Multi-Terminal Unsynchronized Fault Location for Distribution Networks Based on MM and SVR–PSO Hybrid Optimization

Complex distribution-network topologies limit the accuracy of traveling-wave fault location, because the zero-mode velocity decays nonlinearly while conventional double-ended methods still require synchronized clocks. A clock-offset-invariant multi-terminal scheme combining mathematical morphology (MM), support vector regression (SVR), and particle swarm optimization (PSO) is proposed to remove dependence on double-ended synchronization and constant zero-mode velocity. SVR first fits the nonlinear mapping between fault distance and zero-mode velocity to establish a velocity-decay predictor. Backward fault-current traveling waves measured at multiple nodes are then processed through cycle subtraction and dynamic-window denoising, constrained by the underlying zero-mode physics. A morphological-gradient operator identifies the line- and zero-mode arrival times, from which a cross-dispersion sum-of-products equation that eliminates zero-mode velocity is constructed. Preliminary auxiliary-node solutions are obtained, and PSO performs a global search by minimizing the residual between the measured modal time difference and the theoretical value obtained from the SVR-predicted velocity. Weighted fusion yields the final fault distance. Simulations of a 35 kV distribution network in the power systems computer-aided design/electromagnetic transients including DC (PSCAD/EMTDC) environment show that the method maintains high accuracy at different fault locations and under high transition resistance within the tested parameter range, demonstrating adaptability and reliability under these conditions.