Sequence Impedance Modeling and Stability Analysis of dVOC-Based Grid-Forming Inverters with Different Inner-Loop Control Structures

To elucidate the stability mechanisms of grid-forming (GFM) inverters governed by dispatchable virtual oscillator control (dVOC), this paper develops a comprehensive sequence-impedance modeling and stability analysis framework for dVOC-based GFM inverters with different inner-loop control structures. Three representative configurations are investigated: open-loop dVOC control, dVOC with dual-loop voltage–current control (DLC), and dVOC with virtual admittance control (VAC). For each configuration, unified positive-sequence impedance models are derived and analytically validated. Based on these models, the stability characteristics are first analyzed in a single-inverter grid-connected system under different grid strengths. The analysis is then extended to a mixed inverter system consisting of grid-forming and grid-following (GFL) inverters. Particular attention is paid to the impedance interaction between GFM impedance shaping and the capacitive negative damping introduced by GFL inverters under weak-grid conditions. Quantitative analyses reveal that the dVOC–DLC configuration significantly enhances oscillation damping in mixed systems. Under benchmark scenarios, stable operation can be ensured with approximately a 25% GFM capacity penetration. In contrast, the open-loop and VAC configurations require around 50% and 75% capacities, respectively, to maintain stability. These findings indicate that the DLC-based inner-loop design offers superior stability margins while substantially reducing the required GFM capacity, thereby improving economic efficiency. This study establishes a quantitative impedance-based criterion for inner-loop control selection and provides practical design guidelines for deploying dVOC-based GFM inverters in future converter-dominated power systems.