Under unbalanced grid voltage faults, the output power oscillation of a grid-connected inverter is an urgent problem to be solved. In the traditional topology of inverters, it is impossible to eliminate power oscillation and simultaneously maintain balanced output current waveform. In this paper, considering the solvability of reference current matrix equation, the inherent mechanism of inverter output power oscillation is analyzed, and a modified topology with auxiliary modules inserted in series between the inverter output filter and the point of common coupling (PCC) is proposed. Due to the extra controllable freedoms provided by auxiliary modules, the inverter could generate extra voltage to correct PCC voltage while keeping balance of output current, so as to eliminate the oscillation of output power. Simulation and experimental results verify the effectiveness of the proposed topology.