基于频率测量值的相量及电气量的DFT修正算法
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摘要
为解决频率偏移时电力系统相量及电气量的测量误差大的问题,提出了一种改进的离散傅里叶(DFT)修正算法。建立了相量的实部、虚部与幅值、初相角、频率偏移量之间的函数关系式,根据此关系式得到实部、虚部与频率之间所满足的一个恒等式。在频率已知条件下计算出修正后的相量幅值和相角,进一步推导出了修正后的相量实部与虚部,最后得到其他电气量的修正算法。仿真结果表明,当系统频率偏移时,在信号为纯正弦信号,或者含有高次谐波及随机噪声等情况下,算法均可有效地提高相量及电气量的计算精度。同时,该算法对采样频率和频率误差不敏感,计算量小,不增加额外的延迟时间。
To solve the problem of the measurement error of phasor and electrical parameters in the power system when frequency offset, an improved DFT correction algorithm is proposed. The function relation between the real part, the imaginary part of the phase and the amplitude, the initial phase angle, the frequency offset is established. According to this relation expression, the real part, the imaginary part and the frequency offset satisfy an identities. Therefore, the correction algorithm of the amplitude and phase angle of the phase can be obtained under the known frequency. Further, the corrected real and imaginary parts of the phasor are derived. Finally, a correction algorithm for other electrical quantities is obtained. Simulation results show that when the system frequency is shifted, the algorithm can effectively improve the accuracy of phasor and electrical quantity when the signals are pure sinusoidal signals or the signals with higher harmonics and random noise. Meanwhile,the algorithm is insensitive to the sampling frequency and frequency error, and the algorithm has a small amount of calculation and does not increase the extra delay time.
To solve the problem of the measurement error of phasor and electrical parameters in the power system when frequency offset, an improved DFT correction algorithm is proposed. The function relation between the real part, the imaginary part of the phase and the amplitude, the initial phase angle, the frequency offset is established. According to this relation expression, the real part, the imaginary part and the frequency offset satisfy an identities. Therefore, the correction algorithm of the amplitude and phase angle of the phase can be obtained under the known frequency. Further, the corrected real and imaginary parts of the phasor are derived. Finally, a correction algorithm for other electrical quantities is obtained. Simulation results show that when the system frequency is shifted, the algorithm can effectively improve the accuracy of phasor and electrical quantity when the signals are pure sinusoidal signals or the signals with higher harmonics and random noise. Meanwhile,the algorithm is insensitive to the sampling frequency and frequency error, and the algorithm has a small amount of calculation and does not increase the extra delay time.
引文
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[9]张俊敏,刘开培,汪立,等.基于四谱线插值FFT的谐波分析快速算法[J].电力系统保护与控制,2017,45(1):139-145.ZHANG Junmin,LIU Kaipei,WANG Li,et al.A rapid algorithm for harmonic analysis based on four-spectrum-line interpolation FFT[J].Power System Protection and Control,2017,45(1):139-145.
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[13]吴继维,童晓阳,廖小君,等.一种滤除衰减直流分量的全波傅氏改进算法研究[J].电力系统保护与控制,2016,44(2):9-17.WU Jiwei,TONG Xiaoyang,LIAO Xiaojun,et al.A full-wave Fourier improved algorithm of filtering decaying DC component[J].Power System Protection and Control,2016,44(2):9-17.
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[15]李一泉,何奔腾.一种基于傅氏算法的高精度测频方法[J].中国电机工程学报,2005,26(2):78-81.LI Yiquan,HE Benteng.A high-accuracy algorithm for measuring frequency of power system based on Fourier filter[J].Proceedings of the CSEE,2005,26(2):78-81.
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[17]倪玉玲,郑建勇,梅军,等.基于偏p/4直角坐标的DFT相角测量算法[J].电网技术,2014,38(9):2544-2550.NI Yuling,ZHENG Jianyong,MEI Jun,et al.A lean p/4rectangular coordinate based phase-angle measurement algorithm corrected by discrete Fourier transform[J].Power System Technology,2014,38(9):2544-2550.
