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Owing to the direct coupling between the input and output of matrix converter, the abnormal power supply could disturb the output voltage easily. In this study, three modulation strategies for matrix converter based on mathematical construction are proposed under unbalanced input voltage conditions. The strategies are developed based on the construction of the rectifier and inverter modulation vectors in three different ways. By regulating appropriately the modulation index of inverter vector, the output voltages of matrix converter can maintain sinusoidal and balanced. The different rectifier vectors result in different input currents. Moreover, the analytical solutions for input currents with the three methods are presented, and the approximated solutions are derived to estimate their low-order spectrums. Comprehensive comparisons among the three methods are made in the aspects of the complexity of realisation, voltage-transfer capability and input current quality. Simulation and experimental results verify the correctness and effectiveness of the proposed methods.