Under grid voltage unbalance, grid-connecting converters should be always connected to the grid. However, voltage unbalance has adverse effect on the stable operation of the converters, such as active power oscillation, DC link voltage ripple and overloading. Thus, it is needed to investigate parallel operation of grid-connecting converters interfacing DC and AC buses and propose flexible control strategies to solve the aforementioned issues. In this digest, a thorough study on factors that influence the peak current of single converter is conducted. In addition, based on the principle that total output active power should be oscillation free, a coordinated control strategy is proposed for two parallel converters. Case study has been conducted to demonstrate the effectiveness of this proposed control strategy.