[18]姚文轩,滕召胜,唐求,等.非同步采样下电力系统相量测量修正算法[J].仪器仪表学报,2013,34(7):1518-1524.YAO Wenxuan,TENG Zhaosheng,TANG Qiu,et al.Power system phasor measurement and correction algorithm under asynchronous sampling[J].Chinese Journal of Scientific Instrument,2013,34(7):1518-1524.
[19]周念成,廖彦洁.基于虚拟ab静止坐标系的相角测量算法[J].电力系统自动化,2012,36(21):61-65.ZHOU Niancheng,LIAO Yanjie.A phase angle measurement algorithm based on virtual ab stationary coordinate[J].Automation of Electric Power Systems,2012,36(21):61-65.
[20]王超,汪芳宗.基于DFT的高精度相量测量的新算法[J].电测与仪表,2009,46(522):13-16,20.WANG Chao,WANG Fangzong.A high-precision algorithm for phasor measurement based on DFT[J].Electrical Measurement&Instrumentation,2009,46(522):13-16,20.
[21]邵璞,赵庆生,郭贺宏,等.全相位-混合基FFT在相量测量装置中的实现[J].电力系统保护与控制,2016,44(20):65-69.SHAO Pu,ZHAO Qingsheng,GUO Hehong,et al.Realization of all phase-mixed radix FFT on the phase measurement device[J].Power System Protection and Control,2016,44(20):65-69.
[2]吕思颖,黎丹,要航,等.基于无迹Kalman滤波的基波分量提取[J].电力系统保护与控制,2016,44(13):79-84.LüSiying,LI Dan,YAO Hang,et al.Fundamental component extraction based on unscented Kalman filter[J].Power System Protection and Control,2016,44(13):79-84.
[3]张姝,何正友,何文.基于递归小波的相量测量算法[J].电网技术,2011,35(4):194-200.ZHANG Shu,HE Zhenyou,HE Wen.A recursive wavelet-based algorithm for phasor measurement[J].Power System Technology,2011,35(4):194-200.
[4]张伏生,耿中行,葛耀中.电力系统谐波分析的高精度FFT算法[J].中国电机工程学报,1999,19(3):63-66.ZHANG Fusheng,GENG Zhongxing,GE Yaozhong.FFT algorithm with high accuracy for harmonic analysis in power system[J].Proceedings of the CSEE,1999,19(3):63-66.
[5]柴旭峥,文习山,关根志,等.一种高精度的电力系统谐波分析算法[J].中国电机工程学报,2003,23(9):67-70.CHAI Xuzheng,WEN Xishan,GUAN Genzhi,et al.An algorithm with high accuracy for analysis of power system harmonics[J].Proceedings of the CSEE,2003,23(9):67-70.
[6]SIDHU T S,SACHDEV M S.An iterative technique for fast and accurate measurement of power system frequency[J].IEEE Transactions on Power Delivery,1998,13(1):109-115.
[7]BEGOVIC M M,DURIC P M,DUNLOP S,et al.Frequency tracking in power networks in the presence of harmonics[J].IEEE Transactions on Power Delivery,1993,8(2):480-485.
[8]蔡晓峰,张鸿博,鲁改凤.应用三谱线插值FFT分析电力谐波的改进算法[J].电力系统保护与控制,2015,43(2):33-39.CAI Xiaofeng,ZHANG Hongbo,LU Gaifeng.Improvement algorithm for harmonic analysis of power system using triple-spectrum-line interpolation algorithm based on window FFT[J].Power System Protection and Control,2015,43(2):33-39.
[9]张俊敏,刘开培,汪立,等.基于四谱线插值FFT的谐波分析快速算法[J].电力系统保护与控制,2017,45(1):139-145.ZHANG Junmin,LIU Kaipei,WANG Li,et al.A rapid algorithm for harmonic analysis based on four-spectrum-line interpolation FFT[J].Power System Protection and Control,2017,45(1):139-145.
