Distributed generation systems often appear as a weak-grid

where the voltage is prone to be unbalanced

and the performance of the inverters within the system will be affected as the conventional control scheme cannot deal with the negative sequence (NS) component. A decoupled double synchronous reference frame (DSRF) phase locked loop (PLL) is proposed to obtain the positive sequence (PS) and NS phases of the unbalanced voltage. Meanwhile

an instantaneous power model under the unbalanced grid is analyzed

and then an unbalanced control strategy based on the DSRF-PLL is designed by injecting an NS current into the PS reference current via a negative-sequence-to-positive-sequence (NS-PS) transformation. Quasi-proportional-resonant (QPR) links are introduced to track the PS reference current and suppress the harmonics from the grid so as to suppress the ripples of the DC voltage to guarantee maximum power point tracking (MPPT) accuracy and smaller total harmonic distortion (THD) of the grid-connected current. Finally

the validity and reliability of the proposed scheme is verified via a 10 kW photovoltaic grid-connected inverter.