Modeling Fault Recovery and Transient Stability of Grid-Forming Converters Equipped With Current Reference Limitation

TL;DR

The paper tackles transient stability of grid-forming converters that employ current reference limitation CACRS during severe disturbances. It derives a closed-form expression for the returning-angle set ${\mathcal R}(\beta)$ as a function of the saturated current angle $\beta$, and analyzes conditions under which the system may fail to escape the current-saturation mode. The results show that the saturated current angle $\beta$ critically shapes post-fault trajectories and satSEP existence, with grid parameters such as $Z$ and $X/R$ influencing stability. Case studies validate the theory and highlight practical guidance for adaptive $\beta$ selection and for revisiting DOA/CCT assessments in current-saturated GFM IBRs.

Abstract

When grid-forming (GFM) inverter-based resources (IBRs) face severe grid disturbances (e.g., short-circuit faults), the current limitation mechanism may be triggered. Consequently, the GFM IBRs enter the current-saturation mode, inducing nonlinear dynamical behaviors and posing great challenges to the post-disturbance transient angle stability. This paper presents a systematic study to reveal the fault recovery behaviors of a GFM IBR and identify the risk of instability. A closed-form expression for the necessary condition that a GFM IBR returns from the current-saturation mode to the normal operation mode is presented. Based on these analyses, it is inferred that the angle of the magnitude-saturated current significantly affects the post-fault recovery and transient stability; with different angle selection, the system may follow multiple post-fault trajectories depending on those conditions: 1) Convergence to a normal stable equilibrium point (SEP), 2) convergence to a saturated stable equilibrium point (satSEP), or 3) divergence (instability). In this paper, the circumstances under which a GFM IBR cannot escape from the current-saturation mode are thoroughly investigated. The theoretical analyses are verified by dynamic simulations.

Figures (20)

• Figure 1: The structure of a three-layer VSG GFM IBR Arjomandi2024YazdaniWang2023.
• Figure 2: Phasor-Diagram of the voltages in (a) steady-state normal operation mode, (b) voltage sag, (c) extra APC angle, and (d) extra APC angle with CRS.
• Figure 3: Illustration of entering and returning sets represented by the solid and hatched fill areas, respectively. Here, $Z=0.46$ p.u. and $X/R=\infty$.
• Figure 4: Power-Angle curve for a GFM IBR equipped with the CRS.
• Figure 5: Post-fault trajectory and active power for the case where $\mathcal{C}_1$ holds.