The core issue of depressing subsynchronous resonance（SSR） with static var compensator（SVC） is to make its current output contain components of complementary frequencies to torsional modes of the turbine-generator shaft. For this purpose， the control principle and mathematical model of subsynchronous modulation of fundamental admittance for SVC are proposed. Theoretical analysis shows that by subsynchronously modulating the reference value of SVC's fundamental admittance with appropriate amplitude and phase， the generated current components of the complementary frequencies can be controlled to generate damping torque and realize the SSR-damping objective. The proposed control scheme meanwhile results in supersynchronous as well as other fractional harmonic currents. Both nonlinear electromagnetic simulations with the detailed power-electronic circuit and field tests on the actual SVC equipment validate the proposed control scheme and mathematical model. The subsynchronous damping control system is further applied to a practical system threatened by SSR， i.e.， the Jinjie series-compensated transmission project. Extensive digital simulations have demonstrated its effectiveness in mitigating multi-modal SSR.