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The paper presents several theories related to definitions of powers and power factors in non-sinusoidal and non-symmetrical regimes. The theories must meet some requirements: (a) to facilitate the measuring of power quantities by using acquired electrical waveforms; (b) to support the correct quantification of powers and power factors for a fair charge; (c) to support solutions for efficient compensation of non-sinusoidal and non-symmetrical regimes, simultaneous with the power factor compensation along the fundamental harmonic. Only theories meeting the above-mentioned requirements are approached. Aspects specific to power definitions are discussed and commented. Three theories rely on the Fourier decomposition of non-sinusoidal waveforms, valid only for steady signals, whilst the fourth relies on the Discrete Wavelet Transform (DWT) and can also be applied to unsteady signals. Dedicated original data acquisition systems were used to acquire experimental data for three case studies. Data were analysed with original software tools, based on the Fast Fourier Transform and Discrete Wavelet Transform, implementing the approached theories. Comparisons between results yielded for analogue quantities proved that the approached theories satisfy the requirements for which they were created, except for the fourth theory, which can be used only for compensation purposes.

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