The power system is one of the most susceptible systems to failures, which are most frequently caused by transmission line faults. Transmission line failures account for 85% of all power system malfunctions. However, over the last decade, numerous fault detection methods have been developed to ensure the reliability and stability of power systems. A hybrid detection method based on the idea of redundancy property is presented in this paper. Because the continuous wavelet transform itself does not extract fault features for small defects effectively, the stationary wavelet transform approach is employed to assist in their detection. As a result of its ability to decompose the signal into high- and low-frequency components, undecimated reconstruction by using the algebraic summation operation (ASO) is used. This approach creates redundancy, which is useful for the feature extraction of small defects and makes faulty parts more evident. The numerical value of the redundancy ratio’s contribution to the original signal is approximately equal to 36%. Following this method for redundant signal reconstruction, a continuous wavelet transform is used to extract the fault characteristic significantly easier in the time-scale (frequency) domain. Finally, the suggested technique has been demonstrated to be an efficient fault detection and identification tool for use in power systems. In fact, using this advanced signal processing technique will help with early fault detection, which is mainly about predictive maintenance. This application provides more reliable operation conditions.