In this paper a weighting function for voltage unbalance correction is proposed to be integrated into the control of distributed grid-interfacing systems. The correction action can help decrease the negative-sequence voltage at the point of connection with the grid. Based on the voltage unbalance factor and system power capacity, the interfacing converter delivers a small amount of negative-sequence current to the grid and helps correcting the negative-sequence voltage. Although the reduced amplitudes contributed by each individual DG system are very small compared to the total negative-sequence component, many DG system modules can collectively achieve substantial results in the grid. As a practical example, a three-phase grid-interfacing converter servicing sensitive loads with distributed sources is employed to integrate this additional function. Design principles, simulation and experimental results are presented to verify the proposal.