Renewable energy sources (RES) penetration levels are increasing in the power grid. However, it does not have inertia as a traditional synchronous generator, causing a reduction in the inertia and damping in the power grid, impacting the stability during power changes in the grid, causing large frequency deviations. The virtual synchronous machine (VSM) concept has become an attractive solution to emulate the synchronous machine characteristics and supply the inertia and damping property in the system. It consists of emulating the synchronous machine’s static and dynamic properties by power electronic converters and energy storage systems. Nevertheless, the implementation and design of the VSM is a challenge since it must be flexible in the presence of load fluctuations, preventing the oscillations and frequency overshoot from increasing during system disturbances. Hence, the VSM with adaptive inertia has become a potential solution because it provides the inertia and damping factor to the grid according to the load variations and different RES penetration levels in the system. Therefore, the inertia estimation is necessary to use the special techniques that guarantee the balance between the power and frequency response...