Based on IEEE SSR first benchmark model, series compensation scheme is proposed to damp subsynchronous resonance (SSR). The control and simulation model of thyristor controlled series compensation (TCSC) to damp SSR is established in PSCAD/EMTDC. The combination scheme of TCSC and fixed series compensation is analyzed through simulation. The test signal method is adopted to analyze the performance of damping SSR from the perspective of electrical damping characteristics. Considering the damping effect as well as the cost of TCSC, the compensation scheme which can better meet both security and economy requirement of the grid is proposed.