With the load growth and the power grid expansion, the problem of short-circuit current (SCC) exceeding the secure limit in large-scale power grids has become more serious, which poses great challenge to the optimal secure operation. Aiming at the SCC limitations, we use multiple back-to-back voltage source converter based (B2B VSC) systems to separate a large-scale AC power grid into two asynchronous power grids. A multi-objective robust optimal secure operation model of large-scale power grid with multiple B2B VSC systems considering the SCC limitation is established based on the AC power flow equations. The decision variables include the on/off states of synchronous generators, power output， terminal voltage, transmission switching, bus sectionalization, and modulation ratios of B2B VSC systems. The influence of inner current sources of renewable energy generators on the system SCC is also considered. To improve the computational efficiency, a mixed-integer convex programming (MICP) framework based on convex relaxation methods including the inscribed N-sided approximation for the nonlinear SCC limitation constraints is proposed. Moreover, combined with the column-and-constraint generation (C&CG) algorithm, a method to directly solve the compromise optimal solution (COS) of the multi-objective robust optimal secure operation model is proposed. Finally, the effectiveness and computational efficiency of the proposed solution method is demonstrated by an actual 4407-bus provincial power grid and the modified IEEE 39-bus power grid, which can reduce the consumed CPU time of solving the COS by more than 90% and obtain a better COS.