The large-scale integration of renewable energy units and high-voltage direct current transmission systems poses challenges of declining inertia and reduced short-circuit ratio to power systems. The energy storage synchronous condenser (ESSC)

combining both active power support and reactive power compensation capabilities

has emerged as a critical solution for enhancing grid voltage/frequency stability. However

the influence mechanisms of its damper effects (including rotor slot wedge eddy currents and structural parameters) on operational characteristics remain unclear. This paper investigates the damper effects in ESSCs

focusing on revealing the impact of damping parameters on their steady-state and transient operational behaviors. First

dynamic and steady-state models with damper effects are established for high-inertia ESSCs

and an asynchronous-synchronous equivalent circuit is developed. Subsequently

rotor voltage and current under varying damping parameters and rotor speeds are calculated and compared. The influence of damper windings under severe grid faults is also analyzed. Finally

a simulation model is constructed to evaluate ESSC performance under different damping parameters. The simulation results validate the accuracy of the mathematical models and prove the optimization effect of the damper windings on the ESSC.