This article proposes a linear filtering procedure to improve the performance of a PLL algorithm, based on the structure of a generalized second order integrator (SOGI), using a one-cycle Fourier filter (OCF) to filter stationary voltages αβ generated directly by a SOGI structure. In addition, a comparison is made between conventional SOGI and also with a moving average filter (MAF), with this filter applied to the synchronous dq voltages produced by the αβ to dq transformation at the output of the SOGI structure. The comparisons are made with signals affected by different harmonic distortions and with sinking voltages similar to those obtained in power networks under fault conditions. The results of the comparisons show that the two approaches, OCF and MAF, improve the dynamics