To address the challenge of identifying traveling waves with different components, including fault point incident waves, reflected waves, and waves reflected by AT, which makes fault location on all parallel AT traction networks difficult, this paper proposes a wave similarity-based fault location method using Adaptive Projection Intrinsically Transformed Multivariate Empirical Mode Decomposition (APIT-MEMD). The APIT-MEMD algorithm is applied to adaptively decompose the fault signals of multi-conductor lines in both directions to extract transient high-frequency characteristics representing different components of fault traveling waves. By constructing the cross-correlation function matrix of different wave mode components to identify traveling waves along different paths and calculating the corresponding maximum time delay of the cross-correlation function, the fault location of the traction network's traveling waves is achieved. Experimental results demonstrate that the proposed method, based on time-frequency mode feature extraction, achieves fault location accuracy within 102 m with an average absolute error of 49 m.Compared with the results of different projection parameters in the multi-dimensional empirical mode decomposition algorithm, the effectiveness of fault location accuracy is optimized. The optimized fault location algorithm meets the requirements for high-precision fault location.