This paper addresses the issue of power flow control for partially faulty microgrids. In microgrid control systems, faults may occur in both electrical and communication layers. This may have severe effects on the operation of microgrids. In addition, disturbances always coexist with faults in microgrids, which may further deteriorate system performance. To address the faults and disturbances simultaneously, a model predictive control (MPC) method based on set-membership estimation (SME) that transmits information via a communication network is proposed. When electrical devices are nonfunctional or communication failures occur, the corresponding system states will become unavailable. To this end, the SME method is employed to estimate the states with the existence of unknown-but-bounded process and measurement disturbances. The networked MPC method is designed to schedule the power dispatch by using the forecasts of photovoltaic (PV) generation and load demand. With these two methods, the fault-tolerant control can be achieved. Further, a deviation compensation method is proposed to compensate for the forecast errors. The effectiveness of the proposed control strategy is demonstrated through wireless communication tests using Raspberry Pis.