谐波相量测量的FIR滤波算法
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摘要
为实现广域范围内谐波相量监测,需要研究与谐波相量功能相适应的测量算法。参照同步相量测量P类要求,研究长度为2周波有限冲激响应(finite impulse response,FIR)带通滤波器,实现各次谐波同步相量快速准确测量。通过研究滤波器频响特性与频偏条件下由基波、被测谐波、干扰谐波和宽带噪声引起测量误差之间定量关系,定义多项滤波器技术指标,根据误差要求制定滤波器设计准则,并由动态谐波相量虚指数函数模型和加权最小二乘算法实现滤波器的具体设计。仿真试验验证了所设计算法在系统稳态和动态条件下性能良好。
In order to meet the requirements of wide area harmonic phasor monitoring,harmonic phasor measurement algorithms should be elaborately designed. In this paper,two-cycle long FIR( finite impulse response) band-pass filters are designed for fast and accurate harmonic phasor measurement,with the IEEE Std. C37. 118. 1 for a fundamental synchrophasor measurement being followed as the reference for formulation and evaluation of the proposed method. Quantitative relations are firstly derived between the filter frequency response characteristics and the measurement errors caused by the fundamental,the measured harmonic,the other harmonics and the wideband noise. Filter specifications are then defined and filter design criteria is formulated according to the relations and practical considerations. Finally,the measurement filters are designed based on dynamic harmonic phasor model and weighted least square( WLS) technique. Simulation experiments have confirmed excellent performances of the proposed algorithms both under steady and dynamic conditions.
In order to meet the requirements of wide area harmonic phasor monitoring,harmonic phasor measurement algorithms should be elaborately designed. In this paper,two-cycle long FIR( finite impulse response) band-pass filters are designed for fast and accurate harmonic phasor measurement,with the IEEE Std. C37. 118. 1 for a fundamental synchrophasor measurement being followed as the reference for formulation and evaluation of the proposed method. Quantitative relations are firstly derived between the filter frequency response characteristics and the measurement errors caused by the fundamental,the measured harmonic,the other harmonics and the wideband noise. Filter specifications are then defined and filter design criteria is formulated according to the relations and practical considerations. Finally,the measurement filters are designed based on dynamic harmonic phasor model and weighted least square( WLS) technique. Simulation experiments have confirmed excellent performances of the proposed algorithms both under steady and dynamic conditions.
引文
[1]熊杰锋,李群,袁晓冬,等.电力系统谐波和间谐波检测方法综述[J].电力系统自动化,2013,37(11):125-133Xiong Jiefeng,Li Qun,Yuan Xiaodong,et al. Detection methods of harmonics and inter-harmonics in power systems[J]. Automation of Electric Power Systems,2013,37(11):125-133.
[2]肖雁鸿,毛筱,周靖林,等.电力系统谐波测量方法综述[J].电网技术,2002,26(6):61-64.Xiao Yanhong,Mao Xiao,Zhou Jinglin,et al. A survey on measuring method for harmonics in power system[J]. Power System Technology,2002,26(6):61-64.
[3] C.-I. Chen and Y.-C. Chen. Comparative study of harmonic and interharmonic estimation methods for stationary and time-varying signals[J].IEEE Transactions on Industrial Electronics,2014,61(1):397-404.
[4] C. Rakpenthai,S. Uatrongjit,N. R. Watson,and S. Premrudeepreechacharn. On harmonic state estimation of power system with uncertain network parameters[J]. IEEE Transactions on Power Systems,2013,28(4):4829-4838.
[5] Reza Arghandeh,Ahmet Onen,Jaesung Jung,et al. Phasor-based assessment for harmonic sources in distribution networks[J]. Electric Power Systems Research,2014,116:94-105.
[6] Vladimir Terzija,Gustavo Valverde,Deyu Cai,et al. Wide-area monitoring,protection,and control of future electric power networks[J].Proceedings of IEEE,2011,99(1):80–93.
[7] Phadke AG,Thorp J S. Synchronized Phasor Measurements and Their Applications[M]. Springer,2008.
[8] IEEE Standard for Synchrophasor Measurements for Power Systems[S].IEEE,C37. 118. 1-2011,2011.
