Phase control of delta-connected single-phase grid-forming inverters for auxiliary signal injection

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• McKechnie, Grant

Contributors dc:contributor

• Dominguez-Garcia, Alejandro

• Grid forming (GFM) inverters
• phase difference control
• Delta connection
• droop control
• linear quadratic integral (LQI) control
• proportional integral (PI) control.

Statement dc:rights

• Copyright 2025 Grant McKechnie

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132541

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132541