This study deals with the faults’ detection and classification in AC transmission lines based on power spectral density (PSD), introducing PSD in time and frequency for analysing transient information under faulted conditions. The discrete wavelet transform is used for scaling current signals in time–frequency at different decomposition levels by approximation and detail coefficients. Then, a wavelet‐covariance matrix is shaped with the aim to obtain its PSD, being this the key to detect and classifying faults. Results show that the proposed method attains the detection in a short time and the classification is accomplished via the Hellinger distance, whose straightforward implementation is carried out in this study. The classification process is compared adopting different classifiers to cope with a set of signals in a time frame. Finally, the proposal is extensively assessed using real and simulated signals stemming from multiple fault cases of radial and interconnected power grids.