In electrified liquefied natural gas (LNG) plants variable frequency drives (VFDs) interact with turbine-generator (TG) units creating torsional vibrations known as sub-synchronous torsional interactions (SSTIs). Torsional vibrations can be dangerous for an LNG plant when they involve torsional instability. The stability of an LNG plant depends on the plant configuration and on the number of TG units and of VFDs. In such peculiar configurations stability cannot be achieved acting of the VFDs control system. Alternatively, dedicated equipment is needed to damp the torsional vibrations. In this paper, a sub-synchronous damper (SSD) converter is used to mitigate the SSTI phenomena. The SSD converter consists of a thyristor H-bridge regulating the phase of the additional torque provided at the TG unit air-gap. A phase control system is proposed and is based on the torsional torque oscillations measurement. An adaptive reference signal is employed, also guaranteeing high performance in island-mode operation. The proposed solution increases the damping of the LNG plant in all the considered configurations. The LNG plant successful operation is validated by comprehensive results.