Ileana-Diana Nicolae

Performances evaluation of a class of original discrete wavelet transform based hybrid algorithms

The paper 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 respectively 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 provided. These algorithms can be used in all regimes and provide the fast “perfect reconstruction” property. Considering the results and other important criteria (run time, memory consumptions), practical recommendations are made with respect to the selection of a proper reliable and fast DWT algorithm depending on the operating conditions.

Instantaneous power theory applied to power conditioning under distorted mains voltages: A MATLAB/simulink approach

The paper presents some problems and solutions for instantaneous power theory applied to active power conditioning under distorted mains voltages in a MATLAB/Simulink approach. Simulation of a real system is made, namely a transformer which feeds a controlled rectifier bridge in an excitation system from a power system generator group, based on measurements acquired with a dedicated data acquisition system. Replacing the old auxiliary excitation generator eliminates the disadvantage of using electrical machines with the mass in motion inertia and wear over time, but with the price of facing two important problems: the line voltage notching due to thyristor switching and also the distorting of line current. The MATLAB/Simulink model allows for testing the instantaneous power theory implementation and dealing with problems arising with distortion of mains voltages, respectively observing its effectiveness based on the results.

Using Discrete Wavelet Transform to analyze quasi-stationary three-phase systems

The paper deals with the Discrete Wavelet Transform (DWT) analysis of quasi-stationary regimes (with small variations of magnitude and harmonic contents) in three-phase systems. The analyzed data, acquired on stand, correspond to a driving system using chopper and DC motor. Unfiltered currents are included in the first data set, unlike those from the second set. The harmonic orders to be filtered (5,7,11,13 etc.) were determined using a FFT analysis. 10 levels decompositions using DWT were made, using Daubechy filters of length 8, implemented by 2 functions. “dwm” assumes that the analyzed signal is periodic, whilst “dwi” performs interpolations to estimate the first 6 values of the decomposed signal beyond its right edge. During analysis, FFT is applied over one period P, whilst DWT operates over 6 consecutive periods starting with P. The analysis concerns instantaneous and global power quality related quantities and provides possible explanations for the cases when differences appear between the results yielded by the various analyzed methods.

Dealing with noise polluting electric signals acquired from a large power group

The paper is focused on finding appropriate procedures of denoising electrical signals (SN) acquired from the secondary winding of the excitation transformer in a large power group and evaluating their benefits. The signals were affected by white Gaussian noise with relatively high Signal to Noise ratios. The currents have significant harmonic contents (total harmonic distortions exceeding 25%). Two sets of 30 consecutive periods from quasi-stationary data, corresponding to different active powers, were analyzed. Firstly “average” signals (AS) of one period length were determined in order to obtain estimated values for the power of noise (EPN). Computations were made afterward by using the 1-st periods from the acquired signals in order to establish the best denoising parameters, considering the EPN and the root mean square differences relative to the AS when compared to signals denoised (SD) in different ways. Once determined the denoising parameters, the 1-st periods from SN, AS and SD were analyzed by using original FFT based programs in order to evaluate power quality (PQ) indices of all types of signals. Conclusions were drawn relative to the effects of denoising over the accuracy in evaluating PQ indices.

Denoising highly distorted small currents in an environment with variable levels of noise

The paper is focused on finding appropriate and systematic procedures of denoising highly distorted small currents with significant “signal to noise” ratios and on evaluating the denoising effects over the power quality (PQ) indices. Real currents were acquired from 2 consumers placed in a small industrial hall with highly variable power consumptions. Denoising procedures relying on wavelet based decomposition trees were considered. First evaluations were made for determining parameters like: number of levels in the tree, method of thrashing and type of level noise estimation. Best results were obtained with a tree having 4 levels, considering a white Gaussian noise and performing “per each tree level” estimation of the noise power. With this tree, acquired signals were denoised considering 4 of the most commonly used wavelet mothers, consequently obtaining sets of 4 different noise signals per acquired signal. An average noise signal was used to get an estimated noise powers. For each acquired signal, sets of 10 Gaussian noises with powers identical to the above mentioned estimations were randomly generated and used to determine in an original (statistical) way the best wavelet mother. FFT based programs were used to evaluate PQ indices of the acquired signals before and after denoising. In the denoised signals all total RMS values were found to be smaller, whilst harmonic spectra for orders with weights > 1% were less affected in the low harmonic range (orders<70), certifying the nature of noise and the denoising procedure. The total harmonic distortions were slightly diminished by denoising.

