A karrenbauer modulus transform-based protection method for metallic return flexible dc grids withstanding high-resistance faults

In the DC transmission system using metal return conductors, the coupling effect introduced by the neutral line makes the traditional traveling wave protection methods difficult to be directly applicable. In response to these challenges, this paper develops an innovative protection scheme for metallic-return grounded DC grids. First, the Karrenbauer transformation is combined with Bergeron line models to decouple the network, thereby enabling the establishment of equivalent models under various fault types. Subsequently, complex frequency domain expressions of DC fault component under various fault types are derived, concluding that transition resistance only impacts the magnitude of fault mode components, without influencing the negative value duration time. On this basis, a fault identification method is introduced that utilizes the negative value duration time of the modulus derivative voltage waveform, enabling differentiation between internal and external faults based on the temporal characteristics of the waveform response. Furthermore, a fault-type phase plane constructed from the ratio of modulus derivative current is introduced to enable selective protection. Finally, simulation and experimental studies confirm the effectiveness of the proposed scheme, demonstrating its high speed and robust reliability.