Traveling-Wave-Based High-Speed Main Protection of Low-Frequency AC Submarine Cables with Analytical-Model-Based Offline Setting

Long-distance low-frequency alternating-current (LFAC) submarine cables exhibit pronounced high-frequency attenuation and dispersion, while background components generated by the modular multilevel matrix converter (M3C) complicate fault-wavefront extraction. This study proposes a single-ended traveling-wave primary protection scheme combining a Bergeron numerical model, variational mode decomposition (VMD), and the Teager energy operator (TEO). The Bergeron model is used offline to calculate theoretical wavefront counts for different fault locations and fault resistances. The most adverse offline result determines a unified fixed wavefront-count threshold for online protection. After the startup criterion is triggered, the 1-mode backward traveling wave within a 2 ms window is differentiated and normalized. VMD decomposes the signal into multiple modal components, and two informative modes are selected based on their energy contribution, wavefront characterization capability, and performance in the presence of noise to reconstruct the traveling-wave feature signal. TEO then maps the reconstructed signal into an energy sequence, where local peaks mark wavefront arrivals. An internal fault is identified when the measured wavefront count reaches the fixed threshold. Case studies conducted in PSCAD/EMTDC show that the starting criterion detects abrupt changes for single-phase grounding faults at different locations, and the proposed protection correctly distinguishes the tested internal and reverse external faults. The scheme operates correctly for all tested internal fault locations, including faults with fault resistances of up to 300 Ω, and remains secure for the tested reverse external faults.