Impedance Reshaping Control for Stability Enhancement of Grid-Following Inverters in Weak Grids

Although the weak-grid stability of grid-following inverters has been widely studied, traditional SCR-based assessment mainly describes grid strength and does not directly quantify the minimum SCR required for stable operation under a specified active-power command. This paper uses a critical-SCR-oriented operating-boundary evaluation to compare the control-dependent dynamic stability requirement with the physical steady-state feasibility limit. It proposes a channel-specific impedance-reshaping extension that retains the PLL-related q-q and d-q compensation paths and adds a voltage-loop-related q-d compensation path. The added path reduces the control-induced dynamic critical SCR, thereby allowing stable operation at lower SCR than with the original control structure. Firstly, the steady-state critical SCR is derived from the steady-state power-transfer relation under a specified active-power command to define the physical feasibility lower bound, and the dynamic critical SCR is identified using a scanning procedure based on the generalized Nyquist criterion. The resulting control-induced SCR gap quantifies the additional grid-strength requirement introduced by the control dynamics. Secondly, a simplified d-q admittance representation is used to relate established PLL-related and voltage-loop-related coupling effects to the corresponding compensation paths. Thirdly, the proposed channel-specific impedance-reshaping design is used to mitigate these effects while retaining the selected voltage-loop bandwidth, and an anti-drift correction is further introduced to improve implementation robustness. Frequency-domain analysis and time-domain simulations validate the dynamic critical-SCR evaluation, while hardware-in-the-loop experiments demonstrate the real-time operation of the proposed controller. The results show that it moves the dynamic critical-SCR boundary close to the steady-state physical boundary and improves the weak-grid stability margin. The hardware-in-the-loop results further confirm bounded operation under SCR and frequency steps.