在线多通道无缝采样分析技术的研究
|
摘要
近年来，电能质量问题逐渐引起人们的重视。一方面由于电力电子器件和非线性设备的广泛应用，使得电网中的电压、电流波形发生畸变，造成电能质量的严重恶化；另一方面由于工业自动化水平的提高，微处理器和PLC等智能器件大量应用于工业过程控制，而这些精细过程控制更容易受到电力系统抖动的影响，因此现代工业对电能质量提出了更高的要求。同时，随着电力工业的快速发展，稳态电能质量问题如电压波动、频率波动、谐波等，已经引起了足够的重视。暂态电能质量问题越来越突出，如电压跌落、骤升、短时断电等现象经常发生，给用户带来了很大的损失。传统的基于有效值理论的监测技术由于时间窗口太长，仅测有效值已不能精确描述实际的电能质量问题，因此必需发展满足要求的新监测技术。
电能质量扰动(如谐波、瞬时电压波动等)往往同时出现。现有电能质量监测仪在线分析多项电能指标时采取“采样—分析—采样”串行处理技术，在两组采样数据之间存在分析数据所产生的时间间隔，信息丢失量大，不利于动态电能质量监测。针对上述问题，本文提出了两种方法：在线多通道无缝采样分析技术和递推FFT算法。前者把把采样控制时序与数据处理分析控制时序分离并能够同步，从而，实现多通道的同步数据采集与数据处理同时进行，避免了数据采集与数据处理分时交替进行导致的部分数据丢失；后者对其运算量进行了合理分配，使之不等量地分配在N(N为采样窗口内采样点数)个采样点间隔内进行，实现了对被测信号的不间断采样与分析。通过对两种方法的分析比较，本文采用了前者。通过具体分析现场监测单元对采样通道、采样同步性和采样窗口长度等方面的要求与设计，这种技术采用了基于FPGA(现场可编程逻辑门阵列)与DSP(数字信号处理器)的在线多通道无缝采样技术的实现，真
正实现了对电力系统电能质量的在线持续监测。
针对电能质量分析，本文采用了周期域分析方法，不仅可对我国现有电能
质量标准方面的大部分参量进行处理和分析，而且也非常适合处理短持续时间
和长持续时间电能质量问题，并能实现实时监测和定量分析。由于数字化测试
系统中定时标尺的有限分辨率，一般而言，取样不可能做到真正意义上的同步。
但是，非同步取样数据与同步取样数据之间必然存在着一定的联系。本文试图
用同步取样序列和一个误差项来表示非同步取样序列，并由此采用了一个基于
FFT的迭代公式。通过非同步取样参量的迭代，使其逐步逼近同步取样参量。
从周期性过程信号频谱分析的角度，这种方法以使频谱泄漏大幅减少甚至消除。
而这种方法并不需要增加单个周期内的取样点数，也不需要几个或更多周期的
取样数据。
In recent years, power quality has gradually become an important concern. The extensive applications for power electronic apparatus and nonlinear equipment distort the waveforms of voltages and currents. As a result, power quality is going much worse. In addition, due to the improvement of industrial automatization, such parts of an apparatus as MPU and PLC are applied to industrial process controls, which are disturbed easily by stirs from power system. Therefore modern industry needs higher power quality than old one does. At the same time, with the rapid development of electric power industry, stabile power quality issues, such as voltage fluctuation and flicker, frequency fluctuation, harmonics, have increasingly captured considerable attention from utility companies and their customers. Transient power quality issues have been becoming extrusive, such as voltage well, voltage sag and voltage interruption, and bring customers amount of loss. Because the length of sampling window is very long, traditional monitoring technique based on the theory of virtual value can not describe factual power quality issues. So it is very necessary to research for new monitoring technique.
In practice, the disturbance of power quality (e.g. harmonic, instantaneous voltage fluctuation and so on) takes place at the same time. Power quality monitors in being adopt the series-processing technique based on 'sampling-analyzing-sampling', which skips over a lot of information on account of the data-analyzing intervals between two-samplings. Hence it doesn't do good to
dynamic monitoring. Aiming at the issues, the paper presents two methods, the multi-channel non-gapped sampling technique on-line and recursive FFT algorithm. The former is to separate and synchronize the clock of sampling control and the clock of data processing control, so it implements synchronously multi-channel data sampling and processing, and no data are lost at intervals when sampling and analyzing go by turns. The later changes concentrated operation into unequally operation among gaps of sampling points, so it can implement continuous sampling of measured signal and continuous FFT analysis. After analyzing the two methods, this paper adopts the former. In addition, after analyzing need and design of monitoring unit, such as sampling channels, synchronized sampling, the length of sampling window and so on, it uses FPGA (Field Programmable Gate Array) and DSP (Digital Signal Processor) to implement the technique. So the on-line multi-channel consecutive monitoring of power quality has been achieved.
