A VMD-GST-SDEO-Based Double-Ended Traveling-Wave Accurate Fault Location Method for Single-Phase-to-Ground Faults in Distribution Networks

A double-ended traveling-wave accurate fault location method based on variational mode decomposition (VMD), generalized S-transform (GST), and a symmetric difference energy operator (SDEO) is proposed for single-phase-to-ground faults in small-current grounding distribution networks. The method is designed for fault conditions in which the fault current amplitude is low, the transient duration is short, and the initial traveling-wave wavefront is easily affected by high-frequency oscillation, reflection, refraction, and noise. The three-phase voltage traveling waves measured at both ends of the fault section are first transformed using Clarke modal transformation, and the voltage line-mode component is selected as the input signal. VMD is then used to decompose the nonstationary traveling-wave signal into several finite-bandwidth intrinsic mode functions. The high-frequency mode containing the initial wavefront mutation is processed using the generalized S-transform to enhance local time–frequency features. Finally, the SDEO instantaneous energy spectrum is used to calibrate the initial wavefront arrival time. For distance calculation, an improved double-ended traveling-wave location formula based on the horizontal section length and the absolute propagation time ratio at both line ends is constructed. This formulation reduces the dependence on a fixed empirical wave velocity and weakens the influence of line length deviation caused by practical line geometry. The method is verified using a deterministic PSCAD/EMTDC v5.0.2 and MATLAB R2021b co-simulation model with a fixed distribution network topology and arc-suppression-coil grounding. The tested cases cover selected fault distances, transition resistances, and fault inception angles. The simulation results show that the absolute location error remains within 100 m under all tested deterministic cases. The representative location error is 15 m at the 2.5 km fault point, 45 m under a 500 Ω transition resistance at the 1.5 km fault point, and 11 m under a 90° fault inception angle at the 6.15 km fault point. Compared with EMD-TEO, VMD-TEO, and VMD-GST, the proposed VMD-GST-SDEO method provides more stable wavefront calibration and lower location error in the studied cases. The results indicate the feasibility of the proposed approach within the stated simulation scope; further validation under stochastic noise, synchronization error perturbation, different sampling frequencies, and measured field waveforms is still required for engineering deployment. The fundamental novelty of the study lies in the task-oriented integration of VMD, GST, and the SDEO as a complete wavefront calibration chain and in coupling this chain with a propagation-time-ratio-based double-ended location formula for small-current grounding distribution networks, rather than in treating VMD, GST, or the SDEO as new standalone signal-processing algorithms.