Stability Design of Single-loop PI Controller for Grid-Forming Converters with Compact LLCL Filter

Grid-forming converters (GFM) and related con-trol strategies in combination with renewable energy sources (RES) and energy storage systems (ESS) are considered a ne-cessity in future more-electronic grids with increasing penetration of controlled switched-mode power supplies. Typically, LC- filters serve for linking inverters and the grid with well-defined current. To stabilize the system and avoid oscillations, the LC resonance frequency is often chosen greater than one third of the sampling frequency. However, the grid impedance changes from site to site and can even change over time so that the effective filter resonance frequency shifts during operation. Such resonance shifts can lead the system into unstable regions. On the other hand, LC filters with high resonance frequency cannot comply with grid codes with respect to the suppression of switching distortion. LLCL filters are a compact higher-order alternative that promises better robustness particularly in weak-grid conditions-after all one of the most important applications of grid forming. However, stable solutions and corresponding design rules are missing. In this paper, a single-loop voltage control with negative proportion gain is presented with a low-resonance-frequency LLCL-filter. Finally, we verify robust and stable operation of the proposed controller with varying grid impedance in a detailed analysis.