Source-grid coordinated current limiting can suppress DC-side fault currents in DC grids; however

it also deteriorates fault-current characteristics

which may cause conventional line pilot protection to fail. This paper proposes a pilot protection method for transmission lines in flexible DC grids based on the similarity of independent modal quantities by introducing a modal transformation matrix for independently operated positive and negative poles

referred to as the independent modal transformation TD. Firstly

the fault characteristics of a bipolar DC system with metallic return under source-grid coordinated current limiting are derived

and equivalent networks of composite modal components for different fault conditions under the TD transformation are established. On this basis

the Fréchet distance is introduced to measure the similarity of modal currents at both ends of the line

thereby enabling reliable discrimination between internal and external faults

while a faulted-pole selection criterion is constructed based on the TD transformation. Finally

the logic and procedure of the pilot protection scheme are designed by integrating fault identification and faulted-pole selection. A four-terminal flexible DC grid simulation model is built in PSCAD/EMTDC. Simulation results show that the proposed protection scheme requires only a 2 ms time window to discriminate between internal and external faults and is only slightly affected by distributed capacitance

fault current limiting

and communication delay. The proposed faulted-pole selection criterion is unaffected by fault resistance and fault current limiting

and offers a significant sensitivity advantage.