邻近基波/谐波的间谐波检测算法
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摘要
新能源大规模并网所引发的低频振荡,其频率分量通常可表现为一个低频信号对基波/谐波信号的调制,也即电力信号中会出现关于基波/谐波对称的邻近间谐波对。在使用离散傅里叶变换(DFT)对这类间谐波进行检测时,频域间的主瓣干扰会影响间谐波参数的准确估计。该文以单峰谱线插值算法为例,分析了传统插值算法在谐波和间谐波发生主瓣干扰时检测失效的原因,并提出了一种多分量频谱叠加算法对邻近基波/谐波的单个间谐波及间谐波对进行分析。首先根据信号DFT后紧邻基波/谐波的间谐波谱线的幅值特性,判别邻近基波/谐波的间谐波分量数;然后将间谐波的频谱按其频率分量数进行矢量叠加,并用紧邻基波/谐波的间谐波谱线构建谱线方程组得到其频率估计值;根据估计出的频率利用窗谱函数构建的关联矩阵求解其幅值和相位。仿真和工程实测分析表明,该方法能有效抑制由主瓣干扰引起的检测误差,在不增加采样数据长度的条件下准确检测出邻近基波或谐波的间谐波。
The frequency component of low frequency oscillation caused by integration of renewable energy is usually expressed as modulation of a low frequency component to fundamental/harmonic components, and there may be a pair of adjacent interharmonics symmetrical to the fundamental or harmonic component in power signals. When using discrete Fourier transform(DFT) to detect interharmonics of this kind, the main lobe interference in frequency domain will affect accurate estimation of interharmonic parameters. Taking single peak spectral line interpolation algorithm for example, detection failure for traditional interpolation algorithm is analyzed when the main lobe interference occurs, and a multiple component spectrum superposition algorithm is proposed to analyze two cases of single interharmonic and symmetrical interharmonics adjacent to fundamental or harmonic component. Firstly, the number of interharmonics adjacent to fundamental or harmonic component is distinguished based on the amplitude characteristics of interharmonic spectrum line adjacent to fundamental or harmonic component. Then the interharmonic spectrum is superimposed according to the distinguished interharmonic number, and then frequency estimation is obtained by constructing spectral line equations with the interharmonic spectral lines adjacent to fundamental or harmonic component. According to estimated frequency, the amplitude and phase are corrected using incidence matrix constructed with window spectral function. Simulation and field test show that the method can effectively restrain the detection error caused by the main lobe interference, and it can accurately detect the interharmonic adjacent to fundamental or harmonic component without increasing the length of sampling data.
The frequency component of low frequency oscillation caused by integration of renewable energy is usually expressed as modulation of a low frequency component to fundamental/harmonic components, and there may be a pair of adjacent interharmonics symmetrical to the fundamental or harmonic component in power signals. When using discrete Fourier transform(DFT) to detect interharmonics of this kind, the main lobe interference in frequency domain will affect accurate estimation of interharmonic parameters. Taking single peak spectral line interpolation algorithm for example, detection failure for traditional interpolation algorithm is analyzed when the main lobe interference occurs, and a multiple component spectrum superposition algorithm is proposed to analyze two cases of single interharmonic and symmetrical interharmonics adjacent to fundamental or harmonic component. Firstly, the number of interharmonics adjacent to fundamental or harmonic component is distinguished based on the amplitude characteristics of interharmonic spectrum line adjacent to fundamental or harmonic component. Then the interharmonic spectrum is superimposed according to the distinguished interharmonic number, and then frequency estimation is obtained by constructing spectral line equations with the interharmonic spectral lines adjacent to fundamental or harmonic component. According to estimated frequency, the amplitude and phase are corrected using incidence matrix constructed with window spectral function. Simulation and field test show that the method can effectively restrain the detection error caused by the main lobe interference, and it can accurately detect the interharmonic adjacent to fundamental or harmonic component without increasing the length of sampling data.
