The timely and accurate extraction of the grid-voltage is essential to the normal operation of the grid-connected converter. The phase-locked loop based on the synchronous reference frame (SRF-PLL) does not have fast response and superior filtering performance at the same time, so it cannot be applied to the applications of non-ideal power grid. By adding some high-order notch filters (NF) on the q-axis of SRF-PLL, a new algorithm called NFSRF-PLL is proposed, which can effectively filter out harmonics while ensuring that the response time is the same as that of SRF-PLL. In addition, for LVRT applications, based on the theory of coordinate transformation, a simple and effective method for detecting the grid-voltage sag-depth is also designed. By adding a second-order notch filter and a low-pass filter to the dq axis, the fundamental negative-sequence components and higher harmonics can be suppressed, respectively. At the same time, the bandwidth of the low-pass filter can be set relatively high. Therefore, the detection method has the characteristics of fast detection speed, high detection accuracy and good robustness. Finally, experimental comparison results verify the effectiveness of the proposed algorithms.