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The problem of a useful electrical power quantification in environments with power quality problems is discussed. As it is difficult to correctly apply a Fourier-based approach, alternative power quantifications in the time-frequency domain, based on a complex wavelet transform, are presented. Using the property that instantaneous amplitudes of voltages and currents as well as instantaneous phase differences can be obtained, power definitions with time and frequency localization properties are derived. The physical interpretation is given and a comparison with traditional formulae is made. Examples, with typical power quality problems, illustrating this methodology are given.