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.

Voltage source behind an impedance is a term widely used in grid-codes requirements for grid forming (GFM) power electronic converters. However, the exact meaning of this requirement is hard to quantify and verify, and its necessity is not adequately justified. This paper identifies key characteristics that GFM controls should possess and evaluates how GFM controls, with and without a current controller, meet these characteristics. The study utilizes the dq-frame admittance and the frequency-domain power flow Jacobian to analyze an ideal voltage source behind an RL impedance, a synchronous generator, and various GFM and grid-following controls implemented in modular multilevel converters (MMCs). The research identifies several essential voltage source characteristics, which can be mathematically calculated and used to define the frequency ranges where the requirements are met. The paper demonstrates that the GFM structures meet the essential voltage source characteristics in a limited frequency range. The GFM with the current controller is particularly affected due to the nonpassivities of the current controller and virtual impedance. The requirements calculated from the essential voltage source characteristics can serve as a screening method to assess the effectiveness of converter controls, and the insights gained can be utilized to enhance the design thereof.