Frequency Shifting And Filtering Algorithm for Power System Harmonic Estimation

Fast Fourier Transform (FFT) is used to obtain the Fourier spectrum of a periodic signal, but it is well known that special care must be taken to avoid severe distortions introduced by the sampling process. The major errors associated with this algorithm are spectral leakage and picket fence effect. This paper discusses the advancement in FFT algorithms for harmonic analysis in power system by applying windowed interpolation techniques. It is observed that the application of different WIFFT algorithms has different effects on the measuring accuracy. The advanced minimized sidelobe window (MSW) algorithm has better performance characteristics when compared to the conventional hanning and hamming windows adopted for harmonic analysis. By considering the practical harmonic data the hanning, hamming and MSW algorithms are validated using matlab programming. The simulation results demonstrate the effectiveness of hanning, hamming and MSW by considering the magnitude and phase angle error variations with respect to the harmonic order.

Nowadays, the Fast Fourier transform (FFT) has been widely adopted for harmonic analysis in power system. However, a direct application of FFT-based algorithms may bring about inaccurate results because of spectral leakage and picket-fence effects. In this paper, a high accuracy method based on the all-phase and interpolated FFT is presented for harmonic analysis. Firstly, the input signal is preprocessed to mitigate spectral leakage through all-phase. Secondly, the interpolation algorithm is adopted to eliminate the picket-fence effects. As a result, the analysis accuracy of the harmonic parameters has been greatly improved and the phase estimation is not biased. The formulas of amplitude, frequency and phase are also obtained based on all-phase and interpolated FFT. The simulation results reflect that this method can better meet the requirements of harmonic detection in power system.

An approach for power system harmonic phasor analysis under asynchronous sampling is proposed in this paper. It is based on smoothing sampled data by windowing the signal with the four-term fifth derivative Nuttall (FFDN) window, and then calculating harmonic phasors in the frequency domain with an improved fast Fourier transform (IFFT) algorithm. The applicable rectification formulas of the IFFT are obtained by using the polynomial curve fitting, dramatically reducing the computation load. The FFDN window can effectively inhibit the spectral leakage and the picket fence effect can be modified by the IFFT algorithm under asynchronous sampling, and the overall algorithm can easily be implemented in embedded systems. The effectiveness of the proposed method was analyzed by means of simulations and practical experiments for multifrequency signals with the fluctuation of the fundamental frequency and with the presence of white noise and interharmonics.

To assess the insulation condition of capacitive apparatus, on-line monitoring of dielectric loss angle is an effective measure. Harmonic analysis algorithm is used to calculate dielectric loss angle traditionally, this method can effectively suppress the DC (Direct Current) offset and harmonic interference. However, when the power system frequency fluctuates, the synchronous sampling condition is difficult to meet, so, traditional harmonic analysis method can produce leakage of spectrum and picket-fence effect, which greatly affects the accuracy of dielectric loss angle measurement. In order to reduce this adverse effect, this paper proposes a method called hamming windowed interpolated DFT (Discrete Fourier Transform) algorithm based on modified ideal sampling frequency. Time series analysis based on modified ideal sampling frequency can be used to modify the time series in non-synchronous sampling condition to meet synchronous sampling condition. Hamming windowed interpolated DFT algorithm can inhibit leakage of spectrum and picket-fence effect. Firstly this paper analyzes the principle of traditional DFT algorithm and the reason that causes leakage of spectrum and picket-fence effect in non-synchronous sampling condition. Secondly, the principle of hamming windowed interpolated DFT algorithm based on modified ideal sampling frequency is elaborated. Finally this paper presents the simulation result which shows that the improved approach has higher accuracy.

