This paper presents an adaptive current-control scheme for a three-phase active-power filter (APF) for use within a microgrid. A vector-proportional-integral (VPI) controller with grid frequency tracking capabilities is used to compensate up to the 18th harmonic in the synchronous-reference-frame. This control scheme utilizes an advanced synchronous-reference-frame phase-locked loop (SRF-PLL) to update the resonant frequency values of the current controllers to ensure the resonant frequency of the VPI remain at the optimum point regardless of changes in the grid frequency. The advanced SRF-PLL uses adaptive digital notch filters based on the adaptive lattice structure to implement an adaptive lattice SRF-PLL (ALSRF-PLL). The ALSRF-PLL is able to reject the grid voltage harmonics thus preventing the estimation of the grid frequency to be polluted, which is essential for the correct behavior of the adaptive VPI controllers. In order to validate the adaptive control structure applied to APF, experimental testing has been carried out in a 70 kVA laboratory microgrid, where a 15 kVA three phase inverter is used as the APF.