When overhead lines are impacted by lightning, the traveling wave of the fault contains a wealth of fault information. The accurate extraction of feature quantities from transient components and their classification are fundamental to the identification of lightning faults. The extraction process may involve modal aliasing, optimal wavelet base issues, and inconsistencies between the lightning strike distance and the fault point. These factors have the potential to impact the effectiveness of recognition. This paper presents a method for identifying lightning strike faults by utilizing Kullback−Leibler (KL) divergence enhanced Variational Mode Decomposition (VMD) and Symmetric Geometry Mode Decomposition (SGMD) improved with Permutation Entropy (PE) to address the aforementioned issues. A model of a 220 kV overhead line is constructed using real faults to replicate scenarios of winding strike, counterstrike, and short circuit. The three-phase voltage is chosen and then subjected to Karenbaren decoupling in order to transform it into zero mode, line mode 1, and line mode 2. The zero-mode voltage is decomposed using KL-VMD and PE-SGMD methods, and the lightning identification criteria are developed based on various transient energy ratios. The research findings demonstrate that the criteria effectively differentiate between winding strike, counterstrike, and short-circuit faults, thus confirming the accuracy and efficacy of the lightning fault identification criteria utilizing KL-VMD and PE-SGMD.