Validation of the Geometric Method for Large-Signal Stability Analysis of Two Parallel Grid-Following Converters

Abstract

The increasing penetration of inverter-based resources (IBRs) is fundamentally changing the power system dynamics, resulting in weaker-grid conditions with reduced system inertia and more frequency fluctuations. These conditions also raise questions about the validity of classical stability analysis. In this paper, the large-signal stability of grid-interfaced power converters in a wind power system application is investigated, comparing the Time-Domain model with the analytical model.First, an average value model of a single grid following (GFL) converter is developed and implemented in a PLECS environment together with its control strategy. Second, the analytical model for the single GFL converter is presented based on the average value model. A transient stability analysis is then performed using the Geometric Method for the analytical model, which is then compared to Time-Domain simulations. The same procedure is subsequently applied to two GFL converters connected in parallel.Results show good agreement between the analytical and Time-Domain models under strong-grid conditions. However, discrepancies between the GFL Time-Domain and the analytical models show the fault trajectories advancing at different speeds. The differences are caused by the reduced order of the analytical model, which does not capture the dynamics represented in the Time-Domain model.Overall, the Geometric Method provides a good approximation of the system behaviour, particularly under strong-grid conditions, although discrepancies with the Time-Domain model become more pronounced as the grid strength decreases. This trend is observed for both the second-order single GFL converter and the two parallel GFL converters.