This paper presents the stability analysis for a single-phase phase-locked loop (PLL) for power systems applications. The dynamical equations of a previously presented single-phase PLL are systematically derived and linearized for design and stability analysis purposes. Based on the linearized model of the PLL, parameters of the loop filter and the PI controller are accurately determined. The main advantages of the PI controller are discussed as well as its design procedure. Moreover, it is shown that, unlike the conventional single-phase PLLs, the mentioned PLL does not suffer from double-frequency ripples. Simulations carried out in MATLAB and SIMULINK verify the performance of the PLL under various operational scenarios; features like frequency and magnitude tracking, noise immunity, and harmonic attenuation are observed.