引文
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[11]覃浩,杨洪耕.用于谐波和间谐波检测的频谱分解法[J].现代电力,2012,29(4):36-40.Qin Hao,Yang Honggeng.An approach for harmonics/interharmonics detection based on spectral deposition[J].Modern Electric Power,2012,29(4):36-40(in Chinese).
[12]李根,庞浩,徐健飞,等.一种基于改进锁相环的谐波分析逻辑电路[J].电力系统自动化,2007,31(21):82-85.Li Gen,Pang Hao,Xu Jianfei,et al.Logic circuit for harmonic analysis based on enhanced PLL[J].Automation of Electric Power System,2007,31(21):82-85(in Chinese).
[13]李宁,左培丽,王新刚,等.基于改进DFT和时域准同步的间谐波检测算法[J].电力自动化设备,2017,37(4):170-178.Li Ning,Zuo Peili,Wang Xingang,et al.Inter-harmonic detection based on improved DFT and time-domain quasi-synchronization[J].Electric Power Automation Equipment,2017,37(4):170-178(in Chinese).
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[16]肖先勇,王楠,刘亚梅.基于多项式逼近的单峰谱线插值算法在间谐波分析中的应用[J].电网技术,2008,32(18):57-61.Xiao Xianyong,Wang Nan,Liu Yamei.Application of polynomial approximation based single peak spectral lines interpolation algorithm in interharmonic analysis[J].Power System Technology,2008,32(18):57-61(in Chinese).
[17]林达斌,江亚群,黄纯,等.一种新的谐波、间谐波参数估计算法[J].电网技术,2012,36(6):170-174.Lin Dabin,Jiang Yaqun,Huang Chun,et al.A new algorithm to estimate parameters of harmonica and interharmonics[J].Power System Technology,2012,36(6):170-174(in Chinese).
[18]丁康,谢明,杨志坚.离散频谱分析校正理论与技术[M].北京:科学技术出版社,2008.
[19]黄晓红,王兆华.基于全相位频谱分析的正弦信号高精度参数估计方法[J].电力自动化设备,2008,28(7):54-57.Huang Xiaohong,Wang Zhaohua.High accuracy parameter estimation of sinusoidal signal based on all-phase spectrum analysis[J].Electric Power Automation Equipment,2008,28(7):54-57(in Chinese).
[20]黄翔东,王兆华.全相位时移相位差频谱校正法[J].天津大学学报,2008,41(7):815-820.Huang Xiangdong,Wang Zhaohua.All-phase time-shift phase difference correcting spectrum method[J].Journal of Tianjin University,2008,41(7):815-820(in Chinese).
[21]Hui Jin,Yang Honggeng,Xu Wilsun,et al.A method to improve the interharmonic grouping scheme adopted by IEC standard 61000-4-7[J].IEEE Transactions on Power Delivery,2012,27(2):971-979.
[22]王泽,杨洪耕,王佳兴,等.消除负频率影响的低频间谐波快速检测方法[J].电力自动化设备,2015,35(3):140-145.Wang Ze,Yang Honggeng,Wang Jiaxing,et al.Rapid low frequency interharmonic detection with negative-frequency elimination[J].Electric Power Automation Equipment,2015,35(3):140-145(in Chinese).
[23]邹培源,黄纯,江辉,等.基于全相位谱细化与校正的谐波和间谐波测量方法[J].电网技术,2016,40(8):2496-2502.Zou Peiyuan,Huang Chun,Jiang Hui,et al.Method of harmonics and interharmonics measurement based on all-phase spectrum zoom and correction[J].Power System Technology,2016,40(8):2496-2502(in Chinese).
[24]Djurovi’c S,Vilchis-Rodriguez D S,Smith A C.Supply induced interharmonic effects in wound rotor and doubly-fed induction generators[J].IEEE Transactions on Energy Conversion,2015,30(4):1397-1408.
[25]毕天姝,孔永乐,肖仕武,等.大规模风电外送中的次同步振荡问题[J].电力科学与技术学报,2012,27(1):10-15.Bi Tianshu,Kong Yongle,Xiao Shiwu,et al.Review of sub-synchronous oscillation with large-scale wind power transmission[J].Journal of Electric Power Science and Technology,2012,27(1):10-15(in Chinese).
