This article presents an energy efficient autonomous grid-synchronized photovoltaic (PV) array battery energy storage (BES) based microgrid with power quality improving capabilities under weak grid conditions. The microgrid is developed to supply consumer loads even at disappearance of the weak grid. The BES is not only beneficial on daily energy saving but it is also sized to furnish smoothening facilities to the PV-BES microgrid. A pseudolinear synchronization scheme is used, which is based on extraction of fundamental positive sequence components from the polluted grid voltages. The islanded controller furnishes reliability by maintaining the voltage and frequency and continuous power to the consumer load. The multivariance generalized adaptive controller is proposed to control the microgrid and to improve the power quality aspects. The effectiveness of microgrid is demonstrated experimentally with estimation of phase and frequency at grid synchronization and desynchronization with polluted grid conditions.