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Multi-functional grid-tied inverters (MFGTIs) have been investigated recently for improving the power quality (PQ) of microgrids (MGs) by exploiting the residual capacity (RC) of distributed generators. Several centralized and decentralized methods have been proposed to coordinate the MFGTIs. However, with the increasing number of the MFGTIs, it demands a method with improved reliability and flexibility, which are characteristics of distributed framework that has not been introduced into the PQ improvement (PQI) field before. In this paper, we propose a distributed consensus method to undertake the PQI task. The task is proportionally shared among the MFGTIs according to their instant RCs. Besides, most of the existing methods assume that the RCs of the MFGTIs are sufficient for tackling the PQ problem (PQP), which is not always true. In the case of insufficient RC, the active power output of each MFGTI is scaled down by the same factor determined by a proposed leader-follower protocol to make room for the task. In summary, the PQP is dealt with in both cases of sufficient and insufficient RC under the distributed control framework. Finally, simulations and hardware-in-the-loop experiments of an MG consisting of three 10kVA MFGTIs are presented to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]