To address transmission capacity bottlenecks of critical transmission corridors in large-scale hybrid AC/DC power grids and to accommodate greater renewable energy output at the sending end, thyristor controlled series compensation (TCSC) and static synchronous compensator (STATCOM) can be rationally deployed in the system. Accordingly, considering the uncertainties of renewable energy output, a multi-objective robust optimization model for the allocation of TCSC and STATCOM in large-scale hybrid AC/DC power grids is established, with the objectives of minimizing the annualized equivalent investment cost, maximizing corridor transmission capacity, and maximizing renewable energy accommodation capacity. First, the original mixed integer nonlinear programming model is transformed into mixed integer second-order cone programming model using convex relaxation technology, thereby improving computational efficiency and the quality of the obtained solutions. Then, the multi-objective robust optimization model is transformed into a series of single-objective optimization models using the normalized normal constraint algorithm. Subsequently, the column and constraint generation algorithm is used to decompose each single-objective model into a master problem and subproblem that are solved iteratively, yielding a set of Pareto-optimal solutions for the multi-objective optimization model under the worst-case uncertainty of maximum available renewable generation at renewable energy plants. The entropy weight method is further applied to identify a compromise optimal solution among the Pareto set. Finally, based on the calculation results of the modified IEEE 39-bus system and an actual large-scale AC-DC power grid, the effectiveness of the proposed model and algorithm is verified.