Two-Terminal Fault Location of MMC-HVDC Flexible Direct Current Transmission Lines Based on WOA-VMD-WSST

Accurate identification of the initial traveling wavefront is essential for two-terminal fault location in modular multilevel converter-based high-voltage direct-current (MMC-HVDC) lines. This study develops a coordinated processing chain that combines a signed-pole modal transformation, offline whale optimization algorithm (WOA) calibration of variational mode decomposition (VMD), wavefront-sensitive intrinsic mode function (IMF) pairing, wavelet synchrosqueezing transform (WSST) diagnostics, and fractional-delay cross-correlation. A common VMD parameter pair is calibrated for both terminals. Candidate IMFs are then screened using wavefront-retention and frequency-consistency constraints. The final time difference is estimated from three fixed correlation windows after band-limited resampling and local parabolic peak refinement. This procedure estimates a sub-sample delay but does not increase the measurement bandwidth. The method is evaluated on a 200 km, 500 kV MMC-HVDC simulation model. The 10 kHz validation matrix contains 36 combinations of four fault types, three fault locations, and three fault resistances. The mean absolute error is 0.374 km, 34 of 36 errors are below 1 km, and the maximum error is 0.920% of the line length. A separate 10/50/100 kHz study evaluates the complete processing chain at all three rates. At the 100 km reference location, the complete method gives a mean absolute error of 0.148 km. The corresponding values are 0.213 km without modal transformation, 11.062 km with fixed VMD parameters, and 0.414 km when CWT replaces WSST. Direct line-mode and WTMM sample-level baselines each give a three-location mean absolute error of 3.433 km. The results support the coordinated design within the tested simulation envelope; noise, synchronization, wave-speed uncertainty, and near-terminal faults require further validation. A six-case robustness matrix with 540 noise realizations gives valid-location rates of 94.4%, 92.8%, and 89.4% at 40, 30, and 20 dB, respectively, with accepted-case median errors of 0.170, 0.181, and 0.270 km. Controlled synchronization, wave-speed, and combined-uncertainty tests further quantify the applicable error envelope.