Aiming at power quality analysis, this paper advances analysis method based on period field, it can process and analyze not only a majority of parameters of our country power quality standard, but also short-time and long-time power quality issues, so it can realize real-time monitoring and quantificational analysis. Because time ruler mark of digital testing system is very limited, sampling is not really synchronized. But there is a kind of relation between non-synchronized sampling data and synchronized sampling data. This paper tries to use synchronized sampling serial and error item to express non-synchronized sampling serial, then advances a iterative formula. Non-synchronized data is close to synchronized data by iterative operation. From the point of view of spectrum of period signal, the method decreases and disappears even spectrum leaking. In addition, the method need not increase the amount of sampling points in one period, and sampling data of several sampling interval.
电能质量扰动(如谐波、瞬时电压波动等)往往同时出现。现有电能质量监测仪在线分析多项电能指标时采取“采样—分析—采样”串行处理技术，在两组采样数据之间存在分析数据所产生的时间间隔，信息丢失量大，不利于动态电能质量监测。针对上述问题，本文提出了两种方法：在线多通道无缝采样分析技术和递推FFT算法。前者把把采样控制时序与数据处理分析控制时序分离并能够同步，从而，实现多通道的同步数据采集与数据处理同时进行，避免了数据采集与数据处理分时交替进行导致的部分数据丢失；后者对其运算量进行了合理分配，使之不等量地分配在N(N为采样窗口内采样点数)个采样点间隔内进行，实现了对被测信号的不间断采样与分析。通过对两种方法的分析比较，本文采用了前者。通过具体分析现场监测单元对采样通道、采样同步性和采样窗口长度等方面的要求与设计，这种技术采用了基于FPGA(现场可编程逻辑门阵列)与DSP(数字信号处理器)的在线多通道无缝采样技术的实现，真
正实现了对电力系统电能质量的在线持续监测。
针对电能质量分析，本文采用了周期域分析方法，不仅可对我国现有电能
质量标准方面的大部分参量进行处理和分析，而且也非常适合处理短持续时间
和长持续时间电能质量问题，并能实现实时监测和定量分析。由于数字化测试
系统中定时标尺的有限分辨率，一般而言，取样不可能做到真正意义上的同步。
但是，非同步取样数据与同步取样数据之间必然存在着一定的联系。本文试图
用同步取样序列和一个误差项来表示非同步取样序列，并由此采用了一个基于
FFT的迭代公式。通过非同步取样参量的迭代，使其逐步逼近同步取样参量。
从周期性过程信号频谱分析的角度，这种方法以使频谱泄漏大幅减少甚至消除。
而这种方法并不需要增加单个周期内的取样点数，也不需要几个或更多周期的
取样数据。
In recent years, power quality has gradually become an important concern. The extensive applications for power electronic apparatus and nonlinear equipment distort the waveforms of voltages and currents. As a result, power quality is going much worse. In addition, due to the improvement of industrial automatization, such parts of an apparatus as MPU and PLC are applied to industrial process controls, which are disturbed easily by stirs from power system. Therefore modern industry needs higher power quality than old one does. At the same time, with the rapid development of electric power industry, stabile power quality issues, such as voltage fluctuation and flicker, frequency fluctuation, harmonics, have increasingly captured considerable attention from utility companies and their customers. Transient power quality issues have been becoming extrusive, such as voltage well, voltage sag and voltage interruption, and bring customers amount of loss. Because the length of sampling window is very long, traditional monitoring technique based on the theory of virtual value can not describe factual power quality issues. So it is very necessary to research for new monitoring technique.
In practice, the disturbance of power quality (e.g. harmonic, instantaneous voltage fluctuation and so on) takes place at the same time. Power quality monitors in being adopt the series-processing technique based on 'sampling-analyzing-sampling', which skips over a lot of information on account of the data-analyzing intervals between two-samplings. Hence it doesn't do good to
dynamic monitoring. Aiming at the issues, the paper presents two methods, the multi-channel non-gapped sampling technique on-line and recursive FFT algorithm. The former is to separate and synchronize the clock of sampling control and the clock of data processing control, so it implements synchronously multi-channel data sampling and processing, and no data are lost at intervals when sampling and analyzing go by turns. The later changes concentrated operation into unequally operation among gaps of sampling points, so it can implement continuous sampling of measured signal and continuous FFT analysis. After analyzing the two methods, this paper adopts the former. In addition, after analyzing need and design of monitoring unit, such as sampling channels, synchronized sampling, the length of sampling window and so on, it uses FPGA (Field Programmable Gate Array) and DSP (Digital Signal Processor) to implement the technique. So the on-line multi-channel consecutive monitoring of power quality has been achieved.
