The utilization of wind and solar energy-based distributed energy sources (DERs) has emerged as an important alternative due to their low carbon footprint and eco-friendly nature. This study presents a control methodology that effectively performs utility-synchronization DER-based microgrid and ensures continuous supply to locally connected loads during mode transitions. Additionally, it maintains the power quality of microgrid, even under unbalanced load conditions. Proposed power quality feature is achieved using an adaptive current control based on generalized robust logarithmic family (GRLF) that utilizes least mean square (LMS) based weight updating. This algorithm offers superior convergence and accuracy under both Gaussian and non-Gaussian noises. GRLF-LMS adaptive current control is utilized for fundamental extraction from input current signals. Control estimates phase angle and frequency of microgrid using a double-loop inertia phase-locked loop (PLL) method. Double-loop structure includes a synchronous reference frame PLL, which operates in a dual-loop fashion to provide synchronization and inherent antidisturbance capability. An overall control is tested on an experimental setup in emulated adverse operating conditions.