Abstract: Power electronic converters, known as interlinking converters, will play a key role in grid-connected applications in the future landscape of interconnected multi-modal grids, enabling precise control of the tidal currents between the interconnected grids. Therefore, this technology is not only suitable for interconnecting AC and DC hybrid systems, but also for flexible connection between AC grids. In this paper, a new interconnected converter control strategy, dual inertia-emulation is proposed to improve the dynamic response of the grid-connected system by simulating the inertia characteristics on both sides of the converter, and the strategy can be adapted to any type of grid interconnection scenarios. Time-domain simulations based on the WSCC 9-node system and the IEEE 14-node standard test system show that the proposed method can significantly improve the equivalent inertial response of the interconnected grid, effectively suppress the frequency oscillations and frequency rate of change, and improve the frequency nadir characteristics.