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The voltage unbalancing issue remains a challenge for the multilevel flying capacitor (FC) converter. It becomes more prominent when the number of levels of the converter is higher than three which needs to be addressed. The phase-shifted sinusoidal PWM (PS-SPWM) method has a certain degree of self-balancing characteristic in the ideal symmetrical circuit. However, the use of only the said method is not sufficient to deal with the problem and a closed-loop control is required to realize the voltage balancing control task. The paper proposes a closed-loop control method based on the PS-SPWM strategy and a novel algorithm for the stated problem. The algorithm takes advantage of switching redundancies in order to adjust the switching time of selected switching states to maintain the capacitor voltages balanced without adversely affecting the system's performance. Description and analysis of the method along with simulation results are presented to confirm its feasibility.