A travelling-wave directional protection method for submarine cable MMC-HVDC lines based on frequency-dependent differential-mode wave impedance

A travelling-wave directional protection method based on frequency-dependent differential-mode wave impedance is proposed for submarine cable MMC-HVDC lines. By establishing a frequency-dependent differential-mode wave impedance model and applying rational fitting, the forward/backward travelling-wave coupling relationship is transformed into a time-domain discrete recursive convolution form for fast wave decomposition. An amplitude consistency correction is introduced to improve feature comparability, and an energy-ratio-based directional criterion is constructed using initial wave arrival-time gating and sliding-window energy accumulation. Tests on the Rudong offshore wind power MMC-HVDC simulation model under various fault and non-fault transient conditions verify that the proposed method provides good reliability and selectivity for fast directional protection of submarine cable MMC-HVDC lines.