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The paper is concerned with the analysis based on the Discrete Wavelet Transform (DWT) of (non)stationary regimes in power systems under real-time operation constraints. Different techniques (some original, other provided by Matlab) are employed to perform decompositions using trees with 10 levels for a signal in stationary regime and respectively in a complex non-stationary regime, when most of the signal's parameters are affected (shape, periodicity, magnitude etc). Power indices are calculated in both regimes with different methods, correlating the results with the energetic evaluations. The abilities of different methods to detect faults and respectively to deal with severe asymmetries are analyzed in various situations. Considering the results and other important criteria (run time, memory consumptions, perfect reconstruction), practical recommendations are made with respect to the selection of the fastest reliable DWT algorithm depending on the operating conditions.