Abstarct: In recent years, due to the need for high-power instruments that use new sources of energy, the usage of H-bridge converters has expanded significantly in the industrial sphere. Since there is a high possibility of unbalance in the input DC voltages of multilevel converters (MLCs), a need to compensate for this unbalance, which has a great effect on the output of the converter, has raised. Three-phase cascade h-bridge (CHB)-MLCs, when under balanced operating conditions, are relatively easy to control. However, when the voltages of the input DC sources have different values (or an unbalance happens in the input DC sources), the complexity of the issue arises. In this thesis, by using a simple algorithm a method for overcoming the input voltage unbalance is provided. With regard to the ANSI C84.1 standard, a criterion for evaluating the unbalance of line voltage and calculating the switching angles is also considered. The proposed method of this paper improves the performance of the selective harmonic mitigation (SHM) modulation method that works under unbalanced conditions of input DC voltages. The unbalanced condition in the DC input voltages can occur in numerous states. In this thesis, suitable switching signals, with symmetry of a quarter of a cycle in each cell are provided. Also an average value method for DC sources in each phase is employed. As a result, the number of the states is reduced and the need to calculate the new switching angles to balance the line voltage is avoided. By optimizing the switching angles, the wide range of odd-order harmonics, except for the third-order harmonic, is also reduced. In an unbalanced system, the third harmonic is not eliminated in a self-activating way, thus adopting an effective method for reducing the third harmonic and balancing the line voltage is necessary. In the end, by simulating the H-bridge seven-level inverter in MATLAB Simulixnk, the accuracy and efficiency of the presented methods in the unbalanced condition of the input DC voltages are shown. Also, the results obtained fom the experimental sample of the H-bridge seven-level inverter confirm the accuracy of the simulation results.