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In this paper, a fully decentralized adaptive droop optimization strategy for inverters is proposed for minimizing power loss during power transmission in islanded microgrids integrated with solar photovoltaic systems. From a hierarchical point of view, the proposed control architecture of the distributed generators encompasses both the primary and secondary levels in a decentralized plug-and-play manner. The primary level, realized by a droop controller, is in charge of the fast response in load sharing among all the generation units in the microgrid. The secondary level control, with a larger operation time scale, has the objective of minimizing the power loss in the system, which is achieved by the proposed adaptive droop functions. The advantage of the proposed droop optimization strategy is that the power generation units are fully decentralized by using only local measurements. The adaptability of the droop functions is achieved by adopting a perturbation and observation (P&O) method. Particularly, when a small perturbation in the offset of the P-f droop functions is introduced, the resultant effects on frequency and generated power are examined in order to select the offsets with the minimum power generation, indicating that the power loss is minimum. The P&O process is performed iteratively by every participating generation unit with a fixed perturbation over a constant time step. Eventually, the system converges to a steady state with minimum power loss. The process within the secondary controller continues indefinitely, and any change in loads or grid configuration will bring the system to a new steady state with minimum power loss.