This paper concerns the control problem of the active and harmonic power sharing caused by the mismatched impedance in resistive feeders-dominated microgrids. A distributed model predictive control (DMPC) scheme is suggested to regulate the virtual impedance of each involved unit for power sharing based on the neighbor's state. With the distributed philosophy, the central controller is not required. Moreover, the proposed method benefits resilience to communication failure by designing the communication matrix. Furthermore, it involves propagating information among units in a short period, significantly reducing the communication and computation burden. Finally, the performance of the proposed control scheme is evaluated in terms of its convergence, robustness to communication delay and load variations, resilience to communication failure, and plug-and-play functionality without communication in an inverter-connected system.