The effective harmonics estimation for measuring power signals has become an important issue in the power quality assessment. By reviewing those commonly used Kalman filter-based models, some limitations for harmonics estimation can be observed. In this paper an extended real model of Kalman filter combined with a resetting mechanism for accurately tracking time-varying harmonic components of power signals is presented. The usefulness of the proposed algorithm is demonstrated by a simple laboratory setup with LabVIEW program and the dedicated hardware for harmonics monitoring. Results show that the proposed method can achieve more accurate and robust measurement of harmonic amplitudes and phase angles for the time-varying power signals among compared methods while the uncertainty testing performances required by IEC standard 61000-4-30 are satisfied.

Extended Real Model of Kalman Filter for Time-Varying Harmonics Estimation

The fast Fourier transform (FFT) has been widely used for the signal processing because of its computational efficiency. Because of the spectral leakage and picket-fence effects associated with the system fundamental frequency variation and improperly selected sampling time window, a direct application of the FFT algorithm with a constant sampling rate may lead to inaccurate results for continuously measuring power system harmonics and interharmonics. An improved FFT-based algorithm to measure harmonics and interharmonics accurately is proposed. In the proposed algorithm, a frequency-domain interpolation approach is adopted to determine the system fundamental frequency, and the interpolatory polynomial method is applied to reconstruct the sampled time-domain signal; it is followed by using the FFT to calculate the actual harmonic components. Then, the frequency-domain interpolation is again applied to find the interharmonic components. The performance of the proposed algorithm is validated by testing the actual measured waveforms. Results are compared with those obtained by directly applying a typical FFT algorithm and by the IEC grouping method. It shows that the solutions determined by the proposed algorithm are more accurate, and a reasonable computational efficiency is maintained.

Measuring power system harmonics and interharmonics by an improved fast Fourier transform-based algorithm

A new technique for estimation of the instantaneous frequency based on simultaneous sampling of three-phase voltage signals is presented. The structure consists of two decoupled modules: the first is for adaptive filtering of input signals, and the second is for frequency estimation. A suitable and robust algorithm for frequency estimation is obtained. This technique provides better performance, compared with the technique based on a single-phase signal in relation to waveforms with noise. The technique is particularly important when asymmetric sags generate zero voltage in one of the three phases. In addition, it allows the measurement of the instantaneous frequency value of real signals for single- or three-phase systems. To demonstrate the performance of the developed algorithm, computer-simulated data records and calibrator-generated signals are processed. The proposed algorithm has been put to test with distorted three-phase voltage signals.

Frequency Estimation of Three-Phase Power System Using Weighted-Least-Square Algorithm and Adaptive FIR Filtering

This paper proposes a robust algorithm based on an extended complex Kalman filter (ECKF) for improving frequency estimation of distorted power system signals. In general, abnormal data obtained from measurements may cause noises and disturbances of power systems as well as affect the accuracy of frequency estimation. For this reason, the proposed algorithm is employed to suppress the abnormalities from abnormal data of measurements for promoting the efficiency in frequency estimation. Moreover, not only can it perform the ECKF without changing any form of it, but it can also save the execution time. Results of frequency estimation for distorted signals using the proposed method are compared with the ECKF.

Frequency Estimation of Distorted Power System Signals Using a Robust Algorithm

A new algorithm based on the least-squares method is proposed for online power system frequency estimation. The algorithm is based on a formula which holds for every three consecutive samples. Several of these formulae are written for some consecutive triples of samples and the least-squares method is applied to estimate the frequency. A revised version of the approach with less computation burden at the cost of little decline in estimation accuracy is presented. Response time and processing time of the algorithm are discussed. The effect of data window size, sampling frequency, noise, harmonic, interharmonic, exponentially decaying dc, and filtering on the performance of the approach is discussed. The approach is compared with that of a recent similar paper and a demodulation approach.

Frequency Estimation: A Least-Squares New Approach

This paper describes the design, analysis and computational aspects of a technique for the measurement of power system voltage, current and frequency. This technique can be used in a digital AVR for the state estimation of turbine-generator terminal quantities or in a digital relay for protection of a power system. This technique provides fast and accurate estimation of power system frequency, and is used in a Kalman-filtering algorithm to estimate power system voltage and current signals. Practical considerations such as the effect of power system harmonics, noise, frequency changes, mechanical and electrical load changes are taken into account during implementation of this technique. Several computer simulation tests are presented to highlight the usefulness of the technique. Simulation results show that the technique can simultaneously estimate the amplitude and frequency of a sinusoidal signal, even in the case that the signal is distorted by harmonics or noise or encounters frequency changes.

R. Aghazadeh

Papers

New technique for frequency and amplitude estimation of power system signals