On the Convergence of the Current-Constrained Power Angle Curve of Virtual Admittance-Based Grid Forming Converters

Haoxiang Zong, Chen Zhang, Yu Zhang, Xu Cai, Marta Molinas

The current-constrained power-angle curve (PAC) is crucial for the transient synchronization stability (TSS) analysis of virtual admittance-based (VA) grid-forming (GFM) converters. Its formulation and application rely on the quasi-steady-state assumption critically, i.e., the active power can converge to its steady-state across the entire angle space in both a stable and fast manner. Despite this assumption is intuitively perceivable, it lack sufficient clarification, particularly on underlying behaviors if violated. To this end, this paper uncovers a new phenomenon on the non-uniform convergence of the VA-PAC. To achieve this, an eigen-sweep-based analysis of the full-order VA-PAC model with detailed controls is conducted, by which the existence of this issue is theoretically confirmed. On this basis, the open-loop stability and response-rate conditions of the full-order VA-PAC model for ensuring its convergence are clarified. Findings of this work can provide deeper insights into the existing TSS analyses of GFM converters, and are expected to provoke new analyses.