverters arranged in a delta configuration. We begin by deriving the simplified $dq$ model of a three-phase ($3\\phi$) grid-forming inverter and discuss proper selection of inner-current loop and outer-voltage loop gains for stability. We then analyze dynamic behavior of $3\\phi$ inverters with different types of primary control (namely droop, virtual synchronous machine, and virtual oscillator control). Using this analysis, we motivate control and modeling methods for single-phase ($1\\phi$) inverters and highlight the similarities and differences. From here we develop a high-fidelity model describing a system of three single-phase delta-connected grid-forming inverters. With this model, we simulate and analyze the phase balancing dynamics of systems with single-phase grid-forming inverters with different types of primary control. We derive a linearized model of the inverter phase dynamics for a system with three droop-controlled grid-forming inverters, and use it to formulate a Linear Quadratic Integral (LQI) controller capable of phase angle reference tracking. The proposed controller enables the system to be operated as a three-phase balanced source. A similar, but much more simple, methodology is used to develop a Proportional-Integral (PI) controller which is used to benchmark the behavior of the LQI controller. Unbalanced operation is also desirable when supplying an unbalanced load or injecting auxiliary signals for fault detection. Both MATLAB and Controller Hardware in-the-loop (C-HIL) are used to validate the proposed controllers and demonstrate performance under both nominal and unbalanced conditions. The LQI and PI controllers ensure minimal overshoot, zero steady-state error, and robust reference tracking in both the linearized and nonlinear model used to derive them. The results exemplify the flexibility of controller tuning for precise shaping of system response, which is essential for adapting inverter-based resources (IBRs) to grid protection requirements. The controller types are compared rigorously.","abstract_has_math":true,"creators":["McKechnie, Grant"],"institution":"University of Illinois Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Dominguez-Garcia, Alejandro"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-22T22:25:07Z","subjects":["Grid forming (GFM) inverters","phase difference control","Delta connection","droop control","linear quadratic integral (LQI) control","proportional integral (PI) control."],"languages":["en"],"rights":["Copyright 2025 Grant McKechnie"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/132541","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dominguez-Garcia, Alejandro"]},{"key":"dc:creator","label":"Author","values":["McKechnie, Grant"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-12","2025-12-12"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Grid forming (GFM) inverters","phase difference control","Delta connection","droop control","linear quadratic integral (LQI) control","proportional integral (PI) control."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Grant McKechnie"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/132541"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis presents a strategy for controlling the phase differences of a three-phase voltage source made up of single-phase droop-controlled grid forming inverters arranged in a delta configuration. We begin by deriving the simplified $dq$ model of a three-phase ($3\\phi$) grid-forming inverter and discuss proper selection of inner-current loop and outer-voltage loop gains for stability. We then analyze dynamic behavior of $3\\phi$ inverters with different types of primary control (namely droop, virtual synchronous machine, and virtual oscillator control). Using this analysis, we motivate control and modeling methods for single-phase ($1\\phi$) inverters and highlight the similarities and differences. From here we develop a high-fidelity model describing a system of three single-phase delta-connected grid-forming inverters. With this model, we simulate and analyze the phase balancing dynamics of systems with single-phase grid-forming inverters with different types of primary control. We derive a linearized model of the inverter phase dynamics for a system with three droop-controlled grid-forming inverters, and use it to formulate a Linear Quadratic Integral (LQI) controller capable of phase angle reference tracking. The proposed controller enables the system to be operated as a three-phase balanced source. A similar, but much more simple, methodology is used to develop a Proportional-Integral (PI) controller which is used to benchmark the behavior of the LQI controller. Unbalanced operation is also desirable when supplying an unbalanced load or injecting auxiliary signals for fault detection. Both MATLAB and Controller Hardware in-the-loop (C-HIL) are used to validate the proposed controllers and demonstrate performance under both nominal and unbalanced conditions. The LQI and PI controllers ensure minimal overshoot, zero steady-state error, and robust reference tracking in both the linearized and nonlinear model used to derive them. The results exemplify the flexibility of controller tuning for precise shaping of system response, which is essential for adapting inverter-based resources (IBRs) to grid protection requirements. The controller types are compared rigorously.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Grant McKechnie, accepted the attached license on 2025-12-11 at 13:01.","The student, Grant McKechnie, submitted this Thesis for approval on 2025-12-12 at 11:17.","This Thesis was approved for publication on 2025-12-12 at 13:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22977 on 2026-02-19 at 18:25:40"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Phase control of delta-connected single-phase grid-forming inverters for auxiliary signal injection"]}]}],"canonical_facts":{"dc:contributor":["Dominguez-Garcia, Alejandro"],"dc:creator":["McKechnie, Grant"],"dc:date":["2025-12","2025-12-12"],"dc:description":["This thesis presents a strategy for controlling the phase differences of a three-phase voltage source made up of single-phase droop-controlled grid forming inverters arranged in a delta configuration. We begin by deriving the simplified $dq$ model of a three-phase ($3\\phi$) grid-forming inverter and discuss proper selection of inner-current loop and outer-voltage loop gains for stability. We then analyze dynamic behavior of $3\\phi$ inverters with different types of primary control (namely droop, virtual synchronous machine, and virtual oscillator control). Using this analysis, we motivate control and modeling methods for single-phase ($1\\phi$) inverters and highlight the similarities and differences. From here we develop a high-fidelity model describing a system of three single-phase delta-connected grid-forming inverters. With this model, we simulate and analyze the phase balancing dynamics of systems with single-phase grid-forming inverters with different types of primary control. We derive a linearized model of the inverter phase dynamics for a system with three droop-controlled grid-forming inverters, and use it to formulate a Linear Quadratic Integral (LQI) controller capable of phase angle reference tracking. The proposed controller enables the system to be operated as a three-phase balanced source. A similar, but much more simple, methodology is used to develop a Proportional-Integral (PI) controller which is used to benchmark the behavior of the LQI controller. Unbalanced operation is also desirable when supplying an unbalanced load or injecting auxiliary signals for fault detection. Both MATLAB and Controller Hardware in-the-loop (C-HIL) are used to validate the proposed controllers and demonstrate performance under both nominal and unbalanced conditions. The LQI and PI controllers ensure minimal overshoot, zero steady-state error, and robust reference tracking in both the linearized and nonlinear model used to derive them. The results exemplify the flexibility of controller tuning for precise shaping of system response, which is essential for adapting inverter-based resources (IBRs) to grid protection requirements. The controller types are compared rigorously.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Grant McKechnie, accepted the attached license on 2025-12-11 at 13:01.","The student, Grant McKechnie, submitted this Thesis for approval on 2025-12-12 at 11:17.","This Thesis was approved for publication on 2025-12-12 at 13:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22977 on 2026-02-19 at 18:25:40"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/132541"],"dc:language":["en"],"dc:rights":["Copyright 2025 Grant McKechnie"],"dc:subject":["Grid forming (GFM) inverters","phase difference control","Delta connection","droop control","linear quadratic integral (LQI) control","proportional integral (PI) control."],"dc:title":["Phase control of delta-connected single-phase grid-forming inverters for auxiliary signal injection"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:07Z"}