Steady-State Angle Stability Analysis of Parallel Grid-Forming Converters in Current Saturation Mode

Grid-forming converters (GFCs) usually operate in parallel to supply power to unknown loads. Nevertheless, unknown loads may lead to overcurrent, causing parallel GFCs to enter the current saturation mode (CSM). The steady-state angle stability of parallel GFCs in CSM is crucial for ensuring reliable operation under unknown loads, yet this issue has not been studied previously. This article presents a novel power model for parallel GFCs in CSM and conducts the first-ever investigation of steady-state angle stability in this context. The analysis results reveal that the steady-state angle stability of the equilibrium points (EPs) under overall inductive load is opposite to that under overall capacitive load. Specifically, it is shown that the EP with even power allocation is unstable, and the parallel GFCs will transition to the EP with circulating currents in the presence of overall capacitive loads. Eventually, all the capacity of GFCs is occupied by the circulating currents, failing to supply voltage to the loads. The proposed model and analysis are validated through experimental results, highlighting the significant risk of power supply failure for parallel GFCs in CSM and providing general guidance for the operation of GFCs in parallel.