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Content available remote O estymacji wartości średniej napięcia sinusoidalnego
Sienkowski Sergiusz, Krajewski Mariusz
Przegląd Elektrotechniczny
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2022
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R. 98, nr 11
139--142
PL
W artykule oceniono dokładność wyników estymacji wartości średniej napięcia sinusoidalnego. W tym celu zastosowano estymator wartości średniej obliczany na podstawie próbek napięcia. Wyznaczono obciążenie, wariancję i błąd średniokwadratowy estymatora.
EN
The article evaluates the accuracy of the estimating results of the mean value of a sinusoidal voltage. For this purpose, a mean value estimator calculated from voltage samples has been used. The bias, the variance and the mean squared error of an estimator have been determined.
2
Content available remote Analiza właściwości iteracyjnego algorytmu najmniejszych kwadratów w pomiarze częstotliwości sieci energetyczne
Krajewski Mariusz, Sienkowski Sergiusz
Przegląd Elektrotechniczny
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2022
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R. 98, nr 11
114--117
PL
W artykule przedstawiono badania symulacyjne i doświadczalne właściwości iteracyjnego algorytmu opartego na metodzie najmniejszych kwadratów, w pomiarze częstotliwości sieci energetycznej. Analizowano możliwość poprawy dokładności algorytmu poprzez zastosowanie filtracji cyfrowej próbek oraz uśrednianie wyników pomiarów. Badania przeprowadzono w warunkach stacjonarnych i dynamicznych. Wyniki badań porównano z wynikami otrzymanymi dla algorytmu opartego na DFT.
EN
The article presents simulation and experimental research of properties of an iterative algorithm based on the least squares method in measuring the frequency of the power grid. The possibility of improving the accuracy of the algorithm by applying digital filtering of samples and averaging the measurement results was analyzed. The research was carried out in stationary conditions and dynamic. The test results were compared with those obtained for the DFT-based algorithm.
3
Content available On the statistical analysis of the harmonic signal autocorrelation function
Sienkowski Sergiusz, Krajewski Mariusz
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 4
729--744
EN
The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable identification of the ACF estimator errors in measurements in which the triggering of the measurements is non-synchronized. This is important because in many measurement situations the initial phase of the measured signal is random. The developed tools enable testing the ACF estimator of a harmonic signal in the presence of Gaussian noise. These are the formulas on the basis of which the statistical properties of the estimator can be determined, including the bias, the variance and the mean squared error (MSE). For comparison, the article also presents the ACF statistical analysis tools used in the conditions of synchronized measurement triggering, known from the literature. Operation of the new tools is verified by simulation and experimental studies. The conducted research shows that differences between the MSE results obtained with the use of the developed formulas and those attained from simulations and experimental tests are not greater than 1 dB.
4
Content available Single-tone frequency estimation based on reformed covariance for half-length autocorrelation
Sienkowski Sergiusz, Krajewski Mariusz
Metrology and Measurement Systems
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2020
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Vol. 27, nr 3
473--493
EN
This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation (RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage (experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error (MSE) to compare the estimators. The errors were juxtaposed with the Cramér-Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR>25dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.
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