Multilevel cascaded H-bridge converters have become a mature technology for applications where high-power medium ac voltages are required. Normal operation of multilevel cascaded H-bridge converters assumes that all power cells have the same dc voltage, and each power cell generates the same voltage averaged over a sampling period using a conventional phase-shifted pulse width modulation (PWM) technique. However, this modulation method does not achieve good results under unbalanced operation per H-bridge in the power converter, which may happen in grid-connected applications such as photovoltaic or battery energy storage systems. In the paper, a simplified mathematical analysis of the phase-shifted PWM technique is presented. In addition, a modification of this conventional modulation method using variable shift angles between the power cells is introduced. This modification leads to the elimination of harmonic distortion of low-order harmonics due to the switching (triangular carrier frequency and its multiples) even under unbalanced operational conditions. The analysis is particularized for a three-cell cascaded H-bridge converter, and experimental results are presented to demonstrate the good performance of the proposed modulation method.