To address the issue of noise sensitivity of the wavelet decomposition modulus maxima algorithm

an energy operator is introduced to measure the frequency-weighted instantaneous energy of signals

and multi-scale signal synthesis is employed for transient mutation detection. Considering the drawbacks of the Teager energy operator (TEO)

such as negative energy values and instability of second-order derivative

a first-order envelope-derivative operator (EDO) is proposed to achieve non-negativity and numerical stability of the extracted energy across different scales. An algorithm for pointwise multiplication of multi-scale non-negative energy values is further introduced to achieve the detection of frequency-weighted instantaneous energy under multiple scales. In addition

an even-symmetric B-spline wavelet function is combined with the EDO to further enhance fault location accuracy. A distribution network model is built in PSCAD/EMTDC

and simulation data under various fault conditions are used for validation. The results demonstrate that the proposed algorithm can effectively extract traveling wave head features

and exhibits strong stability

excellent noise immunity

and high fault location accuracy

with errors controlled within 0.05%

demonstrating strong practical applicability.