LC-Resonance Placement Limits and Damping Recovery in Virtual-Admittance-Based Grid-Forming Inverter Control

Compact LC-filter design and inner-loop control must be coordinated for stable grid-forming operation. This paper quantifies how current-loop proportional gain constrains LC-resonance placement in virtual-admittance-based dual-loop control with unity voltage-feedback decoupling (VFD) and capacitor-voltage active damping. Equivalent-impedance analysis identifies gain-dependent contraction of the positive-resistance region. Delayed inverter-current feedback opposes VFD-assisted damping above one-sixth of the sampling frequency. Simple proportional-path frequency shaping recovers an admissible effective-gain window while retaining unity VFD and leaving the resonant path unchanged. Reduced-model criteria, checked against the complete model, link window closure to a nominal resonance-placement limit near one-third of the sampling frequency under single-sampled single-update operation over the studied gain range. A 3-kVA prototype demonstrates an 83.3% LC-product reduction at comparable voltage and nominal current crossovers. A separate comparison with the same high-resonance filter demonstrates stable operation at 2.68 times the unshaped nominal current crossover. Output-impedance analysis and grid-connected tests identify additional grid-dependent gain constraints.