Next-generation grid codes require large-capacity energy storage converters to support the grid under faults by autonomously injecting both positive and negative reactive currents. The injected reactive currents can suppress the negative sequence voltage and enhance the positive sequence voltage simultaneously. To meet these requirements, this paper proposes a novel current injection strategy based on a voltage droop control method between dual-sequence voltage at the point of common coupling(PCC) and currents. This strategy can realize flexible and dynamic allocation of positive and negative sequence currents. Moreover, the proposed current injection strategy takes the inherent constraints of the converter into consideration and incorporates adaptive current limitation capabilities. The proposed strategy has been validated under both three-phase symmetrical voltage sag and single-phase short-circuit fault conditions. The results demonstrate that the scheme significantly enhances the voltage support capacity of the converter, confirming the effectiveness of the proposed approach.