The precision of fault line identification plays a pivotal role in ensuring the secure and reliable functioning of the power distribution system. The current study introduces a novel approach to identify the single-phase fault location within a low-current power system, employing a hybrid method that integrates particle swarm optimization with variational mode decomposition. In addition to linear models such as logistic regression, we can also integrate Support Vector Machines (SVM) into our predictive framework. Initially, the variational-mode decomposition method is applied to a transient zero-sequence signal originating from the line within small current grounding systems following a fault. This approach successfully addresses the challenge of feature extraction in a dynamic, noisy power grid environment. Subsequently, a fault-line identification methodology is developed that integrates the principles of particle swarm optimization with the computational power of support vector machine neural networks. Once the data is processed and transformed into a structured format, the model undergoes rigorous training and validation phases using this fault-specific dataset to ensure optimal performance. The experimental outcomes validate the precision and speed of this approach in identifying fault lines, as demonstrated through a comprehensive simulation study.