In islanded AC microgrids consisting of renewable energy sources (RES), battery-based energy storage system (BESS), and loads, the BESS balances the difference between the RES power and loads by delivering/absorbing that difference. However, the state of charge (SOC) and charging/discharging power of the battery should be kept within their design limits regardless of variations in the load demand or the intermittent power of the RES. In this paper, a supervisory controller based on fuzzy logic is proposed to assure that the battery power and energy do not exceed their design limits and maintaining a stable power flow. The microgrid considered in this paper consists of a 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 the PV or to supplement the power from the auxiliary unit. The proposed FLC performance is verified by simulation and experimental results.