Unbalanced grid voltages include positive and negative sequence (PNS) components. In particular, the negative sequence components that cause oscillations on the control signals, significantly affect the performance of the grid-connected renewable energy source inverters (RESI). In this study, proportional complex integrator (PCI) based current controller is proposed to deal with the disadvantages such as slow dynamic response, steady-state errors and complex structure of the proportional integral (PI) based dual current controller used for the control of grid connected RESI under non-ideal grid voltage conditions. The reference currents based on the active-reactive power reference signals, PNS components and the flexible control parameter are generated for use in control loops. The relationship between the active and reactive power oscillations, which are caused by non-ideal grid conditions, are comprehensively analysed and controlled with a flexible control parameter. An important contribution to similar previous studies is that the PNS voltage and current components required for the reference current generation are separated by the proposed fast and robust dual average filter based phase locked loop (DAPLL). The performance of the proposed PCI-based current control strategy is compared and tested with the PI-based dual current control strategy using various case studies.