Liquefied Natural Gas (LNG) plants are commonly island-operated weak grids where the interaction of high-power Variable Frequency Drives (VFDs) with the Turbine-Generator (TG) units might cause Sub-Synchronous Torsional Interaction (SSTI) phenomena. SSTI phenomena can lead the LNG plant to instability conditions. Each LNG plant configuration is characterized by a risk level, which is considered high when the electrical damping at the TG Torsional Natural Frequencies (TNFs) is negative. Starting from a real case study, a detailed electromechanical model of an LNG plant is presented. The model is comprehensive of the control system of the power conversion stage and of the TG unit. Sensitivity analysis, performed on control system parameters, allows one to detect the parameters that impact the electrical damping and the stability of the overall LNG plant. A complete simulation platform is developed. Experimental results are carried out on a real LNG plant considering four different configurations. The theoretical model and the simulation platform allow one to estimate the electrical damping and the results are confirmed by the experimental validation. It is demonstrated that fine tuning of the power conversion stage control parameters can reduce the risk related to torsional instability.