Transient stability analysis approach of the SG-GFL-GFM parallel system based on power-angle interaction mechanism

For power systems integrating grid-following (GFL) and grid-forming (GFM) converters, along with synchronous generators (SGs), this paper proposes a new transient stability analysis method based on power-angle interaction mechanism. A nonlinear differential equation model is developed, incorporating phase-locked loop (PLL) dynamics, virtual synchronous generator (VSG) control, and power interaction characteristics. Through a systematic investigation of unbal anced power distribution during transients, the study clarifies the power-angle dynamics of the SG, GFL, and GFM converters subjected to various parameter variations. The theoretical analysis is cross-validated through both phase trajectory assessments and RT-LAB real-time simulations under fault conditions. The findings quantitatively show that: 1) increasing the GFL converter q-axis current from 0.2 p.u. to 1 p.u. raises the power angle deviation from 0.027 rad to 0.053 rad; 2) Increasing the PLL proportional gain from 5 to 9.85 and lowering its integral gain from 200 to 100 enhance the GFLs stability by reducing power angle deviation from 0.055 rad to 0.028 rad; and 3) decreasing the GFM power reference from 1 p.u. to 0.5 p.u. reduces the power angle fluctuation from 0.16 rad to 0.06 rad. The results validate the correctness and efficacy of the proposed stability analysis method.