Stationary Harmonics Research Articles

Wavelet Packet Decomposition for IEC Compliant Assessment of Harmonics under Stationary and Fluctuating Conditions

This paper presents the validation and characterization of a wavelet based decomposition method for the assessment of harmonic distortion in power systems, under stationary and non-stationary conditions. It uses Wavelet Packet Decomposition with Butterworth Infinite Impulse Response filters and a decomposition structure, which allows the measurement of both odd and even harmonics, up to the 63rd order, fully compliant with the requirements of the IEC 61000-4-7 standard. The method is shown to fulfil the IEC accuracy requirements for stationary harmonics, obtaining the same accuracy even under fluctuating conditions. Then, it is validated using simulated signals with real harmonic content. The proposed method is proven to be fully equivalent to Fourier analysis under stationary conditions, being often more accurate. Under non-stationary conditions, instead, it provides significantly higher accuracy, while the IEC strategy produces large errors. Lastly, the method is tested with real current and voltage signals, measured in conditions of high harmonic distortion. The proposed strategy provides a method with superior performance for fluctuating harmonics, but at the same time IEC compliant under stationary conditions.

The Use of a Modified Prony Method to Track the Broken Rotor Bar Characteristic Frequencies and Amplitudes in Three-Phase Induction Motors

The knowledge of the broken rotor bar characteristic frequencies and amplitudes has a great importance for all related diagnostic methods. The monitoring of motor faults requires a high resolution spectrum to separate different frequency components. The discrete Fourier transform (DFT) has been widely used to achieve these requirements. However, DFT can give meaningful information only for stationary harmonics which cannot be guaranteed in real cases. In addition, a long data sequence is necessary for DFT to get high frequency resolution. Nevertheless, the signals are time varying, and the steady-state conditions can be lost for a long time acquisition. As a solution for these problems, this paper proposes an efficient time-domain technique based on a modified Prony method for the estimation of the frequencies/amplitudes of broken rotor bar faults. Using this technique, the stator current is divided into short overlapped time windows, and each one is analyzed by the least squares Prony method. The proposed technique provides a linear time–frequency/amplitude representation with high frequency resolution and adjustable time resolution. It is shown that this technique allows tracking the frequencies and amplitudes of the sidebands around the fundamental frequency component with a very high accuracy. The efficiency of the proposed method is verified by simulation and experimental tests.

Non-Stationary Harmonics Analysis Based on Wavelet Packet Transform and Neural Network

The method for analysis of stationary harmonics in power system is FFT, but it is unsuitable for non-stationary harmonics. Because of the feature that non-stationary harmonics’ frequency spectrum has a certain bandwidth and with some noise interference usually. A new method for detection, based on wavelet packet transform and neural network was presented in this paper. This method improved the traditional wavelet analysis method. The non-stationary harmonics were decomposed in different frequency bands by wavelet packet transform at first, and then complete the analysis of the non-stationary harmonic in different frequency bands. Through software simulation, the analysis results show that, the method has better accuracy, and provided an effective means for analyzing non-stationary harmonics.

Power quality index based on discrete wavelet transform

Changing power system regulations and increased use of nonlinear devices have made power quality (PQ) a highly important issue. The short duration transient disturbances, along with the stationary harmonics have become very common due to the increased use of power electronic switches. These transients are defined in terms of their spectral content, duration and magnitude by IEEE 1159-2009 standards and are non-stationary in nature. The conventional PQ indices based on Fourier transform fails to indicate them, since Fourier transform gives amplitude frequency distribution and the time information gets void. In this paper, a PQ index, based on discrete wavelet transform (DWT) is proposed in order to determine the amount of deviation from the desired pure signal. The proposed PQ index is defined as the weighted sum of percentage energy deviation of the DWT details. The test system is simulated using ATP/EMTP software. Transients resulted from ten different switching instants covering a full cycle of the signal and having natural frequency ranging from 500Hz to 47kHz, are considered to validate the proposed index. The proposed index is also tested with the signals containing harmonics. Further, the proposed index is verified with the real signals acquired by the laboratory experimentation.

Auditory segregation of competing voices: absence of effects of FM or AM coherence.

Four experiments sought evidence that listeners can use coherent changes in the frequency or amplitude of harmonics to segregate concurrent vowels. Segregation was not helped by giving the harmonics of competing vowels different patterns of frequency or amplitude modulation. However, modulating the frequencies of the components of one vowel was beneficial when the other vowel was not modulated, provided that both vowels were composed of components placed randomly in frequency. In addition, staggering the onsets of the two vowels, so that the amplitude of one vowel increased abruptly while the amplitude of the other was stationary, was also beneficial. Thus, the results demonstrate that listeners can group changing harmonics and can segregate them from stationary harmonics, but cannot use coherence of change to separate two sets of changing harmonics.

Continental elevation influence on the stationary harmonics of the atmospheric motion

The effect of lifting of a latitudinally uniform zonal current of air by the continental elevations, on the stationary harmonics of the atmospheric motion, is investigated. Use of spherical harmonics up to the 15th degree is made within the framework of a simple quasigeostrophic linear theory. The results indicate that such an effect, though significant, cannot alone explain the observations. Some other interesting points regarding some of the assumptions involved (e.g., regarding the Coriolis parameter) are discussed.