Overvoltage and overcurrent resulting from various faults cause instability in Doubly Fed Induction Generator (DFIG)-based wind turbines connected to a grid. The grid code requirement must be met during faults to minimize the effect of these problems. Low Voltage Ride Through (LVRT) capability is used to meet the grid code requirement. It is important to use coordinate control for transient states in LVRT capability. This study aimed to improve the stator dynamics for ease of calculation and the rotor dynamic model by damping oscillations caused by balanced and unbalanced faults on the grid side. For this, electromotive force (emf) models were developed for stator and rotor dynamic modeling. Furthermore, for the coordinate control of the DFIG, models were developed for a lookup-table-based supercapacitor and a decoupled Static Synchronous Compensator (STATCOM). Using these models, analyses of three-phase and two-phase faults were conducted. Following different balanced and unbalanced faults within the grid, the system was stabilized in a short time, and the oscillations occurring during the faults were quickly damped using the LVRT models developed in this study.