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Cascaded H-bridge multilevel inverters have gained a significant popularity in medium to high power motor drive applications and grid-connected renewable energy systems in recent years. Under equal DC voltages, cascaded H-bridge multilevel inverters use phase-shifted pulse width modulation (PS-PWM) technique to generate the output voltage. However, under unequal DC voltages which may happen because of the renewable energy sources connected to front-end of the multilevel inverter, traditional PS-PWM method fails to achieve good output harmonics. In this paper, a frequency domain analysis of PS-PWM is presented. By using the analysis, a phase angle modification of traditional PS-PWM is introduced. The proposed method helps eliminate first order harmonics of triangular carrier frequency and its sidebands under randomly selected DC voltages and DC voltage fault conditions. Finally, simulation results for single phase seven- level cascaded H-bridge multilevel inverter are presented to validate the good performance of the proposed method. GENERALIZED ADAPTIVE PHASE-SHIFTED PWM FOR SINGLE-PHASE SEVEN-LEVEL CASCADED H-BRIDGE MULTILEVEL INVERTERS