With the growing integration of renewable energy sources (RES) into advanced power grids, through power electronic converters, comes a critical reduction in overall system inertia. This reduction in inertia exposes the grid to fast frequency fluctuations, which can impair its stability and reliability. Although power converters provide rapid control, they do not have the inherent inertial response characteristic of conventional synchronous machines, e.g., those used in conventional power plants such as thermal power plants. To overcome this problem, this project discusses modelling and simulation of a grid-connected inverter based on Virtual Synchronous Generator (VSG) control with a PI controller. This advanced approach replicates the dynamic characteristics of a synchronous Machine and provides a virtual inertia and damping to the low-inertia power grid system. The project involves modelling a MATLAB/Simulink model combining the VSG control with the Grid-Connected Inverter. The effect of important parameters such as inertia and damping on the dynamic response of the system is explored and validated using the simulation results. The results prove that VSG control effectively improves frequency and voltage stability, further enhancing the overall performance of the grid. The work forms the basis of future research and hardware-in-the-loop implementation, beyond the constraints of constant DC inputs, and helps ensure the stability of power systems rich in renewables.