[9] IEEE Standard for Synchrophasor Measurements for Power Systems—Amendment 1:Modifcation of Selected Performance Requirements(Amendment to IEEE Standard C37. 118. 1-2011)[S]. IEEE Standard C37. 118. 1a-2014,Apr. 2014.
[10]H. Ukai,K. Nakamura,and N. Matsui. DSP-and GPS-based synchronized measurement system of harmonics in wide-area distribution system[J]. IEEE Transactions on Industrial Electronics,2003,50(6):1159-1164.
[11]I. Kamwa,J. Béland,G. Trudel,R. Grondin,C. Lafond,and D.Mc Nabb. Wide-area monitoring and control at Hydro-Québec:Past,present and future[J]. Presented at the IEEE/Power Energy Soc. Gen.Meeting,Montreal,QC,Canada,Jun. 18–22,2006.
[12]A. Carta,N. Locci,and C. Muscas. A PMU for the measurement of synchronized harmonic phasors in three-phase distribution networks[J].IEEE Transactions on Instrumentation and Measurement,2009,58(10):3723-3730.
[13]IEC 61000-4-7:2002,Electromagnetic compatibility(EMC),part 4-7:testing and measurement techniques-general guide on harmonics and interharmonics measurements and instrumentation,for power supply systems and equipment connected thereto[S].
[14]GB/T 17626. 7-2017.电磁兼容试验和测量技术供电系统及所连设备谐波、间谐波的测量和测量仪器导则[S].
[15]G. Andria,M. Savino,and A. Trotta. Windows and interpolation algorithms to improve electrical measurement accuracy[J]. IEEE Transactions on Instrumentation and Measurement,1989,88(4):856–863.
[16]庞浩,李东霞,俎云霄,等.应用FFT进行电力系统谐波分析的改进算法[J].中国电机工程学报,2003,23(6):50-54.Pang Hao,Li Dongxia,Zu Yunxiao,et al. An improved algorithm for harmonic analysis of power system using FFT technique[J]. Proceedings of the CSEE,2003,23(6):50-54.
[17]B. Zeng,Z. Teng,Y. Cai,S. Guo,and B. Qing,“Harmonic Phasor Analysis Based on Improved FFT Algorithm[J]. IEEE Transactions on Smart Grid,2011,2(1):51–59.
[18]M. Chakir,I. Kamwa,and H. Le Huy. Extended C37. 118. 1 PMU algorithms for joint tracking of fundamental and harmonic phasors in stressed power systems and microgrids[J]. IEEE Transactions on Power Delivery,2014,29(3):1465–1480.
[19]Sachin K. Jain,Preeti Jain,and Sri Niwas Singh. A Fast Harmonic Phasor Measurement Method for Smart Grid Applications[J]. IEEE Transactions on Smart Grid,2017,8(1):493-502.
[20]张佳怡,符玲,熊思宇,等.计及频率偏移的动态谐波相量测量算法[J].中国电机工程学报,2017,37(8):2270-2278.Zhang Jiayi,Fu Ling,Xiong Siyu,et al. Dynamic harmonic phasor measurement algorithm considering frequency deviation[J]. Proceedings of the CSEE,2017,37(8):2270-2278.
[21]Mai R K,He Z Y,Fu L,et al. A dynamic synchrophasor estimation algorithm for online application[J]. IEEE Transactions on Power Delivery,2010,25(2):570-578.
[22]Platas-Garza M A,de la O Serna J A. Dynamic harmonic analysis through Taylor-Fourier transform[J]. IEEE Transactions on Instrumentation and Measurement,2011,60(3):804-813.
[23]汪芙平,靳夏宁,王赞基.实现动态相量测量的FIR数字滤波器最优设计[J].电机工程学报,2014,34(15):2388-2395.Wang Fuping,Jin Xianing,Wang Zanji. Optimal Design of FIR Digital Filters for Dynamic Phasor Measurement[J]. Proceedings of the CSEE,2014,34(15):2388-2395.
[24]汪芙平,赵伟,郭雷,等.同步相量和频率测量最优滤波器设计[J].中国电机工程学报,2017,37(22):6691-6699.Wang Fuping,Zhao Wei,Guo Lei,et al. Optimal filter design for synchrophasor and frequency measurement[J]. Proceedings of the CSEE,2017,37(22):6691-6699.
