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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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The p a p er is concerned with the analysis based on the Discrete Wavelet Transform (DWT) of (non)stationary regimes in power systems. Different techniques are employed to perform decompositions using trees with 10 levels for different signals in (non)stationary regimes. The abilities of different methods to detect faults and res p ectively to deal with severe asymmetries are discussed. Power indices are calculated with different methods. A class of original hybrid algorithms is described, analyzed and discussed, generalization being p rovided. These algorithms can be used in all regimes and provide the fast "perfect reconstruction" property. Considering the results and other im p ortant criteria (run time, memory consum p tions), p ractical recommendations are made with res p ect to the selection of a p ro p er reliable and fast DWT algorithm de p ending on the operating conditions.

Decompositions relying on trees used to implement the Wavelet Package Transform (WPT) provide numerous advantages but require a significant runtime. When the parameters of relatively narrows ranges of harmonic orders change, only few vectors from the final nodes and the vectors hosted by the associated "parent nodes" from upper levels are affected. The counterpart decomposition relying on a tree which implements the Discrete Wavelet Transform (DWT) with the same number of levels requires a 20 times smaller runtime. An estimation of the energetic sensitivity of all DWT details vectors to harmonic orders from the interval [2,256] was made. Both types of trees were connected by means of harmonic orders affecting the levels in the DWT tree and terminal nodes in the WPT tree. Through an original labeling of the WPT nodes, 18 topologies of WPT subtrees were deduced. These subtrees correspond to individual levels or to pairs/triplets of adjacent levels from the DWT tree. Tests on synthetic and real signals validated the DWT/WPT trees based algorithm used to perform faster identification of harmonic orders whose magnitudes change from one period to another. Runtime savings varying from 90% to 10% were obtained.