This paper presents a three-phase harmonic and sequence components measurement method based on modulated sliding discrete Fourier transform (mSDFT) and a variable sampling period technique. The proposal allows measuring the harmonic components of a three-phase signal and computes the corresponding imbalance by estimating the instantaneous symmetrical components. In addition, an adaptive variable sampling period is used to obtain a sampling frequency multiple of the main frequency. By doing so, DFT typical errors, known as spectral leakage and picket-fence effect, are mitigated in steady state. The proposal is tested with different disturbances by simulation and experimental results. Some results obtained with a power quality monitor implemented with the proposed system are also presented. The high rejection to distortion in the electrical network, frequency adaptability, flexibility, and good performance in power quality monitor application render the proposed method a promising alternative for signal processing from the mains.

The discrete Fourier transform (DFT) is still a widely used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems, such as aliasing effect, spectral leakage, and picket-fence effect. This paper establishes a relationship between DFT-based spilled energy and harmonics/noninteger harmonics using the numerical induction method. Based on this study, a strategy of group-harmonics energy diffusion algorithm has been developed for both stationary and nonstationary harmonic/interharmonic evaluation in power systems. Especially, the frequency deviation range is used for frequency estimation, and the restored amplitude is used for retrieving dispersed amplitude. Accordingly, the harmonic/interharmonic frequency and its respective amplitude component can be accurately estimated using a simple mathematic computation. The numerical examples are presented to verify the performance of the proposed algorithm in terms of speed, accuracy, and efficiency.

The Discrete Fourier Transform (DFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of Piecewise-overlapped Group-harmonic Energy Restoring (PGER) algorithm is developed for both stationary and non-stationary harmonic evaluation in power systems. The proposed algorithm can restore dispersing spectral leakage energy caused by the DFT, and thus retrieve the respective real harmonic value. Based on the piecewise-overlapped method, especially every time-varying harmonic can be extracted fast and accurately. The numerical examples are presented to verify the proposed algorithm in term of robust, fast and high-precision performance.

For the frequency spectrum leakage and fence effect generated in Fast Fourier Transform (FFT) during asynchronous sampling and integral period truncation affect the precision of harmonic detection, a new algorithm for harmonic analysis based on four-spectrum-line interpolation FFT with second-order self-convolution window with five-term Maximum-Sidelobe-Decay (MSD) was proposed and the polynomial fitting method was used to construct the four-spectrum-line interpolation correction formula. The simulation results showed that this algorithm could improve the detection accuracy of amplitude, phase and frequency by 1-2 orders of magnitude compared with other commonly used windowed interpolation algorithms.

This paper focuses on the low-computation harmonic-analysis procedure with sufficient suppression of spectral leakage and picket-fence effect. The interpolated FFT algorithm based on the minimized sidelobe window is considered, and its calculate procedure and formulas are given, which is free of solving high-order equations. The implementation of the proposed algorithm in the digital-signal-processor (DSP) based three-phase harmonic ammeter is also introduced. The proposed algorithm has the major advantages that the calculate formulas for harmonic parameters can be easily implemented by hardware multipliers, making the method a good choice for real-time applications. The simulation and application results validate the accuracy and efficiency of the proposed algorithm.

The discrete Fourier transform (DFT) is the main method of electrical harmonic analysis since it’s easily realized in an embedded system. But there were some difficulties in performing synchronized sampling. The spectral leakage caused by asynchronous sampling affects the accuracy of harmonics analysis. Using window functions and interpolation algorithms can improve the accuracy of harmonics analysis. An approach for electrical harmonic analysis based on the interpolation DFT was proposed. A window function reduces DFT leakage and the interpolation algorithm modifies the calculation results of frequency, amplitude and the initial phase angle. The simulation results indicate that, by using the interpolation DFT electrical harmonic analysis method based on the Hanning window or the Blackman window, the error of calculating amplitudes and frequencies is not greater than 0.5%.