[25]迟忠君,李玲,李国昌,等.谐波责任评估指标及应用[J].电测与仪表,2018,55(24):64-71.Chi Zhongjun,Li Ling,Li Guochang,et al. Harmonic responsibility evaluation indices and application[J]. Electrical Measurement&Instrumentation,2018,55(24):64-71.
[26]李文俊,肖辉,江维,等.双速率同步采样法在谐波间谐波测量中的应用[J].电测与仪表,2018,55(22):96-99,109.Li Wenjun,Xiao Hui,Jiang Wei,et al. Application of dual rate synchronous sampling method in harmonic interharmonics measurement[J]. Electrical Measurement&Instrumentation,2018,55(22):96-99,109.
[27]吴姿婷,田铭兴.计及谐波的功率因数测量方法[J].电测与仪表,2018,55(16):100-104.Wu Ziting,Tian Mingxing. A method for power factor measurement considering harmonics[J]. Electrical Measurement&Instrumentation,2018,55(16):100-104.
[28]彭咏龙,张坤锋,李亚斌,等.基于自适应算法的谐波检测方法研究[J].电测与仪表,2018,55(9):6-9.Peng Yonglong,Zhang Kunfeng,Li Yabin,et al. Research on harmonic detection method based on adaptive algorithm[J]. Electrical Measurement&Instrumentation,2018,55(9):6-9.
[2]肖雁鸿,毛筱,周靖林,等.电力系统谐波测量方法综述[J].电网技术,2002,26(6):61-64.Xiao Yanhong,Mao Xiao,Zhou Jinglin,et al. A survey on measuring method for harmonics in power system[J]. Power System Technology,2002,26(6):61-64.
[3] C.-I. Chen and Y.-C. Chen. Comparative study of harmonic and interharmonic estimation methods for stationary and time-varying signals[J].IEEE Transactions on Industrial Electronics,2014,61(1):397-404.
[4] C. Rakpenthai,S. Uatrongjit,N. R. Watson,and S. Premrudeepreechacharn. On harmonic state estimation of power system with uncertain network parameters[J]. IEEE Transactions on Power Systems,2013,28(4):4829-4838.
[5] Reza Arghandeh,Ahmet Onen,Jaesung Jung,et al. Phasor-based assessment for harmonic sources in distribution networks[J]. Electric Power Systems Research,2014,116:94-105.
[6] Vladimir Terzija,Gustavo Valverde,Deyu Cai,et al. Wide-area monitoring,protection,and control of future electric power networks[J].Proceedings of IEEE,2011,99(1):80–93.
[7] Phadke AG,Thorp J S. Synchronized Phasor Measurements and Their Applications[M]. Springer,2008.
[8] IEEE Standard for Synchrophasor Measurements for Power Systems[S].IEEE,C37. 118. 1-2011,2011.
[9] IEEE Standard for Synchrophasor Measurements for Power Systems—Amendment 1:Modifcation of Selected Performance Requirements(Amendment to IEEE Standard C37. 118. 1-2011)[S]. IEEE Standard C37. 118. 1a-2014,Apr. 2014.
[10]H. Ukai,K. Nakamura,and N. Matsui. DSP-and GPS-based synchronized measurement system of harmonics in wide-area distribution system[J]. IEEE Transactions on Industrial Electronics,2003,50(6):1159-1164.
[11]I. Kamwa,J. Béland,G. Trudel,R. Grondin,C. Lafond,and D.Mc Nabb. Wide-area monitoring and control at Hydro-Québec:Past,present and future[J]. Presented at the IEEE/Power Energy Soc. Gen.Meeting,Montreal,QC,Canada,Jun. 18–22,2006.
[12]A. Carta,N. Locci,and C. Muscas. A PMU for the measurement of synchronized harmonic phasors in three-phase distribution networks[J].IEEE Transactions on Instrumentation and Measurement,2009,58(10):3723-3730.
[13]IEC 61000-4-7:2002,Electromagnetic compatibility(EMC),part 4-7:testing and measurement techniques-general guide on harmonics and interharmonics measurements and instrumentation,for power supply systems and equipment connected thereto[S].
[14]GB/T 17626. 7-2017.电磁兼容试验和测量技术供电系统及所连设备谐波、间谐波的测量和测量仪器导则[S].
