A conventional synchronous (rotating) reference frame control requires small-signal models and introduces cross-coupling terms. In this study, a virtual charge-based scheme for grid synchronisation with only current measurements has been proposed for a three-phase grid-connected inverter with a first-order filter. The methodology described in this study curbs the dependency of the inverter on the information of the grid voltage to generate unit vectors from the phase-locked loop. This kind of estimation is especially important during grid voltage sensor failures or a distant point common coupling or weak grid conditions. In the proposed estimation scheme, no noisy differentiation is involved and only the nominal values of the interfacing filter parameters are utilised, making the implementation easier in digital microcontrollers. Also, a current control architecture based on feedback linearisation concept has been explored and embedded with the proposed grid voltage estimation technique, and the corresponding performance has been evaluated via simulation and experimental studies.