Virtual inertia control is a methodology to make inverter-based resources (IBR) behave like a synchronous machine. However, an IBR cannot fully emulate the response of synchronous machine because of its low-current capacity. When the inertial response of an IBR is affected by the current limitation, the synchronization of the synchronous machine simulated virtually inside the IBR controller with the other synchronous generators in the grid is affected, which may cause step-out of the simulated generator. We propose a methodology which can keep the synchronization by modifying internal induced voltage of the simulated generator to follow the system voltage change. The proposal is validated by the simulation using a nine-bus transmission system model including two synchronous generators and a large-scale IBR. The result of the generator trip simulation shows that the proposed method suppresses the phase angle variation while the current is limited, and avoids the instability regarding the synchronism. Furthermore, the impact of the current limitation on frequency stability is also evaluated through the simulation study and it is found that as the amount of output suppression increases, the frequency nadir falls, but the rate-of-change of frequency is hardly affected.
