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

Jul 16, 2026

The current-constrained power-angle curve (PAC) is essential for transient synchronization stability (TSS) analysis of virtual admittance-based (VA) grid-forming (GFM) converters. Its standard formulation depends on a quasi-steady-state assumption that active power converges to the steady-state across the full angle range, yet violations remain insufficiently characterized. This work identifies a non-uniform convergence phenomenon in the VA-PAC, theoretically confirmed using an eigen-sweep-based analysis of a full-order VA-PAC model with detailed controls, and derives conditions on open-loop stability and response rate to ensure convergence.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages4

Reading Time10 min

Introduction

Non-Uniform Convergent Phenomenon

On the Convergence of the Current-Constrained Power Angle Curve of Virtual Admittance-Based Grid Forming Converters Haoxiang Zong, Member, IEEE, Chen Zhang, Member, IEEE, Yu Zhang, Member, IEEE, Xu Cai, IEEE, and Marta Molinas, Fellow, IEEE Abstract—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 lacks 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. Index Terms—converter, grid forming, virtual admittance, transient stability, power angle, current constrained. I. INTRODUCTION GRID-forming (GFM) converters are promising technique for operating the regarded as one renewable power generations (RPGs)-dominated power systems. Given its significance, dynamic issues of the GFM converter, ranging from the grid support function to the transient synchronization stability (TSS), etc., have been widely studied. Among these, the TSS, as a fundamental issue in power system operation, has attracted particular attention lately. Analysis of the GFM converter’s TSS issue is closely related to that of synchronous generator (SG), as the GFM converter is intentionally designed to mimic the dominant behavior of the SG. Under this context, a series of SG-inspired TSS analysis methods, e.g., the equal area criterion (EAC) [1]-[3], the energy function [4], etc., have been developed. For these methods, the power angle curve (PAC) serves as an essential tool. However, the PAC of the GFM converter is fundamentally different from This work was supported by the National Natural Science Foundation of China under Grant 52577207. (Corresponding author: Chen Zhang). Haoxiang Zong, Chen Zhang, Yu Zhang and Xu Cai are with the School of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China.(e-mail: [nealbc@sjtu.edu.cn](nealbc@sjtu.edu.cn)). Marta Molinas is with the Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway. ([e-mail: marta.molinas@ntnu.no](e-mail: marta.molinas@ntnu.no)). that of the SG due to the current limitation effect. Once being activated, an abrupt change in the PAC will occur, depending on the limitation strategy. For example, GFM converters’ PACs using the circular-based and the d-axis priority-based limitation strategies are reported in [4] and [5], etc., respectively. Although these PACs [4], [5] are well developed, they rely on quasi-steady-state assumptions. This means, these PACs are valid if and only if the dynamics associated with the circuit and inner-loop current control are adequately fast. However, there lacks a formal clarification on the conditions for which the actual PAC can converge to its steady-state. While, apparently, this clarification is significant for understanding the existing PAC-based TSS analyses’ applicability and limitations. To fill this gap, this letter will reveal a new phenomenon associated with the convergence issue of the PAC along with a formal theoretical justification. To the authors' best knowledge, this is the first attempt to demonstrate t

FAQs

Why is the current-constrained power-angle curve (PAC) important for VA grid-forming converters?

It plays a crucial role in transient synchronization stability (TSS) analysis by characterizing how power varies with the power angle during transients.

What limitation of existing PAC-based analyses is addressed in the paper?

The paper points out that existing PAC formulations rely on a quasi-steady-state assumption without clearly stating the conditions under which the actual PAC converges to its steady-state.

What new phenomenon does the paper reveal about VA-PAC convergence?

It reveals non-uniform convergence behavior, supported by eigen-sweep-based analysis of the full-order VA-PAC model, including how the convergence can oscillate and deviate in specific angle regions.

Jul 16, 2026

Upload by Theodora