In this paper, a discrete wavelet transform (DWT) based approach is proposed for power system frequency estimation. Unlike the existing frequency estimators mainly used for power system monitoring and control, the proposed approach is developed for fundamental frequency estimation in the field of energy metering of nonlinear loads. The characteristics of a nonlinear load is that the power signal is heavily distorted, composed of harmonics, inter-harmonics and corrupted by noise. The main idea is to predetermine a series of frequency points, and the mean value of two frequency points nearest to the power system frequency is accepted as the approximate solution. Firstly the input signal is modulated with a series of modulating signals, whose frequencies are those frequency points. Then the modulated signals are decomposed into individual frequency bands using DWT, and differences between the maximum and minimum wavelet coefficients in the lowest frequency band are calculated. Similarities among power system frequency and those frequency points are judged by the differences. Simulation results have proven high immunity to noise, harmonic and inter-harmonic interferences. The proposed method is applicable for real-time power system frequency estimation for electric energy measurement of nonlinear loads.
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 errorswere 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 > 25 dB. 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.
Based on real-time multi-domain communication signal analysis architecture, a high-efficiency blind carrier frequency estimation algorithm using the power spectrum symmetry of the measured modulated signal is presented. The proposed algorithm, which utilizes the moving averaged power spectrum achieved by the realtime spectrum analysis, iteratively identifies the carrier frequency in according to the power difference between the upper sideband and lower sideband, which is defined and revised by the estimated carrier frequency in each iteration. When the power difference of the two sidebands converges to the preset threshold, the carrier frequency can be obtained. For the modulation analysis, the measured signal can be coarsely compensated by the estimated result, and the residual carrier frequency error is eliminated by a following carrier synchronization loop. Compared with previous works, owing to the moving averaged power spectrum normalization and the smart iterative step variation mechanism for the two sidebands definition, the carrier frequency estimation accuracy and speed can be significantly improved without increasing the computational effort. Experimental results are included to demonstrate the outstanding performance of the proposed algorithm.
This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.
Fast and accurate grid signal frequency estimation is a very important issue in the control of renewable energy systems. Important factors that influence the estimation accuracy include the A/D converter parameters in the inverter control system. This paper presents the influence of the number of A/D converter bits b, the phase shift of the grid signal relative to the time window, the width of the time window relative to the grid signal period (expressed as a cycle in range (CiR) parameter) and the number of N samples obtained in this window with the A/D converter on the developed estimation method results. An increase in the number b by 8 decreases the estimation error by approximately 256 times. The largest estimation error occurs when the signal module maximum is in the time window center (for small values of CiR) or when the signal value is zero in the time window center (for large values of CiR). In practical applications, the dominant component of the frequency estimation error is the error caused by the quantization noise, and its range is from approximately 8×10-10 to 6×10-4.