This paper considers the reference signal generation problem for the multi-functional operation of single-phase dynamic voltage restorers. For this purpose, a single-phase quasi type-1 phase-locked loop (QT1-PLL) is proposed. The pre-loop filter part of this PLL is composed of a frequency-fixed delayed signal cancellation method and a two-stage all-pass filter. Thanks to the frequency-fixed nature, the pre-loop filter is easy to implement and can provide rejection of any measurement offset. Moreover, this PLL benefits from the excellent harmonic robustness property of the conventional QT1-PLL. Small-signal modeling and gain tuning procedures are detailed in this paper. In order to track the reference voltage signals generated by the proposed PLL, a super-twisting sliding mode controller is also presented, which helps to achieve fast dynamic responses. Laboratory-scale prototype-based experimental studies were conducted to validate the developed reference generator and the controller. Experimental results show that the proposed method is fast in detecting and compensating any grid voltage anomalies to maintain constant load voltage despite voltage sag, swell, and harmonic distortions.