Adaptive Controller Based on Stability Boundaries for Grid-Forming and Grid-Following Inverters Under Varying Grid Impedance

The stability of Grid-Forming (GFM) inverters and Grid-Following (GFL) inverters exhibits duality and is closely related to the Short-Circuit Ratio (SCR) and the grid impedance ratio (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_g</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_g</i>). Variations in grid impedance in real-world scenarios pose challenges for the stable operation of inverters with fixed control. To address this issue and enhance inverter stability across diverse grid conditions, this paper proposes an adaptive control for Power Plant Controller (PPC) based on stability boundaries related to SCR and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_g</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_g</i>. Firstly, considering that the inverter model is encrypted by inverter manufacturers, this paper identifies the coefficients based on generic opensource models to match the actual model, treating it as a greybox problem. Then, based on the obtained model, small-signal stability boundaries for both GFM and GFL inverters are demonstrated in the two-dimensional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_g</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_g</i> − SCR plane, revealing the relationship between stability and model parameters. More importantly, this paper designs adaptive PΔ and fΔ in the PPC to equivalently reshape stability boundaries and expand the stable operating range, thereby ensuring the stability of the inverter under varying grid impedance. Additionally, to enhance tolerance for errors in model identification and impedance estimation, stability margins are incorporated into the control design. Finally, the effectiveness of the proposed adaptive controller is validated through simulations and real-time Hardware-in-the-Loop (HIL) experiments.