To address the challenge of identifying traveling wave components, including fault point incident waves, reflected waves, and waves reflected by auto-transformer (AT), which complicates fault location in all-parallel AT traction networks, 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 fault signals from multi-conductor lines in both directions to extract transient high-frequency characteristics representing different components of fault traveling waves. By constructing the cross-correlation coefficient matrix of different wave mode components to identify traveling waves along different paths and calculating the corresponding maximum time delay, fault location in the traction network is achieved. Experimental results demonstrate that the proposed method, based on time-frequency mode feature extraction, achieves a fault location error within 102 m with an average absolute error of 49 m. Compared with the results of the multivariate empirical mode decomposition (MEMD) algorithm using different projection parameters, the proposed method effectively improves fault location accuracy.