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The development of complex continuous wavelet transform based harmonic analysis and dynamic waveform reconstruction algorithms

Tse Chung Fai, N. (2007). The development of complex continuous wavelet transform based harmonic analysis and dynamic waveform reconstruction algorithms. (Unpublished Doctoral thesis, City, University of London)


The wide spread use of power electronic equipment has been causing serious current harmonics in electrical power distribution system. Harmonic currents that flow in the electrical power distribution system would cause extra copper loss and immature operation of overcurrent protection devices. Voltage distortion due to harmonic voltage drop in the electrical power distribution system impairs the operation of voltage sensitive equipment. The harmonic distortion of the current and voltage waveforms can be caused by sub-harmonics, integer harmonics and inter-harmonics. Traditionally harmonic distortions are predominately caused by integer harmonics. With the advance of power electronic technology, the amount of sub-harmonics and inter-harmonics are rising and cause problems not experienced before.

In order to improve the electrical power quality and reduce energy wastage in the electrical power distribution system, especially under the deregulated environment, the nature of the harmonics must be identified so that the causes and effects of the harmonics would be studied. Moreover corrective measures cannot be easily implemented without knowing the characteristics of the harmonics existing in the electrical power distribution system.

Power harmonic analysis in electrical power distribution system is essentially related to the topic of waveform distortion analysis commonly encountered in signal processing. Waveform distortion analysis relates to the identification of all harmonics components, including sub-harmonics, integer harmonics and inter-harmonics. Harmonics identification consists of identifying harmonic frequencies, amplitudes and instantaneous phases. In classical signal processing, waveforms are classified into stationary (time-invariant) waveforms and non-stationary (time-variant) waveforms. For non-stationary waveforms, time information is also required.

Traditionally Discrete Fourier Transform (DFT) implemented with Fast Fourier Transform (FFT) is used to analyze stationary waveform distortions with integer harmonics. DFT is not suitable for analyzing waveform distortions caused by sub-harmonics and inter-harmonics. Short-time Fourier Transform (STFT) and Gabor Transform (GT) which are windowed version of DFT were developed for the analysis of time-variant waveforms.
These methods have their own usages and limitations. With STFT, one must compromise frequency resolution with time resolution, or vice versa. With GT, the accuracy lies in selecting the right time and frequency parameters, which cannot be done wisely without a prior knowledge of the waveform characteristics.

This thesis reports on the development of a new approach for harmonic analysis which is able to analyze distorted waveforms containing sub-harmonics, integer harmonics and inter-harmonics by identifying their respective harmonics frequencies, amplitudes and instantaneous phases. Wavelet Transform (WT) is used for the new approach. WT is a comparatively new mathematical tool originally developed for signal analysis, which have found applications in many areas of science and engineering. WT makes use of a wavelet which is an oscillating waveform of short duration with magnitudes decaying quickly to zero at both ends. WT is performed by shifting and dilating a mother wavelet. Dilating a mother wavelet varies the frequency of oscillation and time duration simultaneously, while the time duration of DFT is fixed. Shifting the dilated wavelet captures time information of the waveform. With these properties, the WT is most suitable for harmonic analysis. In particular, Continuous Wavelet Transform (CWT) is used for harmonic analysis because of its ability to identify harmonic frequencies accurately.

The simplified Complex Morlet Wavelet (CMW) is selected for the new approach introduced in this thesis. CMW is basically a sinusoid-modulated Gaussian function with harmonic-like shape and smooth decaying magnitudes. CMW achieves the best compromise between time and frequency localization, and therefore can identify frequency information and time information reasonably accurate. A modified CMW is introduced in this thesis which is better suited for harmonics analysis.

A WT-based harmonic analysis algorithm is developed based on the modified CMW, with detailed study on settings of the modified CMW parameters for discriminating adjacent frequencies, determining minimum sampling frequency and minimum harmonic signal duration. The proposed WT-based harmonic analysis algorithm is tested with synthesized waveforms and field harmonic waveforms vigorously. Harmonic analysis results obtained from DFT implemented with FFT are used to compare with the results obtained from the proposed WT-based algorithm.

Overall, the proposed algorithm is able to identify all harmonic components including integer, non-integer and sub-harmonics. Comparing with DFT, the proposed algorithm achieves exact estimation of the harmonic frequency, amplitude and phase of the harmonic components in power harmonic signals. The power harmonic signal length required by the proposed algorithm is much shorter than the DFT-based algorithm.

The thesis also reports on the development of a WT-based dynamic waveform reconstruction algorithm which is able to identify amplitude variations of harmonic components of the distorted waveform in the examined period. The performance of the WT-based waveform reconstruction algorithm is compared with the performance of the Discrete Waveform Transform based techniques which is used to reconstruct the fundamental frequency component only. It is found that the proposed algorithm is more accurate in reconstructing the waveform of the fundamental frequency component and can be used to reconstruct waveforms of any harmonic components.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Science & Technology > Engineering > Electrical & Electronic Engineering
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
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