In recent years, the use of synchronous generators (SGs) has been displaced due to the increased use of renewable energy sources. These types of plants mostly use power electronic converters to connect to power grids, which, due to their mode of operation, cannot provide the same services. This paper analyzes the synchronization of Grid-Forming converters (GFM) without phase-locked loop (PLL) through the active power control loop. Stability analysis shows that when increasing the emulated moment of inertia in a voltage source converter (VSC) using grid-forming control, the system becomes oscillatory. The paper proposes a novel compensation mechanism in order to damp the system oscillation, allowing the implementation of inertia emulation. Finally, the real-time implementation is executed using a Hardware in the Loop experimental set-up. The response of VSC under grid disturbances is simulated in a real time simulator, while the proposed control system is implemented in a real-time controller platform.