With the rapid development and wide application of the flexible DC transmission system, its starting conditions are more and more diverse. Traditional open-loop charging strategy of MMC valve requires comprehensive consideration of the system state variables for parameter configuration, and the configuration is difficult. Therefore, a general-purpose closed-loop charging strategy for the converter valve is proposed, which can control the steady state of the sub-module at a rated voltage without detecting the system state, and has a good adaptability. First of all, three kinds of charging loops and active voltage equalization charging strategies of flexible HVDC transmission systems are analyzed. Secondly, based on the analysis of equalization requirements of submodules with inconsistent characteristics, a complete universal closed-loop charging strategy and the coordination start strategy of multi-terminal flexible DC transmission system are proposed. Finally, a three-terminal DC grid model is built through PSCAD/EMTDC. Simulation results show that the closed-loop charging strategy can be generally applicable to the startup charging process of various converter stations, ensuring the submodules steadily charge to the rated voltage without bridge arm overcurrent and submodules overvoltage. This work is supported by National Science and Technology Grant Program of China (No. 2015ZX02301003) and Science and Technology Project of State Grid Corporation of China (No. [2017]).