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This paper proposes a novel inertia-enhanced distributed control method to complement the inertia of microgrids. The rate of change of frequency (RoCoF) and the rate of change of voltage (RoCoV) are employed in this paper to quantify the frequency inertia and voltage inertia, respectively. Then, a fully distributed algorithm with constrained changing rates is proposed. By bounding the changing rates of frequency and voltage during the consensus control, the algorithm can address the consensus problem while enhancing the inertia of microgrids. Compared with most inertia control methods, the proposed method can utilize the reserve power of scattered DGs to supply inertia. Besides, it performs better under disturbances and delays than conventional distributed control methods. The effectiveness of the proposed method is validated by several cases in MATLAB/Simulation and a hardware experiment. [ABSTRACT FROM AUTHOR]