The penetration of growing microgrid systems within the ac distribution network is leading to several challenges to have a safe and reliable operation of the power system. For the utility system, it is mandatory to maintain the voltage and frequency within the prescribed limits at the local bus under diverse conditions of the renewable energy sources (RESs), loads, and grid. With these conditions, the need for energy storage system (ESS) becomes extremely important for effective operation of critical and frequency sensitive loads. The vital role of ESS based on dc-bus regulation and monitoring of grid frequency in the microgrid is a challenging task and needs to be investigated in detail. Therefore, in this paper, the storage and microgrid are scheduled to work in a grid supportive manner. Also, these ESSs need to be operated within its safe state of charge limits. Hence, based on all the above constraints, an appropriate grid adaptive power management strategy (GA-PMS) is formulated to generate current references for RES, ESS, and microgrid-connected converters. Furthermore, this algorithm includes seamless microgrid operation under abnormal conditions, priority-based load shedding, and ensuring power quality standards at the local bus. The performance of proposed GA-PMS is tested and validated through the simulation and experimental studies.