Influence of Control Strategies on the Output Impedance of Grid-Connected LCL Inverters in the <i>dq</i> -Domain

This paper presents an analytical method for deriving the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i>-domain output impedance matrix (dqOIM) of a grid-connected LCL inverter operating in grid-following mode. Combined with the grid impedance matrix (GIM), the dqOIM—dependent on the current control system and the phase-locked loop (PLL)—enables small-signal stability assessment of the inverter–grid interface using the generalized Nyquist criterion. The paper also examines the influence of three previously proposed control strategies on the dqOIM and overall system stability. These strategies differ in how they address <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i>-axis coupling in current control and damping of the LCL filter resonance. Their tuning methods typically focus on the internal current-loop stability, neglecting PLL effects and grid impedance variations, and consequently overlooking external stability of the inverter–grid connection. Results show that the dqOIM q-q element exhibits negative resistance behavior within the PLL bandwidth across all evaluated controllers, consistent with observations for L-type inverters. The q-d element displays a similar trend, further challenging external stability. Such destabilizing effects, however, can be alleviated through established measures, including virtual impedance insertion, PLL bandwidth reduction, or auxiliary active-damping loops. These findings suggest that advanced decoupling and damping techniques may increase susceptibility to external instability. Overall, the study underscores the role of dqOIM as a valuable tool for control design and stability assessment of grid-connected inverters. Theoretical results are validated through hardware-in-the-loop simulations and experimental tests.