[2]李明节,于钊,许涛,等.新能源并网系统引发的复杂振荡问题及其对策研究[J].电网技术,2017,41(4):1035-1042.Li Mingjie,Yu Zhao,Xu Tao,et al.Study of complex oscillation caused by renewable energy integration and its solution[J].Power System Technology,2017,41(4):1035-1042(in Chinese).
[3]王晖,李莹,李文锋,等.并网逆变器复合电流环引起次/超同步振荡机理研究[J].电网技术,2017,41(4):1061-1067.Wang Hui,Li Ying,Li Wenfeng,et al.Mechanism research of subsynchronous and supersynchronous oscillation caused by compound current loop of grid-connected inverter[J].Power System Technology,2017,41(4):1061-1067(in Chinese).
[4]王晖,吴命利.电气化铁道低频振荡研究综述[J].电工技术学报,2015,30(17):70-78.Wang Hui,Wu Mingli.Review of low-frequency oscillation in electric railways[J].Transactions of China Electrotechnical Society,2015,30(17):70-78(in Chinese).
[5]王晖,吴命利.牵引网低频振荡及其抑制方法的仿真分析[J].电网技术,2015,39(4):1088-1095.Wang Hui,Wu Mingli.Simulation analysis on low-frequency oscillation in traction power supply system and its suppression method[J].Power System Technology,2015,39(4):1088-1095(in Chinese).
[6]王兴亮,姚钢,周荔丹,等.基于DFIG风电场功率振荡的成因分析[J].电网与清洁能源,2017,33(7):97-104.Wang Xingliang,Yao Gang,Zhou Lidan,et al.Analysis of causes of oscillation in the wind farm system based on DFIG[J].Power System and Clean Energy,2017,33(7):97-104(in Chinese).
[7]王毅,张祥宇,李和明,等.永磁直驱风电机组对系统功率振荡的阻尼控制[J].电工技术学报,2012,27(12):162-171.Wang Yi,Zhang Xiangyu,Li Heming,et al.Damping control of PMSG-Based wind turbines for power system oscillations[J].Transactions of China Electrotechnical Society,2012,27(12):162-171(in Chinese).
[8]陶顺,姚黎婷,廖坤玉,等.光伏逆变器直流电压扰动引起的间谐波电流解析模型[J].电网技术,2018,42(3):878-885.Tao Shun,Yao Liting,Liao Kunyu,et al.Analytical model for interharmonic current caused by DC voltage disturbance of photovoltaic inverter[J].Power System Technology,2018,42(3):878-885(in Chinese).
[9]刘灏,李珏,毕天姝,等.基于PMU相量的次/超同步间谐波识别方法[J].电网技术,2017,41(10):3237-3245.Liu Hao,Li Jue,Bi Tianshu,et al.Subsynchronous and supersynchronous inter-harmonic identification method based on phasor measurements[J].Power System Technology,2017,41(10):3237-3245(in Chinese).
[10]金维刚,刘会金,李智敏.间谐波引起电力系统次同步振荡:工程实例、机理、作用形式及应对措施[J].电力系统保护与控制,2010,38(9):31-36.Jin Weigang,,Liu Huijin,Li Zhimin.Interharmonic exciting subsynchronous oscillation in electric power systems-engineering examples,mechanism,types of interaction and counter-measures[J].Power System Protection and Control,2010,38(9):31-36(in Chinese).
[11]覃浩,杨洪耕.用于谐波和间谐波检测的频谱分解法[J].现代电力,2012,29(4):36-40.Qin Hao,Yang Honggeng.An approach for harmonics/interharmonics detection based on spectral deposition[J].Modern Electric Power,2012,29(4):36-40(in Chinese).
[12]李根,庞浩,徐健飞,等.一种基于改进锁相环的谐波分析逻辑电路[J].电力系统自动化,2007,31(21):82-85.Li Gen,Pang Hao,Xu Jianfei,et al.Logic circuit for harmonic analysis based on enhanced PLL[J].Automation of Electric Power System,2007,31(21):82-85(in Chinese).
