The existing model predictive control schemes for the matrix converter perform well under ideal input conditions, but are not optimal when source voltages are unbalanced and distorted. The analysis shows that, under input disturbances, the input filter capacitors cause active power fluctuation and further output power quality degradation, which has been ignored in literature. Therefore, a method is proposed to extract the fluctuation with a digital filter and compensate it in the reference generation of source active power, so as to eliminate the output low-frequency harmonics. In the case of input voltage unbalance, a method is proposed to generate the reference source reactive power which could achieve sinusoidal source currents, without the need of separating sequence components. Moreover, effects of source voltage distortions, which degrade the input power quality significantly and are ignored in literature, are suppressed with the proposed generation method of reference reactive power. The extensive experimental results in nine cases have verified the satisfactory steady-state and dynamic performance of the proposed methods. INDEX TERMS Model predictive control, matrix converter, source voltage disturbances, current distortions.