With local synchronous generators in receiving-end grids being replaced by multi-infeed line-commutated converter-based (LCC) high-voltage direct currents (HVDCs), the dynamic voltage supportability of the power grid decreases. Moreover, the reactive power consumption of LCC-HVDCs during the recovery process brings risks to voltage stability. Hence, the transient control of LCC-HVDCs should be optimized coordinately to support short-term voltage stability under credible contingencies. In this paper, the dynamic reactive power characteristics between AC/DC systems are derived mathematically. Based on the coupling mechanism among the voltage-dependent current order limiter (VDCOL), AC dynamic voltage, and HVDC power recovery, an "autonomous-synergic" optimization strategy incorporating short-term voltage stability constraints is proposed for multi-infeed LCC-HVDCs. To handle the problem of large-scale differential-algebraic equations (DAEs), the optimization is iteratively solved based on time-domain simulation (TDS) and trajectory sensitivities. The stability is quantified by an indicator and the trajectory sensitivity analysis is utilized to relax stability constraints. The effectiveness and feasibility of the proposed methods are verified with a benchmark system and a real system in China. The short-term voltage stability under all credible contingencies can be guaranteed, while the total power recovery of LCC-HVDCs is improved.