Practical aspects related to paired nodes and paired harmonics in WPT analysis

Aspects of evaluating even harmonics by exploiting characteristics of energies produced by them in the terminal nodes of a tree determined with the WPT are approached. Two wavelet mothers (WM) were analyzed. db14 involves smaller runtimes, but the per-node weights of “node-dominant” harmonics have often smaller values when compared to those yielded by db20. For both WM, 14 nodes from the final level could be grouped in pairs considering that: energies of nodes in a group G are affected only by a pair of odd harmonics and the paired corresponding harmonics affect only the nodes from G. The weights of energies generated by signals polluted by a single harmonic remain constant for a certain node. When the paired harmonics acted jointly, the weights vary. Therefore a harmonic evaluation based on the solving of linear systems yields sometimes high errors and negative energies. Lookup table techniques were conceived and tested. Tests considered sets of 50 signals. Statistics on errors were computed. For the pair of harmonics (3,5) and (59,61), usually it is enough to solve the associated linear system, the use of lookup techniques becoming compulsory only when negative energies are obtained. Otherwise the lookup techniques represent a better option.

DWT analysis of high order harmonics influence over distorted regimes with fast variable loads

The paper studies high order harmonics in distorted regimes with fast variable loads. Our experimental setup uses a three-phase load, built in laboratory by connecting in pairs, in different configurations, several laptops (from different manufacturers) across phases of a three-phase system. Our original dedicated data acquisition system acquired single phase waveforms, each of 5 periods, corresponding to phase currents and voltages, with a sampling frequency of 19 kHz. The acquired data were decomposed with a Discrete Wavelet Transform relying on our original function implementing a Daubechy filter of length 8. Considering the high variable operating regimes of laptops, the analysis was made individually for the first 4 periods of each analyzed sequence. Per period validations were performed considering the total RMS, calculated firstly according to definition, with a definite integral as the limit of a Riemann sum, and secondly as defined by Morsi, with DWT. 3-D diagrams were built to represent, for each level, the weights of details energy that we used as power-quality indices. The DWT analysis revealed that the weights of energies provided by harmonics with orders higher than 32 (sometimes 64) cannot be neglected when considering the signals overall distorting residue, mainly for voltages. Transients were also detected on high order harmonics and the unbalance generated by them in the energetic picture was also discussed.

Performance comparison between active and passive power filters for a static excitation system in a power generator group: A MATLAB/Simulink approach

This paper presents a comparison of the performances related to compensation and transient response of active and passive power filters when operation relies on distorted mains voltages. MATLAB/Simulink models are used. Measurements acquired with a dedicated data acquisition system provided the parameters required by the real system simulation, namely a static excitation system of a power generator group. The simulated system consists of a transformer which feeds a controlled rectifier bridge. Replacing the old auxiliary excitation generator raises two important problems: the line voltage notching due to thyristors switching and additional line current distortion. Theoretical aspects of line notching and passive and active solutions for compensation and their limitations are also discussed.

Using stationary wavelet transform to evaluate the instantaneous components of fundamental frequency

The capabilities related to active filtering of the Stationary Wavelet Transform — SWT were evaluated considering 3 Daubechy wavelet mothers. Firstly a study on errors was performed on synthetic waveforms. The waveforms were obtained from sinusoids polluted by single harmonics with orders from the range 3…40 and magnitudes, respectively phase differences varied in a systematic manner. The differences between the fundamental components (synthetic vs value yielded by SWT) were evaluated with 2 metrics: extreme values and RMSD. 3D representations of the metrics are provided, along with a study of instantaneous values of errors. Afterward 3 sets of signals polluted by 4 harmonics were decomposed. Low harmonics, high harmonics and respectively mixed harmonics were used. A study of errors was performed again. At the end the algorithm was applied over real data. A comparison to FFT analysis results was made. Conclusions on the usability of each of the studied wavelet mother are drawn.

Limits and usability of fast Fourier, Discrete wavelet and wavelet packet transforms applied at signals from a primary winding of a locomotive transformer

Single phase currents and voltages were acquired from the primary winding of a locomotive transformer. Four operating regimes were considered (acceleration, running at constant speed, normal and respectively regenerative braking). 6 data sets consisting of 3 consecutive periods were considered as representative for this study and analyzed: one per each of the first 3 mentioned operating regimes and 3 for the regenerative braking. Fast Fourier Transform) and Wavelet Packet Transform were used to evaluate the harmonic spectra, Discrete Wavelet Transform was used to plot the instantaneous variations over frequency ranges of the distortions and all methods were used to evaluate the 3 major root mean square values (for fundamental frequency, for distorting residue and total). Total harmonic distortions were also evaluated. The results yielded by different methods were compared. A good convergence of methods was noticed. Explanations for the small differences are proposed.