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  • Author: Jarosław Zygarlicki x
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Jarosław Zygarlicki and Janusz Mroczka

Variable-Frequency Prony Method in the Analysis of Electrical Power Quality

The article presents a new modification of the the least squares Prony method. The so-called variable-frequency Prony method can be a useful tool for estimating parameters of sinusoidal components, which, in the analyzed signal, are characterized by time-dependent frequencies. The authors propose use of the presented method for testing the quality of electric energy. It allows observation of phenomena which, when using traditional methods, are averaged in the analysis window. The proposed modification of least squares Prony method is based on introduction and specific selection of a frequency matrix. This matrix represents frequencies of estimated components and their variability in time.

Open access

Jarosław Zygarlicki and Janusz Mroczka

Short Time Algorithm of Power Waveforms Fundamental Harmonic Estimation With Use of Prony's Methods

This paper presents an example of practical use of Prony's method for monitoring of power waveform fundamental harmonic fluctuations, which is required for the analysis of window synchronizations in frequency analyses in power monitoring systems. The example presented offers verification of the authors' theoretical considerations published earlier in articles about Prony's method and its opportunities for practical use for real life signals. The investigations shown are based on the least squares Prony's method, which, in connection with digital filtrations, enables estimations of fundamental frequency at the rate of even tens of times per one fundamental harmonic period.

Open access

Jarosław Zygarlicki

Abstract

The paper presents a method of adaptation of the original second order Prony’s method for applications in lowcost digital measurement systems with low computing performance. The presented method can be used in measuring systems where it is important to obtain in real time the values of amplitude, frequency, initial phase and damping coefficient of a single sinusoidal component of an analysed signal. The paper presents optimized, in terms of the number of mathematical operations, implementation of the method in selected embedded devices as well as the calculation times of the method for each platform.

Open access

Anna Khoma and Jarosław Zygarlicki

Abstract

The paper presents a new method of surface topology reconstruction from a white light interferogram. The method is based on interferogram modelling by complex exponents (Prony method). The compatibility of white light interferogram and Prony models has already been proven. Effectiveness of the method was tested by modelling and examining reconstruction of tilted and spherical surfaces, and by estimating the reconstruction accuracy.

Open access

Jarosław Zygarlicki and Janusz Mroczka

Abstract

This article presents a way of analyzing the transfer function of electronic signal amplifiers. It also describes the possibility of using signal precorrection which improves the parasitic harmonics in the THD (Total Harmonic Distortion) of the amplified signal by correcting linearity of the tested amplifier’s transfer function. The proposed method of analyzing and presenting the transfer function allows to diagnose the causes of generating parasitic harmonics, what makes it a useful tool when designing low distortion amplifier systems, such as e.g. amplifiers in measurement systems. The presented THD correction can be used in e.g. amplifier systems that cooperate with arbitrary generators.

Open access

Jarosław Zygarlicki and Janusz Mroczka

Abstract

This paper presents a new modification of the least-squares Prony’s method with reduced sampling, which allows for a significant reduction in the number of the analysed signal samples collected per unit time. The specific combination of non-uniform sampling with Prony’s method enables sampling of the analysed signals at virtually any average frequency, regardless of the Nyquist frequency, maintaining high accuracy in parameter estimation of sinusoidal signal components. This property allows using the method in measuring devices, such as for electric power quality testing equipped with low power signal processors, which in turn contributes to reducing complexity of these devices. This paper presents research on a method for selecting a sampling frequency and an analysis window length for the presented method, which provide maximum estimation accuracy for Prony’s model component parameters. This paper presents simulation tests performed in terms of the proposed method application for analysis of harmonics and interharmonics in electric power signals. Furthermore, the paper provides sensitivity analysis of the method, in terms of common interferences occurring in the actual measurement systems.

Open access

Jarosław Zygarlicki and Janusz Mroczka

Abstract

The article presents an application of Prony’s method with some known components in the analysis of electric power quality. Modifications of the Prony algorithm broaden the scope of method application. Modification of the filter of known components enables more accurate analysis of the parameters of unknown components and components with known or assumed frequencies. This article presents a comparison of the results of analyses conducted with the proposed algorithm for simulated and real signals and the results obtained by means of a commercial electric power quality testing device, operating in class A and using the Fourier transform. The proposed method enables to estimate the levels of the harmonic components, the frequency of the fundamental signal and real parameters of the interharmonic components, which are grouped and averaged in the contemporary monitoring equipment. Knowledge of the individual parameters of the interharmonics has considerable diagnostic importance while removing causes of incorrect operation affecting sensitive equipment in some electric power systems. Additionally, the algorithm is capable of analyzing exponentially damped components and finds its application in analysis of disturbances, for example, transient oscillations.