In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA), is proposed. This powerful tool permits, in n-sinusoidal/ nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetz's phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach.
The Fourier transform can be used for analysis of nonstationary signals, but the Fourier spectrum does not provide any time-domain information about the signal. When the time localization of the spectral components is needed, a wavelet transform giving the time-frequency representation of the signal must be used. In this paper, using wavelet analysis and neural systems as a new tool for the analysis of power system disturbances, disturbances are automatically detected, compacted, and classified. An example showing the potential of these techniques for diagnosis of actual power system disturbances is presented.
For three-phase four-wire circuits, two compensation criteria have been established: one based on the instantaneous value concept and the other on the average value concept. Thus, according to the instantaneous value concept the non instantaneous power current is reduced, without altering the instantaneous active power. According to the average value concept, the nonactive average-current is reduced, without altering the average power. When the zero-sequence voltage component exists, both compensation types would not enable the zero-sequence (neutral) source current elimination. Then, two approaches are marked in this paper. The first one is for eliminating the non instantaneous power current or the nonactive average-current but the neutral current can still flow. The second one for eliminating the modified non instantaneous power current or the modified nonactive average-current, thus the neutral current component is compensated. According to recent recommendations in this work three-phase systems are considered as four-conductor systems. Experimental results are obtained to confirm the theoretical properties and to show the compensator performance.Index Terms-Active power-line conditioner, compensation, instantaneous power theory.
Funbental results of the generalized instantaneous power theory have been applied for power factor correction in three-phase systems. Instantaneous and full compensation were considered to set the differences between compensation in general conditions (periodic or non-periodic waveforms) and compensation in steady states @eriodic waveforms). An active power filter is simulated as reactive power compensator to confirm the theory.
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