Power industry taken severe torsional oscillations induced in turbine-generator shaft systems due to Sub synchronous Resonance (SSR). SSR occurs when a natural frequency of a series compensated transmission system coincides with the complement of one of the torsional modes of the turbine-generator shaft system. The frequency can be oscillationates corresponding to the torsional mode frequency and unless corrective action taken. , the torsional oscillations can grow and may result in shaft damage in a few seconds The problem is a control scheme for a VSC-HVDC back to back active power controller to damp all SSR torsional oscillations. In this context are conducted on a HVAC/DC system incorporating a large turbine-generator and a VSC HVDC back-to-back system. The results of the investigations conducted in this thesis show that the achieved control design is effective in damping all the shaft torsional torques over a wide range of compensation levels.