Online Estimation Algorithm For Harmonic And Interharmonic In Power Systems Based On The Quasi-synchronous Sampling

Harmonics and interharmonics are typical power quality events. Aharmonic of the voltage or current is the component whose frequency isan integer multiple of the fundamental frequency, while aninterharmonic is the distorted component whose frequency is not aninteger multiple of the fundamental frequency. Nonlinear elements indifferent kinds of power electronic equipments may produce harmonicsor interharmonics, thus cause harmonic and interharmonic pollution tobe widespread and more and more serious in power systems. Harmonicand interharmonic distortion will threaten the stability of the powersystem and cause serious damages to equipments working in that system.Thus, harmonic and interharmonic treatments have gained increasingattention.Accurate measurement of harmonic and interharmonic is aprerequisite for compensating harmonic and interharmonic distortion. Inorder to realize the optimal configuration of the compensation device, itis necessary to determine the harmonics and interharmonics parametersin time via online monitoring. However, fluctuations in voltages andcurrents make the accurate measurement difficult to realize. In addition,interharmonics have the characteristics of small amplitudes anduncertain frequencies. Therefore, interharmonics may be close toharmonics on the spectrum, and thus mutual interferences between themmay further increase the difficulty of harmonic and interharmonicdetermination.Fast Fourier transform (FFT) is a common method for harmonic and interharmonic estimation. The advantage of the FFT method is simpleprocedure and low computational cost, while its disadvantage is that themeasurement accuracy is affected by spectral leakage and picket-fenceeffect in the case of asynchronous sampling. The windowed interpolatedFFT method is an effective approach to eliminate the spectral leakageand picket-fence effect. However, there is a conflict between thefrequency resolution and the computational cost: with the increase of theorder of the window function, the spectral leakage decreases whereasthe main-lob width of the window function increases. Wide main-lobrestrains the capability of spectral resolution. In order to keep highenough spectral resolution, the length of the sampling data has to beenlarged, which will obviously increase the computational cost.According to the analyses of the characteristics and defects of thediscrete Fourier transform, a harmonic estimation algorithm based onthe quasi-synchronous sampling has been proposed. This algorithmrestrains spectral leakage and picket-fence effect by means of thequasi-synchronization of the asynchronous sampling signal. Hence, it issuitable for estimation of slow change harmonics in power systems. Theproposed algorithm firstly applies a finite impulse response (FIR) filterto preprocess the asynchronous sampling signal by filtering out allfrequency components except the fundamental one. Secondly, azero-crossing method is developed for fundamental-period estimation.With the estimated period, the original sampling sequence isreconstructed by Newton's interpolation, so that the reconstructed signalcan be approximately regarded as the synchronous sampling signal.Because of the significant decrease of the spectral leakage andpicket-fence effect, parameters of all harmonics can be determineddirectly from the FFT results of the reconstructed signal. Effects oferrors, including the threshold, the sampling frequency and the noiseinterference, are investigated theoretically. Moreover, error estimate of4-order Newton's interpolation algorithm is also discussed on the basisof the results of the simulation experiment. According to the harmonic estimation algorithm, an interharmonicestimation algorithm based on the quasi-synchronous sampling has beenproposed. This algorithm, which separates harmonics andinterharmonics to restrain the mutual interferences, can estimateharmonics and interharmonics simultaneously. Using thequasi-synchronous sampling technique proposed in the harmonicestimation algorithm, the interharmonic estimation algorithm firstlyquasi-synchronizes all harmonic components in the original signal. Inthe process of quasi-synchronization, a multi-rate narrow bandpass FIRfilter is applied to preprocess the asynchronous sampling signal. Thisfilter can decrease the filter order by almost one order of magnitudecompared with the filter designed by the window function method or theoptimal method. Secondly, a comb FIR filter is adopted to separateharmonics and interharmonics in the reconstructed signal. Consequently,as for the extracted interharmonics, a peak-search method is employedto find the maximum spectral line related to every interharmonic. Inaccordance with those maximum spectral lines, the interharmonicsparameters can be determined by the widowed interpolation FFTalgorithm. As for the extracted harmonics, the proposed algorithmdetermines the parameters directly from the FFT results.Simulation experiments under MATLAB environment have beencarried out to compare the proposed algorithms with the commonharmonic and interharmonic estimation methods. Simulation resultsverify the measurement accuracy of the harmonic estimation algorithmunder the condition of different noise inferences and low frequencyresolution, and show the dynamic response of the algorithm forwaveform fluctuation as well. Moreover, the simulation results alsoverify the measurement accuracy of the interharmonic estimationalgorithm with noise and show the linear phase characteristics of therelated filters. The proposed harmonic and interharmonic estimationmethods are applied in the self-developed online power quality analyzerPQM-F3and the digital signal process platform TDS6713EVM, respectively. The application of the algorithms to estimate the harmonicsand interharmonics produced by the standard signal sources furtherprove the validity of these two algorithms. At last, the power qualityanalyzer is used to monitor the voltage in the public grid and thenestimate harmonics in the voltage.