Robust Stability Design for Inverters Using Phase Lag in Proportional-Resonant Controllers

Engineers often reduce proportional-resonant (PR) controllers to simpler proportional controllers, neglecting the phase lag at midfrequencies. This reduction can lead to the incorrect assumption that a single-loop-control inverter with grid-side current feedback destabilizes when the inductor-capacitor-inductor (LCL) resonant frequency (ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub>) is below the critical frequency (ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">crit</sub>), i.e., when ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≤ ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">crit</sub>. In contrast, we found that the PR controllers can provide adequate phase lag at midfrequencies. Adjusting the controller parameters to increase this phase lag can stabilize the inverter under ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≤ ω<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">crit</sub> conditions without additional damping. Our research offers a robust stability design process that involves tuning PR controller parameters and optional phase margin (PM) compensation to ensure inverter stability and maintain good dynamic performance despite fluctuations in grid impedance. Initially, we establish a mathematical relationship between the controller parameters and the phase crossover frequency. This relationship is then used to set the phase crossover frequency to match the antiresonant frequency created by the inverter-side filter inductor and capacitor. Subsequently, we introduce an optional PM compensator to speed up the convergence of tracking error and reduce high-frequency oscillations. Finally, a case study highlights the control system’s robustness, transient performance, and flexibility of the design approach.