Purpose -A highly accurate method of current spectrum estimation of a nonlinear load is presented in this paper. Using the method makes it possible to evaluate the current injection frequency domain model of a nonlinear load from previously recorded time domain voltage and current waveforms. The paper aims to discuss these issues. Design/methodology/approach -The method incorporates the idea of coherent resampling (resampling synchronously with the base frequency of the signal) followed by the discrete Fourier transform (DFT) to obtain the frequency spectrum. When DFT is applied to a synchronously resampled signal, the spectrum is free of negative DFT effects (the spectrum leakage, for example). However, to resample the signal correctly it is necessary to know its base frequency with high accuracy. To estimate the base frequency, the first-order Prony's frequency estimator was used. Findings -It has been shown that the presented method may lead to superior results in comparison with window interpolated Fourier transform and time-domain quasi-synchronous sampling algorithms.Research limitations/implications -The method was designed for steady-state analysis in the frequency domain. The voltage and current waveforms across load terminals should be recorded simultaneously to allow correct voltage/current phase shift estimation. Practical implications -The proposed method can be used in case when the frequency domain model of a nonlinear load is desired and the voltage and current waveforms recorded across load terminals are available. The method leads to correct results even when the voltage/current sampling frequency has not been synchronized with the base frequency of the signal. It can be used for off-line frequency model estimation as well as in real-time DSP systems to restore coherent sampling of the analysed signals. Originality/value -The method proposed in the paper allows to estimate a nonlinear load frequency domain model from current and voltage waveforms with higher accuracy than other competitive methods, while at the same time its simplicity and computational efficiency is retained.
Results of analysis of transient states in a series circuit of the class RL β C α , supplied by an ideal voltage source, have been described in the paper. This circuit consists of a coil L β and a supercapacitor C α described by fractional-order differential equations. A method for determining the current and voltage waveforms in the analyzed circuit, based on the decomposition of rational functions into partial fractions, has been described. This method allows to determine transient waveform shapes in the system for any kind of voltage excitation. Two cases of the problem solutions have been considered. The first case concerns a situation where poles of rational functions are real, and the second where rational functions have complex poles. Effective relations enabling the determination of transient waveforms in a closed form have been given. Analytical formulae describing transient state waveforms in the system for different types of voltage excitations: constant, monoharmonic, periodic and arbitrary being an element of a Hilbert space, have been determined, too. The obtained results have been illustrated by an example.
Abstract-Some new approaches to active compensator allocation and sizing in distribution networks have been proposed in the paper. A few objective functions as well as their advantages and disadvantages have been given. Moreover, software which enables practical verification of the strategies has been described.
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