This paper addresses the problems associated with the dc-link capacitor voltages of the three-level neutral-point-clamped power converter: the imbalance of the capacitor voltages as well as the presence of an ac-voltage low-frequency oscillation in the dc link of the converter. In order to cope with them, a mathematical analysis of the capacitor voltage difference dynamics, based on a direct average continuous model, is carried out, considering a singular perturbation approach. The analysis leads to a final expression where a sinusoidal disturbance appears explicitly. Consequently, the two problems can be handled together using the ordinary formulation of a problem of regulating the output of a system subject to sinusoidal disturbances, applying classical control theory to design the controller. In this way, the controller is designed including the disturbance estimate provided by a Luenberger observer to asymptotically cancel the disturbance, while keeping also balanced the capacitor voltages. Experiments for a synchronous threelevel neutral-point-clamped converter prototype are carried out to evaluate the performance and usefulness of the converter working as a grid-connected inverter under the proposed control law.