Distributed renewable energy sources (DRESs) have additional benefits compared with conventional fossil fuel-based energy sources. These sources are connected to the utility grid using a suitable synchronization method. It requires accurate information on grid voltage magnitude and phase angle. But the presence of harmonics, DC Offset, and voltage unbalances makes the synchronization process more challenging. Conventionally synchronous reference frame (SRF)- PLL is implemented for this purpose, however, it has a problem with 100Hz ripple during distorted grid conditions. A double integration method (DIM) is administered for the synchronization of a 3-phase inverter under non-ideal grid conditions. It is important for DIM implementation to remove the DC offset or integrating constants of pure integrators without involving any phase shift. This method is also compared with conventional SRF-PLL based on mathematical modelling and simulations using a MATLAB/Simulink toolbox. The results are verified based on ideal and non–ideal grid conditions and also tested on grid-connected 3-phase Inverter.