In this paper we introduce a novel algorithm for harmonic steady-state analysis of power systems that is based on the equivalent split-circuit models recently introduced for power flow analysis. By using an equivalent circuit with current and voltage as the state variables, we extend the harmonic balance method that is used for nonlinear circuit simulation in the frequency domain to capture the frequency harmonics and inter-harmonics induced into a power grid due to nonlinear components. This enables the direct incorporation of physics-based steady-state models of power electronics and smart grid devices directly within the power-system simulation framework. For demonstration, steady-state models of a diode and a nonlinear core saturation inductor are derived and incorporated into the steady-state models of a three-phase full bridge rectifier and a magnetic core saturation transformer. These components are simulated within the proposed power flow analysis framework for a multi-bus power system.

Spatial data in the Earth and environmental sciences acquired by instrument collection or simulation are constrained to finite, discrete, (ir)regular grids whose geometry is delineated by a boundary within which missingness, either random or structured, may exist. We model (ir)regularly sampled Cartesian spatial data as realizations of discrete two- and three-dimensional random fields whose covariance structure we estimate parametrically with a spectral-domain maximum-likelihood estimation strategy using the debiased Whittle likelihood, which efficiently counters the effects of aliasing and spectral leakage that arise from finite sampling and boundary effects. We work with the general, flexible Matérn class of covariance functions, which characterizes the shape of a field through three parameters that quantify its amplitude, smoothness, and correlation length. We quantify parameter covariance analytically and asymptotically based on the parametric model and sampling grid alone, agnostic of observed data. Our uncertainty quantification allows us to study how sampling geometry imparts uncertainty on a covariance model and provides a path for optimizing the design of a sampling grid to reduce error for an anticipated model. We formulate several approaches for interrogating our model residuals to interpret where real Earth data depart from the null hypotheses of Gaussianity, stationarity, and isotropy. We explore select case studies that demonstrate the broad applicability of our models across Earth science disciplines and develop software in MATLAB and Python for implementation by domain scientists, in hydrology, and elsewhere.

Algorithm Research and Implementation of Power Quality Parameters Analysis

After more than 6 years in full operational mode, the Gravity Recovery and Climate Experiment (GRACE) satellite mission provides the opportunity to derive global secular mass changes from space‐geodetic observations. Crucial for a reliable estimate of secular mass changes is the ability to correct for spectral and spatial leakage effects. In order to account for any leakage signal, we present and apply a four‐step procedure, including a validation step based on forward gravity modeling. Most notably, our method is characterized by the separation and quantification of individual leakage sources. We test and apply our procedure to the Greenland area, which exhibits the strongest secular trend signal. On the basis of simulation studies, we demonstrate that leakage‐out effects are dominant for the Greenland area, and if not accounted for, mass‐change rates will be underestimated. Analyzing time‐variable GRACE gravity fields covering 6 whole years (August 2002 to July 2008, inclusive), we estimate the ice‐volume loss over Greenland to be −177 ± 12 km3 a−1. This value is the average derived from monthly gravity field models provided by CSR, GFZ and JPL, with individual contributions of −242 ± 14 km3 a−1, −194 ± 24 km3 a−1 and −96 ± 23 km3 a−1, respectively. We highlight that without taking leakage effects into account, mass‐change amplitudes over Greenland are reduced by a factor of 2. Despite the rather large spread of the results among GRACE processing centers, our results are in better agreement with the findings from alternative GRACE analysis methods and InSAR observations.

A revised interpolated DFT is proposed to estimate the harmonic parameters accurately. Firstly, a 4-order Hann self-convolving window is employed to restrain the interferences caused by spectral leakage and sidelobes. The corresponding error can be restrained at a degree of 10−15 theoretically. Then, an equidistant two-point interpolated formula is proposed to deal with the picket-fence effect. It avoids the systematic error caused by the polynomial fitting in common interpolation method. For estimating precision, the theoretical relative errors of harmonic parameters would approximate 10−11. The relative frequency error of the fundamental wave is about 10−7 in a 50-dB-noise environment. Moreover, in a 20-dB-noise background, the signal reconstructed could reduce the variances to 0.001 of its own, which is feasible and useful in practical harmonic detection.