In an islanded AC microgrid consisting of renewable energy sources, battery, and load, the battery balances the difference between power generated by renewable sources and that consumed by the load. However, battery charging capacity is limited and its state of charge needs to be maintained within the safety limits. Furthermore, battery has limited maximum charging and discharging power. This paper proposes a controller based on fuzzy logic to prevent the battery state of charge and charging/discharging power from exceeding their limits regardless of variations in load and intermittent power of renewable sources. The microgrid considered in this paper consists of PV, battery, load and auxiliary supplementary unit. The fuzzy logic controller alters the AC bus frequency which is used by the local controllers of the parallel units to curtail the power generated by PV or to supplement power from the auxiliary unit. The main merits of the proposed controller are simplicity and easiness of implementation without the need for any communication links between the parallel units. Matlab/Simulink results are presented to validate the performance of the proposed controller.