[15]G. Andria,M. Savino,and A. Trotta. Windows and interpolation algorithms to improve electrical measurement accuracy[J]. IEEE Transactions on Instrumentation and Measurement,1989,88(4):856–863.
[16]庞浩,李东霞,俎云霄,等.应用FFT进行电力系统谐波分析的改进算法[J].中国电机工程学报,2003,23(6):50-54.Pang Hao,Li Dongxia,Zu Yunxiao,et al. An improved algorithm for harmonic analysis of power system using FFT technique[J]. Proceedings of the CSEE,2003,23(6):50-54.
[17]B. Zeng,Z. Teng,Y. Cai,S. Guo,and B. Qing,“Harmonic Phasor Analysis Based on Improved FFT Algorithm[J]. IEEE Transactions on Smart Grid,2011,2(1):51–59.
[18]M. Chakir,I. Kamwa,and H. Le Huy. Extended C37. 118. 1 PMU algorithms for joint tracking of fundamental and harmonic phasors in stressed power systems and microgrids[J]. IEEE Transactions on Power Delivery,2014,29(3):1465–1480.
[19]Sachin K. Jain,Preeti Jain,and Sri Niwas Singh. A Fast Harmonic Phasor Measurement Method for Smart Grid Applications[J]. IEEE Transactions on Smart Grid,2017,8(1):493-502.
[20]张佳怡,符玲,熊思宇,等.计及频率偏移的动态谐波相量测量算法[J].中国电机工程学报,2017,37(8):2270-2278.Zhang Jiayi,Fu Ling,Xiong Siyu,et al. Dynamic harmonic phasor measurement algorithm considering frequency deviation[J]. Proceedings of the CSEE,2017,37(8):2270-2278.
[21]Mai R K,He Z Y,Fu L,et al. A dynamic synchrophasor estimation algorithm for online application[J]. IEEE Transactions on Power Delivery,2010,25(2):570-578.
[22]Platas-Garza M A,de la O Serna J A. Dynamic harmonic analysis through Taylor-Fourier transform[J]. IEEE Transactions on Instrumentation and Measurement,2011,60(3):804-813.
[23]汪芙平,靳夏宁,王赞基.实现动态相量测量的FIR数字滤波器最优设计[J].电机工程学报,2014,34(15):2388-2395.Wang Fuping,Jin Xianing,Wang Zanji. Optimal Design of FIR Digital Filters for Dynamic Phasor Measurement[J]. Proceedings of the CSEE,2014,34(15):2388-2395.
[24]汪芙平,赵伟,郭雷,等.同步相量和频率测量最优滤波器设计[J].中国电机工程学报,2017,37(22):6691-6699.Wang Fuping,Zhao Wei,Guo Lei,et al. Optimal filter design for synchrophasor and frequency measurement[J]. Proceedings of the CSEE,2017,37(22):6691-6699.
[25]迟忠君,李玲,李国昌,等.谐波责任评估指标及应用[J].电测与仪表,2018,55(24):64-71.Chi Zhongjun,Li Ling,Li Guochang,et al. Harmonic responsibility evaluation indices and application[J]. Electrical Measurement&Instrumentation,2018,55(24):64-71.
[26]李文俊,肖辉,江维,等.双速率同步采样法在谐波间谐波测量中的应用[J].电测与仪表,2018,55(22):96-99,109.Li Wenjun,Xiao Hui,Jiang Wei,et al. Application of dual rate synchronous sampling method in harmonic interharmonics measurement[J]. Electrical Measurement&Instrumentation,2018,55(22):96-99,109.
[27]吴姿婷,田铭兴.计及谐波的功率因数测量方法[J].电测与仪表,2018,55(16):100-104.Wu Ziting,Tian Mingxing. A method for power factor measurement considering harmonics[J]. Electrical Measurement&Instrumentation,2018,55(16):100-104.
[28]彭咏龙,张坤锋,李亚斌,等.基于自适应算法的谐波检测方法研究[J].电测与仪表,2018,55(9):6-9.Peng Yonglong,Zhang Kunfeng,Li Yabin,et al. Research on harmonic detection method based on adaptive algorithm[J]. Electrical Measurement&Instrumentation,2018,55(9):6-9.