The multi-terminal flexible DC distribution system has developed rapidly and has obvious advantages in integrating new energy. However,rapid and reliable fault identification is one of the challenges in its development. To address the issue of the inconspicuous high-resistance fault characteristics of multi-terminal flexible DC distribution lines and the associated protection difficulties,this paper proposes a single-ended protection scheme for flexible DC distribution lines based on measuring voltage Fréchet distance by analyzing the transient voltage fault characteristics before the converter station blocking. Firstly,the protection start-up criterion is constructed based on the transient change rates of voltage and current measured by the positive and negative electrodes. Secondly,single-pole and bipolar faults are distinguished by the voltage change rate measured by the positive and negative electrodes. Finally,the internal and external faults in the unipolar and bipolar regions are identified by using the single and bipolar measurement voltage Fréchet distance to construct the integral,and the unipolar fault is selected according to the positive electrode voltage change rate. The PSCAD/EMTDC simulation results show that this scheme can simultaneously meet the requirements for rapidity and sensitivity in protection,and has good resistance to transition resistance,which is not affected by the distributed capacitance of the line.