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This paper presents a new grid-forming strategy for hybrid AC/DC microgrids using bidirectional virtual inertia support designed to address weak grid conditions. The stability of hybrid AC/DC microgrids heavily relies on the AC mains frequency and the DC-link voltage, and deviations in these factors can lead to undesirable outcomes such as load curtailments and power system congestions and blackouts. This paper introduces a unique approach that leverages bidirectional virtual inertia support to enhance the stability and reliability of hybrid AC/DC microgrids under weak grid conditions. The proposed strategy employs virtual inertia as a buffer to mitigate rapid changes in DC-link voltage and AC frequency, thereby enhancing system stability margins. This strategy significantly contributes to a more stable and reliable grid operation by reducing voltage and frequency fluctuations. A standard hybrid AC/DC microgrid configuration is used to implement the bidirectional virtual inertia support, where a bidirectional interlinking converter control is adjusted to deliver inertia support to both the AC and DC subgrids. This converter utilizes the DC grid voltage and AC grid frequency as inputs, effectively managing active power balance and implementing auxiliary functions. Extensive simulations are conducted under weak grid conditions and standalone mode to validate the effectiveness of the proposed strategy. The simulation results demonstrate a remarkable improvement in frequency nadir, rate-of-change-of-frequency (RoCoF), and DC bus voltage deviation in the hybrid AC/DC microgrids. The bidirectional virtual inertia support substantially reduces voltage and frequency fluctuations, enhancing the microgrid stability and resilience. There is an improvement of over 45% and 25% in the frequency deviation and voltage deviation, respectively, achieved through implementing the proposed control strategy. [ABSTRACT FROM AUTHOR]