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This paper proposes a robust predictive current controller based on a disturbance estimator for a three-phase grid-connected inverter. The various components that deteriorate the performance of a conventional predictive current controller are regarded as disturbances, and a disturbance estimator is constructed using an inverter output voltage and current values. Furthermore, a grid angle is extracted using a phase-locked loop (PLL) with the estimated reactive component of the disturbance; therefore, sensorless grid voltage control is possible. In order to determine the relevant gains in the disturbance estimator, the frequency components corresponding to the unbalanced grid condition and low-order harmonics, as well as the PLL bandwidth, are considered. Moreover, the stability of the disturbance estimator due to parameter errors in the inductor filter is analyzed. The proposed method has an inherent rapid dynamic response due to the conventional predictive current controller, as well as low-cost implementation and robust control performance with regard to the disturbance and noise interference due to use of the combined estimation algorithm. The feasibility of the proposed predictive current control strategy is verified through the examination of experimental results.