The grid code for renewable energy is increasingly strict to circumvent issues with grid stability and reliability. One grid code standard that is enforced for most modern variable speed wind turbines (WTs) is the low-voltage ride-through (LVRT) criteria, where WTs are to be grid-connected during voltage dips. Traditionally, for permanent magnet synchronous generator (PMSG) WTs, LVRT is achieved by using a DC crowbar or DC chopper to dissipate the power difference between the grid and the generator. Alternatively, a popular LVRT strategy proposed by the research community for PMSG-based wind energy conversion system (WECS) is the stored energy in rotor inertia (SEIRI) strategy, which is done by altering the control of the machine-side converter (MSC) with potential cost savings. However, there are some concerns regarding additional mechanical stress to the drivetrain that may pertain to this method. A hybrid LVRT method has been suggested to combine the crowbar and the SEIRI methods to incorporate the benefits from both methods. In this article, we are studying and comparing the electrical and mechanical performance of PMSG WTs operating with the traditional crowbar, the SEIRI, and the hybrid LVRT method. To do so, the electrical and mechanical dynamics of these strategies are simulated using a two-mass drive train model, which is necessary for analyzing WTs under mechanical transient. Finally, the performance of wind farms with power reserves while using an inertia based LVRT method will be investigated to show the impact of the power reserve on the WT's LVRT mechanical dynamics.