The proposed operational strategy is mainly focused on using an appropriate energy management and control strategies to improve the operation of an islanded microgrid, formed by photovoltaic (PV) solar energy, batteries and loads. This control strategy is to achieve decentralized power management of a PV/battery hybrid unit in a droop-controlled islanded microgrid. In contrast to the common approach of controlling the PV unit as a current source, in the proposed strategy, the PV unit is controlled as a voltage source that follows a multi-segment adaptive power/frequency characteristic curve. The proposed power/frequency characteristics, of the hybrid unit and of the whole microgrid, adapt autonomously to the microgrid operating conditions so that the hybrid unit may supply the maximum PV power, match the load, and/or charge the battery, while maintaining the power balance in the microgrid and respecting the battery state-of-charge limits. These features are achieved without relying on a central management system and communications, as most of the existing algorithms do. The control strategy is implemented using multi-loop controllers, which provide smooth and autonomous transitions between the operating scenarios. In this process is enhanced using of fuzzy logic controller.