Structural Analysis and Internal Stability Enhancement of Virtual-Admittance-Based Cascaded GFMIs Under Unity Voltage-Feedback Decoupling

Stephen Arinze Obi, Ki-Hyun Kim, Jae-Jung Jung

Virtual admittance (VA) is widely used in cascaded voltage-control and current-control (VC-CC) grid-forming inverters (GFMIs) because it shapes the converter terminal behavior while preserving the current-regulation path required for current shaping and limiting. However, the achievable VC-loop bandwidth remains strongly coupled to the CC-loop bandwidth and to the VA parameters. Voltage-feedback decoupling (VFD) is commonly used to relax this coupling, but in VA-based control its benefit is not unconditional. This paper shows that unity-gain VFD, which represents the full-decoupling condition, removes the low-frequency restoring term associated with the filter capacitor and drives the voltage loop toward a delay-sensitive double-integrator structure. This internal-stability limitation is referred to here as the VFD trap. To address this trap without attenuating VFD, a proportional active-damping (AD) path is proposed, implemented as negative capacitor-voltage feedback in the current-reference path. The proposed path restores the missing low-frequency support while retaining unity VFD and introduces an additional AD-based degree of freedom for VC-loop tuning. A minimum support condition, a delay-aware phase-margin expression, and compact forward/inverse design equations are derived for operating-point selection. Standalone and grid-connected experiments on a 3-kVA prototype verify the analysis, showing that the proposed path recovers stable unity-VFD operation, reduces the voltage-step settling time from approximately 9~ms to 3~ms, and maintains stable power injection.