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• It is the first application of MPC in MMC-UPFC to handle the unbalanced fault. The current reference of the MPC algorithm for the shunt MMC is obtained in synchronous dq coordinate frame. Previous work has not involved this procedure. • The voltage constraint is considered in the MPC for series MMC. It enables the MMC to operate with the maximum output voltage of the converter by modifying the power reference values in the cost function. It achieves the suppression of the unbalanced current and also makes full use of the capacity of UPFC by operating it on the voltage boundary. This paper proposes a model predictive control (MPC) method to tackle the power flow control of the modular multilevel converter based unified power flow controller (MMC-UPFC) under unbalanced grid conditions. The predictive models corresponding to the discrete-time models of MMC-UPFC are derived. For the shunt MMC, the d-axis and q-axis current references for the MPC are deduced to maintain the dc-link voltage constant according to the energy balance on the dc-link side. The series MMC utilizes a cost function with the voltage constraints to suppress the faulted current and make the power flow controllable, and thus avoid the spread of the fault. Moreover, it makes full use of the capacity of MMC by operating it on the voltage boundary defined by the maximum output voltage of the converter. The model is established using the parameters from a 500 kV MMC-UPFC practical project in Jiangsu, China. Simulation results demonstrate a favorable response of the MMC-UPFC based on the proposed MPC strategy under different unbalanced grid conditions. [ABSTRACT FROM AUTHOR]