[10]禹永植,张忠民,席志红.基于傅里叶变换的高精度频率及相量算法[J].电网技术,2007,31(23):83-86.YU Yongzhi,ZHANG Zhongmin,XI Zhihong.A high-precision algorithm for frequency and phasor based on Fourier transform[J].Power System Technology,2007,31(23):83-86.
[11]刘世明,郭韬,吴聚昆,等.适用于频率偏移情况下同步相量测量的DFT算法研究[J].电网技术,2016,40(5):1522-1528.LIU Shiming,GUO Tao,WU Jukun,et al.Study of DFT algorithm for synchrophasor measurement under frequency offset[J].Power System Technology,2016,40(5):1522-1528.
[12]王茂海,孙元章.基于DFT的电力系统相量及功率测量新算法[J].电力系统自动化,2005,29(2):20-24.WANG Maohai,SUN Yuanzhang.A DFT-based method for phasor and power measurement in power systems[J].Automation of Electric Power Systems,2005,29(2):20-24.
[13]吴继维,童晓阳,廖小君,等.一种滤除衰减直流分量的全波傅氏改进算法研究[J].电力系统保护与控制,2016,44(2):9-17.WU Jiwei,TONG Xiaoyang,LIAO Xiaojun,et al.A full-wave Fourier improved algorithm of filtering decaying DC component[J].Power System Protection and Control,2016,44(2):9-17.
[14]磨少清,李啸骢.一种高精度的改进傅立叶测频算法[J].电力系统自动化,2003,27(12):48-49,54.MO Shaoqing,LI Xiaocong.An improved high-accuracy algorithm for frequency measurement based on Fourier transform[J].Automation of Electric Power Systems,2003,27(12):48-49,54.
[15]李一泉,何奔腾.一种基于傅氏算法的高精度测频方法[J].中国电机工程学报,2005,26(2):78-81.LI Yiquan,HE Benteng.A high-accuracy algorithm for measuring frequency of power system based on Fourier filter[J].Proceedings of the CSEE,2005,26(2):78-81.
[16]XIA T,LIU Y L.Single-phase phase angle measurements in electric power systems[J].IEEE Transactions on Power Systems,2010,25(2):844-851.
[17]倪玉玲,郑建勇,梅军,等.基于偏p/4直角坐标的DFT相角测量算法[J].电网技术,2014,38(9):2544-2550.NI Yuling,ZHENG Jianyong,MEI Jun,et al.A lean p/4rectangular coordinate based phase-angle measurement algorithm corrected by discrete Fourier transform[J].Power System Technology,2014,38(9):2544-2550.
[18]姚文轩,滕召胜,唐求,等.非同步采样下电力系统相量测量修正算法[J].仪器仪表学报,2013,34(7):1518-1524.YAO Wenxuan,TENG Zhaosheng,TANG Qiu,et al.Power system phasor measurement and correction algorithm under asynchronous sampling[J].Chinese Journal of Scientific Instrument,2013,34(7):1518-1524.
[19]周念成,廖彦洁.基于虚拟ab静止坐标系的相角测量算法[J].电力系统自动化,2012,36(21):61-65.ZHOU Niancheng,LIAO Yanjie.A phase angle measurement algorithm based on virtual ab stationary coordinate[J].Automation of Electric Power Systems,2012,36(21):61-65.
[20]王超,汪芳宗.基于DFT的高精度相量测量的新算法[J].电测与仪表,2009,46(522):13-16,20.WANG Chao,WANG Fangzong.A high-precision algorithm for phasor measurement based on DFT[J].Electrical Measurement&Instrumentation,2009,46(522):13-16,20.
[21]邵璞,赵庆生,郭贺宏,等.全相位-混合基FFT在相量测量装置中的实现[J].电力系统保护与控制,2016,44(20):65-69.SHAO Pu,ZHAO Qingsheng,GUO Hehong,et al.Realization of all phase-mixed radix FFT on the phase measurement device[J].Power System Protection and Control,2016,44(20):65-69.