Aiming at power quality analysis, this paper advances analysis method based on period field, it can process and analyze not only a majority of parameters of our country power quality standard, but also short-time and long-time power quality issues, so it can realize real-time monitoring and quantificational analysis. Because time ruler mark of digital testing system is very limited, sampling is not really synchronized. But there is a kind of relation between non-synchronized sampling data and synchronized sampling data. This paper tries to use synchronized sampling serial and error item to express non-synchronized sampling serial, then advances a iterative formula. Non-synchronized data is close to synchronized data by iterative operation. From the point of view of spectrum of period signal, the method decreases and disappears even spectrum leaking. In addition, the method need not increase the amount of sampling points in one period, and sampling data of several sampling interval.
引文
[1] 施奕平，吴国安．基于DSP的电网质量监测仪．电测与仪表，2002(1)，17～19
[2] Dugan R C, McGranaghan M F, Beaty H W. Electrical Power Systems Quality. New York: McGraw-Hill, 1996
[3] Emanuel A E, Orr J A, Gulachenski E M. A Survey of Harmonic Voltages and Currents at the Customer's Bus. IEEE Trans on Power Delivery, 1993, 8(1)
[4] 胡铭，等．电能质量及其分析方法综述．电网技术，2000，24(3)：36～38
[5] 肖湘宁，徐永海．电能质量问题剖析．电网技术，2001，25(3)：65～69
[6] 潘贞存，陈青，王慧，等．电能质量及其检测方法的研究．山东电力技术，1997(5)：55～58
[7] 俞宁，李泰光，黄道基．电力谐波在线测量方法与监测系统设计．电测与仪表，1999(9)：12～15
[8] 王宾，潘贞存，赵建国，等．电能质量监测数据的同步处理与装置设计．电力系统自动化，2002，26(11)：45～49
[9] 郭茂，彭白杨，冯旭．电力系统实时相角测量新方法．电测与仪表，2000，37(11)：21～22
[10] 肖永清，郭自坤，雷惠博．电力系统无功功率实时测量方法评析．电测与仪表，2000，37(11)：8～12
[11] 朱晓华，王建新，是湘全．基于DSP算法的谐波功率测量仪的研究．电测与仪表，2001，38(10)：12～15
[12] 李君凯，丁化成．一种新的电力系统谐波分析仪表采样计算方法．电测与仪表，2000，37(10)：5～7
[13] 廖泽龙．电能质量综合测试系统的设计．电网技术，2000，24(2)：42～44
[14] 李宗华，徐欣，卢启中，周一宁．信号处理中高速计算器的设计与FPGA实现．电子技术应用，1999(11)：67～68
[15] 吴道虎，李玉华，康巍晶．新型多功能电能质量监测仪的研制．电测与仪表，1997，34(6)：27～29
[16] 王小平，杨维翰，王绍兰．便携式电能质量分析仪的研制．电测与仪表，2000，37(3)：19～21
[17] 王宝安，蒋平，等．基于DSP技术的电能质量监测仪的研制．国际电能质量研讨会：244～247
[18] 王宾，潘贞存．电能质量监测系统硬件平台的特点与设计．国际电能质量研讨会：36～39
[19] 陈隆道，等．电能质量监测中的周期域分析．国际电能质量研讨会：258～262
[20] 陈隆道，陈云．电能质量监测中一种减小频谱泄漏的算法．国际电能质量研讨会：253～257
[21] A．V．奥本海姆(A．V．oppenheim)，R．W．谢弗(R．W．Sehafer)．数字信号处理．北京：科出版社，1980
[22] E．O．布赖姆(E．O．Brigham)．快速傅立叶变换．上海：上海科学技术出版社，1979
[23] Ferrero A, Ortobomi R. High-accuracy Fourier Analysis Based on Synchronous Sampling Techniques. IEEE Trans on IM, 1992, 41(6): 380～386
[24] Harris FJ. On the use of windows for Harmonic analysis with the discrete Fourier transform. Proc. IEEE, 1978, 66(1): 51～83
[25] Nara K, Hasegawa Oyama T, et, al. Forwarding to Future Power Delivery System. In: Proceeding of IEEE ICHOP IX. Orlando(USA): 2000,8～18
