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Summary form only given. Power components definitions contained in the IEEE Standard 1459-2000 for unbalanced three-phase systems with non-sinusoidal situations are represented in the frequency domain based on Fourier Transform (FT). However, FT suffers from the high computational effort especially when the number of phases increases and it is unable to provide information concerning time content because it provides only an amplitude-frequency spectrum. On the other hand, the Discrete Wavelet Transform preserves both time and frequency information while reducing the computational effort through dividing the frequency spectrum into bands and thus overcomes the limitations of FT. In this paper the three-phase power components definitions contained in the IEEE Standard 1459-2000 are reformulated using the DWT and thus redefined in the time-frequency domain. Also in order to study system unbalance, the concept of symmetrical components is defined in the wavelet domain. The results obtained from applying the IEEE Standard definitions and the DWT based definitions to balanced and unbalanced three-phase systems under non-sinusoidal operating conditions, indicate that the DWT based definitions are very accurate and the problem of spectral leakages can be reduced by suitable choice of the mother wavelet and the wavelet family. The DWT based definitions are useful in studying non-stationary waveforms.