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

Abstract

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.

Prony’s Method with Reduced Sampling - Numerical Aspects

“…6. By comparing the obtained characteristics with the results of research studies performed for the reduced Prony's method [1] or variable-frequency Prony's method [2], deterioration in the estimation accuracy of the components' parameters, and associated with it, accuracy in signal reconstruction can be observed. However, the effect of this phenomenon due to implementation of the specific sampled signal and the reduced Prony's method is not large enough to disqualify measurement advantages of the presented reduced Prony's method with reduced sampling.…”

“…Absolute reconstruction errors of #1 test signal were calculated as shown in Fig. 3, and amounted to err = 9.5·10 -12 , so they were comparable with the reduced Prony's method for signals without noise [2].…”

“…Reduced method is applied, inter alia, in electric power quality measurement systems, where components of the analysed signals are not damped, and their frequencies are known [2][3].…”

“…Prony's methods allow for accurate estimation of parameters of the analysed signal [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. They provide new measurement opportunities by identifying actual frequencies of the analysed signal components and extending the signal model with data on damping coefficients of particular components.…”

“…The #3 test signal was formed by adding to the #1 test signal, normal white noise (µ = 0, V 2 = 1) of adjusted level SNR [2]. The #4 test signal is a modification of the #1 test signal, where the unit value of amplitude was replaced with a module of randomly selected values, in accordance with normal distribution, µ = 0, V 2 = 1, as well as, the initial phases were randomly selected using the same distribution and multiplied by the value of 180°.…”