Large-Signal Stability of Power Systems with Mixtures of GFL, GFM and GSP Inverters

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators, and convenient concepts such as the equal-area criterion and global energy function do not apply in the same way. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates the interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine the stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This paper establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to accurately determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used based on multiscale analysis. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, which is called the stability radius (SR). Using the proposed framework, the analysis reults of two-inverter system show that both GFM and GSP inverters significantly enhance the large-signal stability of a two-inverter system where the other inverter is GFL, with GFM providing slightly superior performance. This improvement is attributed to the voltage support effects and is maximized when the GFM or GSP inverter is located at the midpoint of the transmission line, where the voltage is lowest. All findings in this paper are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.