This article presents application of generalized robust logarithmic family (GRLF) framework derived least absolute difference (LAD) Algorithm implemented for active power filters (APF) for PQ enhancement. The presented GRLF-LAD algorithm successfully eliminates lower as well as higher order errors from the harmonically rich nonlinear load currents and thus results in accurate fundamental component extraction. Weak power grids are characterised by distorted grid voltages and riddled with inherent harmonics. Conventional techniques such as synchronous reference frame (SRF) algorithm are unable to filter out the harmonics from grid voltages and this results in oscillations in D-Q components. This leads to generation of a distorted reference current and thus unsatisfactory APF performance. In this article, the grid voltages are processed by modified second-order generalized integrator with quadrature signal generator (QSG-SOGI) based algorithm. The harmonic rejection capabilty of QSG-SOGI is far superior than other tested algorithms. QSG-SOGI shows remarkable improvement of approximately 99.35% than SRF and 96.02% than SOGI in terms of percentage improvement. The performance of presented APF is verified experimentally on a developed prototype and tested rigorously against load variations, grid voltage variations as well as grid distortions. The GRLF-LAD algorithm is found to be approximately 36.04% faster than APA and about 45.16% faster than LMS in terms of dynamic response and about 11.19% better than LMS in accurate current component extraction. The total harmonic distortion (THD) content of presented algorithm is found to be well within the IEEE-519 std.