基于准同步采样的电力系统谐波与间谐波在线检测方法研究
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摘要
谐波和间谐波是典型的电能质量问题。谐波是频率为基波频率整数倍的正弦电压或电流，而间谐波是频率为基波频率非整数倍的畸变成分。各种电力电子装置中的非线性元件都会产生谐波或间谐波，导致谐波和间谐波污染在电力系统中广泛存在并日趋严重。谐波和间谐波会危及供电系统的安全稳定运行，影响用电设备的正常稳定工作，因此，谐波和间谐波的治理越来越受到重视。
谐波与间谐波的参数测量是实现谐波和间谐波治理的前提，只有通过在线检测方式及时、准确地获取相关参数，才能实现谐波和间谐波补偿装置的最优配置。电力系统中的电压或电流存在无规律的波动，使得谐波和间谐波的准确测量较难实现。此外，间谐波具有幅值小，频率不确定的特点，在频谱上可能离谐波很近，两者之间会产生互相干扰，从而进一步增加谐波与间谐波测量的难度。
快速傅里叶变换(FFT, fast Fourier transform)是常用的谐波、间谐波检测方法，其优点是算法简单、计算量小，缺点是在非同步采样时存在频谱泄漏和栅栏效应，会对测量准确度造成较大影响。加窗插值FFT算法是抑制频谱泄漏和栅栏效应的有效方法，然而该方法在频率分辨率和计算量之间存在矛盾：阶数越高的窗函数抑制频谱泄漏效果越好，但其主瓣宽度也越宽，导致频谱上的频率分辨能力下降，为了保持足够的频率分辨率，需要增加采样数据长度，从而造成计算量的增加。
在分析离散傅里叶变换特点和缺陷的基础上，提出了基于准同步采样的谐波检测算法。该算法适用于电力系统缓变谐波的测量，通过将非同步采样信号准同步化，达到抑制频谱泄漏和栅栏效应的目的。算法首先采用带通有限冲激响应(FIR, finite impulse response)滤波器对非同步采样下得到的信号进行预处理，滤除基波频率以外的其它频率分量。然后对滤波信号使用过零比较法获取信号的基波周期，根据该基波周期，采用牛顿插值算法重构原始采样序列，使重构信号近似于同步采样信号。由于频谱泄漏和栅栏效应得到了显著抑制，根据重构信号的FFT结果就能获得各次谐波的准确参数。通过理论分析和仿真实验，讨论了阈值、采样频率、噪声等对谐波检测算法的影响，以及4阶牛顿插值算法的误差估计。
在谐波检测算法的基础上，提出了基于准同步采样的间谐波检测算法，该算法通过分离信号中的谐波与间谐波成分，达到抑制两者互扰的目的，能够同时实现谐波和间谐波参数的准确测量。间谐波检测算法首先利用谐波检测算法中的准同步化技术重构采样信号，将信号中的所有谐波分量准同步化。在准同步化过程中，设计了多采样率结构的窄带带通FIR滤波器对原始采样信号进行预处理，该滤波器阶数比窗函数法或最优方法设计的滤波器阶数少一个数量级。然后，使用梳状FIR滤波器分离重构信号中的所有谐波与间谐波分量。对于分离后的间谐波分量，使用谱峰搜索法找到各间谐波在频谱上对应的最大谱线，通过加窗插值FFT算法计算各间谐波的参数。对于提取到的谐波分量，根据其FFT结果直接计算各次谐波的参数。
在MATLAB环境下，通过与常用谐波、间谐波检测方法的对比仿真试验，验证了谐波检测算法在不同噪声干扰、低频率分辨率下的测量准确度，以及对信号波动的动态响应特性；验证了间谐波检测算法在噪声干扰下的测量准确度，以及相关滤波器的线性相位特性。将检测算法分别应用于自主研制的在线式电能质量分析仪PQM-F3和数字信号处理平台TDS6713EVM中，通过对标准源生成的谐波和间谐波信号进行测量，验证算法的有效性。最后，使用电能质量分析仪对市电电压信号进行了现场测试，测量了信号中的谐波含量。
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.
谐波与间谐波的参数测量是实现谐波和间谐波治理的前提，只有通过在线检测方式及时、准确地获取相关参数，才能实现谐波和间谐波补偿装置的最优配置。电力系统中的电压或电流存在无规律的波动，使得谐波和间谐波的准确测量较难实现。此外，间谐波具有幅值小，频率不确定的特点，在频谱上可能离谐波很近，两者之间会产生互相干扰，从而进一步增加谐波与间谐波测量的难度。
快速傅里叶变换(FFT, fast Fourier transform)是常用的谐波、间谐波检测方法，其优点是算法简单、计算量小，缺点是在非同步采样时存在频谱泄漏和栅栏效应，会对测量准确度造成较大影响。加窗插值FFT算法是抑制频谱泄漏和栅栏效应的有效方法，然而该方法在频率分辨率和计算量之间存在矛盾：阶数越高的窗函数抑制频谱泄漏效果越好，但其主瓣宽度也越宽，导致频谱上的频率分辨能力下降，为了保持足够的频率分辨率，需要增加采样数据长度，从而造成计算量的增加。
在分析离散傅里叶变换特点和缺陷的基础上，提出了基于准同步采样的谐波检测算法。该算法适用于电力系统缓变谐波的测量，通过将非同步采样信号准同步化，达到抑制频谱泄漏和栅栏效应的目的。算法首先采用带通有限冲激响应(FIR, finite impulse response)滤波器对非同步采样下得到的信号进行预处理，滤除基波频率以外的其它频率分量。然后对滤波信号使用过零比较法获取信号的基波周期，根据该基波周期，采用牛顿插值算法重构原始采样序列，使重构信号近似于同步采样信号。由于频谱泄漏和栅栏效应得到了显著抑制，根据重构信号的FFT结果就能获得各次谐波的准确参数。通过理论分析和仿真实验，讨论了阈值、采样频率、噪声等对谐波检测算法的影响，以及4阶牛顿插值算法的误差估计。
在谐波检测算法的基础上，提出了基于准同步采样的间谐波检测算法，该算法通过分离信号中的谐波与间谐波成分，达到抑制两者互扰的目的，能够同时实现谐波和间谐波参数的准确测量。间谐波检测算法首先利用谐波检测算法中的准同步化技术重构采样信号，将信号中的所有谐波分量准同步化。在准同步化过程中，设计了多采样率结构的窄带带通FIR滤波器对原始采样信号进行预处理，该滤波器阶数比窗函数法或最优方法设计的滤波器阶数少一个数量级。然后，使用梳状FIR滤波器分离重构信号中的所有谐波与间谐波分量。对于分离后的间谐波分量，使用谱峰搜索法找到各间谐波在频谱上对应的最大谱线，通过加窗插值FFT算法计算各间谐波的参数。对于提取到的谐波分量，根据其FFT结果直接计算各次谐波的参数。
在MATLAB环境下，通过与常用谐波、间谐波检测方法的对比仿真试验，验证了谐波检测算法在不同噪声干扰、低频率分辨率下的测量准确度，以及对信号波动的动态响应特性；验证了间谐波检测算法在噪声干扰下的测量准确度，以及相关滤波器的线性相位特性。将检测算法分别应用于自主研制的在线式电能质量分析仪PQM-F3和数字信号处理平台TDS6713EVM中，通过对标准源生成的谐波和间谐波信号进行测量，验证算法的有效性。最后，使用电能质量分析仪对市电电压信号进行了现场测试，测量了信号中的谐波含量。
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.
引文
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