Synchronous reference frame phase-locked loops (SRF-PLLs) are widely used in different technologies, such as wind turbines, electric vehicles, more electric aircraft, and motor drives, to estimate system's variables. The SRF-PLL is an adaptive notch filter that is used to estimate a sinusoidal signal's amplitude, phase angle, and frequency. However, when the input signal is subjected to a considerable variation or includes a significant noise, its stability and performance become challenging. In this paper, the stability of the SRF-PLL for substantial changes in the input signal's variables are investigated. To do so, the nonlinear time-varying (NTV) model of the system is proposed and is used for the large-signal stability assessment. Then, an adaptive tuning method, based on the proposed NTV model, is designed to improve its transient performance during and after the variation. Simulation and experimental results are used to validate the proposed method.