Passivity-Based Design Methodology for Current-Controlled Grid-Forming MMCs

This paper proposes a controller design methodology based on passivity to mitigate control interactions between the transmission grid and current-controlled (CC) grid-forming (GFM) converters. To this end, the paper derives an analytical dq-frame model valid above 20 Hz for a GFM modular multilevel converter (MMC) with cascaded virtual impedance and current controller. The paper identifies how the different CC-GFM control parameters impact the MMC's AC side admittance passivity. Furthermore, the study shows that straightforwardly enforcing passivity requirements on the AC admittance conflicts with ensuring essential grid-forming characteristics, such as the ‘voltage-source-behind-impedance’ behavior, and that a trade-off is needed. To address this trade-off, the proposed framework employs dedicated loop-shaping techniques, which ensure passivity within predefined frequency ranges while preserving essential grid-forming characteristics. Moreover, the methodology extends beyond MMCs and is relevant to other voltage source converters. Experimental and numerical results in time and frequency domains, respectively, show that the design effectively mitigates potential adverse interactions while maintaining the desired ‘voltage-source-behind-impedance’ behavior.