The output power and current quality of the system under grid voltage imbalance are the main indicators of grid-connected inverters. First, quantitative analysis is performed on the corresponding reference currents under the two control targets. Based on this analysis, a power fluctuation suppression and current balance coordinated control strategy is proposed. The control strategy uses a reduced-order resonator to extract the harmonic signal in the reference current, and uses a weight coefficient to adjust the magnitude of the harmonic component in the reference current, and implements the proposed strategy based on the deadbeat-free current control. The method does not need to use a phase-locked loop and a positive and negative sequence separation module, and uses the instantaneous voltage to calculate the current reference value, which simplifies the control structure. The effectiveness and feasibility of the control strategy are verified by Matlab/Simulink simulation and RT-LAB semi-physical experiment platform. This work is supported by National Key Research and Development Program of China (No. 2016YFC0600906).