This work presents a simple approach to eliminate DC power ripple in a three-phase Modular Multilevel Converter (MMC) while operating with balanced (load) currents during unbalanced grid faults. In this study, the MMC is connected to an AC grid on one of its terminals, and to a constant ideal DC source on the other, while a single phase fault takes place. The presented ''first'' approach is based on the combined application of a Notch filter and a Resonant PI controller. The main idea is to eliminate the zero-sequence oscillations that occur in the MMC differential currents when the unbalanced fault takes place. This strategy may be applied jointly with a constant circulating current controller on the one hand or with a constant energy per phase (implying an injection of a second harmonic to the differential current), on the other. Moreover, the load currents are kept balanced even during the fault in order to demonstrate the potential application of the MMC as a power oscillation firewall of some sort; i.e., to simultaneously keep constant DC power and balanced load currents at all time.