Dynamic Time Warping-Based Differential Protection Scheme for Transmission Lines in Flexible Fractional Frequency Transmission Systems

The integration of large-scale offshore wind power, facilitated by Flexible Fractional Frequency Transmission Systems (FFFTS), presents significant challenges for traditional transmission line protection. The fault current fed by the Modular Multilevel Matrix Converter (M3C) exhibits weak-infeed and controlled characteristics during faults, severely degrading the sensitivity of conventional current differential protection. Moreover, the stringent synchronization requirement for data from both line ends further compromises reliability. To address this issue, this paper proposes a novel differential protection scheme based on the Dynamic Time Warping (DTW) algorithm. The method leverages the DTW algorithm to quantify and compare the variation trends of current waveforms on both sides of the line before and after a fault. By utilizing the pre-fault current as a reference sequence, the scheme constructs a protection criterion that is inherently insensitive to synchronization errors. A key innovation is its capability for fault identification and phase selection under weak synchronization conditions. Simulation results demonstrate that the proposed scheme operates correctly within 0.5 ms, exhibits high sensitivity with a DTW ratio significantly greater than 2.0 during internal faults, and remains stable during external faults. It also shows strong robustness against high transition resistance, noise interference, and current transformer sampling errors.