The configuration of synchronous condensers is currently a commonly used measure to enhance the oscillatory stability of renewable energy integration systems. However

there is limited research on the mechanism of frequency-coupled impedance in synchronous condensers. Discrete numerical solutions for the frequency-coupled impedance of synchronous condensers can only be obtained through frequency-sweep measurements or programmatic calculations. The internal mechanism of the condenser impedance model remains unclear

posing numerous limitations to studies on sub/super-synchronous oscillation suppression in power grids using impedance analysis methods. To address this

this paper proposed an analytical method for the impedance of synchronous condensers. Based on the analytical results

the study analyzed the decisive parameters affecting the external impedance characteristics at the mechanistic level

providing research insights for the oscillatory stability analysis of regional power grids with synchronous condensers and additional damping control methods.