In this paper a new methodology to compensate double-frequency power oscillations in unbalanced 4-leg distribution networks is presented. The zero sequence components in the voltages and currents are used to provide an extra degree of freedom to compensate reactive and active power pulsations. A novel closed-loop algorithm for the compensation of fluctuations in the converter side, instead of the grid side is presented in this work. Simulation results are discussed, validating the proposed control system.