This paper provides a systematic analysis of the large scale PMSG (permanent magnet synchronous generator)-based WECS (wind energy conversion system) torsional vibration problem under MPPT (maximum power point tracking) control and constant power control. This is from the perspective of SSO (sub-synchronous oscillation), SSH (sub-synchronous harmonics) and forced torsional vibration. The cause of SSO is the negative total system damping, weakened by the constant power control. The system is susceptible to inducing SSH in the grid current and voltage in the under-damped condition. To effectively suppress the torsional vibration of PMSG-based WECS, a stiffness compensation control strategy based on adaptive damping is proposed. The results show that SSO, SSH and the forced torsional vibration can be suppressed at the source using the proposed suppression strategy.