Effects of Line Dynamics on Stability Margin to Hopf Bifurcation in Grid-Forming Inverters

Abstract: This paper studies the parameter sensitivity of grid-forming inverters to Hopf bifurcations to address oscillatory instability. An analytical expression for the sensitivity of the stability margin is derived based on the normal vector to the bifurcation hypersurface. We identify the most effective control parameters through comprehensive analysis. In particular, the impacts of line dynamics on the stability margin to Hopf bifurcation are investigated. The results indicate that the feedforward gain in the voltage control loop is the most effective parameter for enhancing the stability margin. Furthermore, it is observed that line dynamics introduce a uniform reduction in the stability margin across all parameters. However, the reduction is generally small for most parameters except for the voltage-reactive power droop gain, which shows a more pronounced effect.