On the Interaction in Transient Stability of Two-Inverter Power Systems containing GFL inverter Using Manifold Method

Abstract: Many renewable energy resources are integrated into power systems via grid-following (GFL) inverters which rely on a phase-locked loop (PLL) for grid synchronization. During severe grid faults, GFL inverters are vulnerable to transient instability, often leading to disconnection from the grid. This paper aims to elucidate the interaction mechanisms and define the stability boundaries of systems of two inverters, including GFL, grid-forming (GFM), or grid-supporting (GSP) inverters. First, the generalized large-signal expression for the two-inverter system under various inverter combinations is derived, revealing that no energy function exists for systems containing GFL inverters. This implies that the traditional direct method cannot be applied to such systems. To overcome these challenges, a manifold method is employed to precisely determine the domain of attraction (DOA) of the system, and the transient stability margin is assessed by a new metric termed the critical clearing radius (CCR). A case study of the two-inverter system under various inverter combinations is conducted to explore large-signal interactions across different scenarios. Manifold analysis and simulation results reveal that GSP inverters using PLL for grid synchronization exhibit behavior similar to GFM inverters when the droop coefficients in the terminal voltage control loop (TVC) are sufficiently large. Compared to GFL inverters, GSP inverters incorporating a TVC significantly enhances the transient stability of other inverters. In the STATCOM case, the optimal placement of the STATCOM, realized by GSP or GFM inverters, is identified to be at the midpoint of a transmission line. All findings in this paper are validated through electromagnetic transient (EMT) simulations