[13]李宁,左培丽,王新刚,等.基于改进DFT和时域准同步的间谐波检测算法[J].电力自动化设备,2017,37(4):170-178.Li Ning,Zuo Peili,Wang Xingang,et al.Inter-harmonic detection based on improved DFT and time-domain quasi-synchronization[J].Electric Power Automation Equipment,2017,37(4):170-178(in Chinese).
[14]IEC 61000-4-7.General guide on harmonics and interharmonics measurements,for power supply systems and equipment connected thereto[S].Geneva,Switzerland:International Electrotechnical Commission,2009.
[15]Jain V K,Collins W L,Davis D C.High-accuracy analog measurements via interpolated FFT[J].IEEE Transactions on Instrumentation and Measurement,1979,28(2):113-122.
[16]肖先勇,王楠,刘亚梅.基于多项式逼近的单峰谱线插值算法在间谐波分析中的应用[J].电网技术,2008,32(18):57-61.Xiao Xianyong,Wang Nan,Liu Yamei.Application of polynomial approximation based single peak spectral lines interpolation algorithm in interharmonic analysis[J].Power System Technology,2008,32(18):57-61(in Chinese).
[17]林达斌,江亚群,黄纯,等.一种新的谐波、间谐波参数估计算法[J].电网技术,2012,36(6):170-174.Lin Dabin,Jiang Yaqun,Huang Chun,et al.A new algorithm to estimate parameters of harmonica and interharmonics[J].Power System Technology,2012,36(6):170-174(in Chinese).
[18]丁康,谢明,杨志坚.离散频谱分析校正理论与技术[M].北京:科学技术出版社,2008.
[19]黄晓红,王兆华.基于全相位频谱分析的正弦信号高精度参数估计方法[J].电力自动化设备,2008,28(7):54-57.Huang Xiaohong,Wang Zhaohua.High accuracy parameter estimation of sinusoidal signal based on all-phase spectrum analysis[J].Electric Power Automation Equipment,2008,28(7):54-57(in Chinese).
[20]黄翔东,王兆华.全相位时移相位差频谱校正法[J].天津大学学报,2008,41(7):815-820.Huang Xiangdong,Wang Zhaohua.All-phase time-shift phase difference correcting spectrum method[J].Journal of Tianjin University,2008,41(7):815-820(in Chinese).
[21]Hui Jin,Yang Honggeng,Xu Wilsun,et al.A method to improve the interharmonic grouping scheme adopted by IEC standard 61000-4-7[J].IEEE Transactions on Power Delivery,2012,27(2):971-979.
[22]王泽,杨洪耕,王佳兴,等.消除负频率影响的低频间谐波快速检测方法[J].电力自动化设备,2015,35(3):140-145.Wang Ze,Yang Honggeng,Wang Jiaxing,et al.Rapid low frequency interharmonic detection with negative-frequency elimination[J].Electric Power Automation Equipment,2015,35(3):140-145(in Chinese).
[23]邹培源,黄纯,江辉,等.基于全相位谱细化与校正的谐波和间谐波测量方法[J].电网技术,2016,40(8):2496-2502.Zou Peiyuan,Huang Chun,Jiang Hui,et al.Method of harmonics and interharmonics measurement based on all-phase spectrum zoom and correction[J].Power System Technology,2016,40(8):2496-2502(in Chinese).
[24]Djurovi’c S,Vilchis-Rodriguez D S,Smith A C.Supply induced interharmonic effects in wound rotor and doubly-fed induction generators[J].IEEE Transactions on Energy Conversion,2015,30(4):1397-1408.
[25]毕天姝,孔永乐,肖仕武,等.大规模风电外送中的次同步振荡问题[J].电力科学与技术学报,2012,27(1):10-15.Bi Tianshu,Kong Yongle,Xiao Shiwu,et al.Review of sub-synchronous oscillation with large-scale wind power transmission[J].Journal of Electric Power Science and Technology,2012,27(1):10-15(in Chinese).