[26] 吕润余．电力系统高次谐波．北京：中国电力出版社，1998
[27] 段晓明．DZJ-1F型电能质量监测仪的研制．华北电力技术，1998(4)
[28] 孙树勤．电压波动与闪变．北京：中国电力出版社，1999
[29] Mancao R T. Power Quality Monitoring of a Distribution System. IEEE Trans on Power Delivery, 1994, 9(2): 1136～1140
[30] M.T.Bishop, A.V.Do, S.R.Mendis. Voltage Flicker Measurement and Analysis System. IEEE CompterApplications in Power. 1994, 7(2): 34～38
[31] HANOCH Lev-Ari, Senior Member, et al. Application of Staggered Undersampling to Power Quality Monitoring. IEEE Transactions on Power Delivery. 2000, 15(3): 864～869
[32] Heydt G T, Fjeld P S, Liu C C, et al. Application of the Windows FFT to Electric Power Quality Assessment. IEEE Transon Power Delivery, 1999, 14(4): 1411～1416
[33] Bollen M H J. Understanding power quality problems, voltage sags and interruptions. IEEE PRESS, Piscataway, New Jersey, 2000
[34] 陈振晖，蔡灿勇等．锁相环倍频软件实现及在电力谐波参数检测系统中应用．电子测
量技术，2001(3)
[35] 李树森，江帆．电力系统在线谐波测量中的误差分析．电测与仪表，1991(4)
[36] 徐震，陈山林，孙成明．谐波分析仪中采样截断误差的分析及抑制．电测与仪表，1990(2)
[37] 陈隆道．过程信号周期域分析域应用的研究．浙江大学博士学位论文．杭州，1998．8
[38] Jiangtao Xi, J F Chicharo. A New Algrithm for Improving the Accuracy of Periodic Signal Analysis. IEEE Trans. IM.1996. 45(4): 827～831
[39] Dan Sabin. A Systems Approach to Power Quality Monitoring for Performance Assessment, Mark McGranaghan-Electrotek Concepts, Knoxville, Tennessee, Ashok Sundaram-Electric Power Research Institue
[40] 陈隆道，钱照明，张圣训．周期域分析中非同步取样数据的同步化．电子学报，2001，29(7)：950～953
[41] X.Z.Dai. Quasi-synchronous sampling algorithm and its applications. IEEE Trans., 1993,IM-43(2): 204～209
[42] H.C.Lin, C.S.Lee. Enhanced FFT-based parametric algorithm for simultaneous multiple harmonics analysis. IEEProc., 2001, GTD-148(3): 209～214
[43] Jiangtao Xi, Chicharo, J.F., A New Algorithm for Improving the Accuracy of Periodic Signal Analysis. IEEETrans., 1996, IM-45(4): 827～831
[44] 王念旭，等．DSP基础与应用系统设计．北京：北京航空航天大学出版社，2001
[45] 诸振勇，翁木云．FPGA设计及应用．西安：西安电子科技大学出版社，2002
[46] 刘凌，胡永生．数字信号处理的FPGA实现．北京：清华大学出版社，2003
[47] 黄正道，徐坚，等．CPLD系统设计技术入门与应用．北京：电子工业出版社，2002
[48] 柳义利，刘海霞，周涓．高速连续频率测量．电子测量技术，1999(7)：19～22
[49] 张伏生，耿中行，葛耀中．电力系统谐波分析的高精度FFT算法．中国电机工程学报，1999，19(3)：63～66
[50] 于海生，潘松峰．基于复序列FFT和锁相原理的电参数测量．电网技术，2000(3)
[51] Andria, G., Savino, M., Trotta. A Windows and Interpolation Algorithms to Improve Electical Measurement Accuracy. IEEE Trans., 1989, IM-38(4): 856～863
[52] Fusheng Zhang, Zhongxing Geng, Wei Yuan. The Algorithm of Interpolating Windowed FFT for Harmonic Analysis of Electric Power System. IEEE Trans on Power Delivery, 2001, 16(2): 160～164
[53] 马小斌，金连文，尹俊勋．利用DSP和CPLD增加数据采集的可扩展性．电子技术应用，2003(3)：78～80
[54] 赵晨，吉安，刘军成．电能质量的SCADA系统及其应用．电能质量国际研讨会：27～30
[55] N.Kagan, E.L.Ferrari, et al. A Methodology for Monitoring Harmonic Distortions in Electric Power Distribution Systems. 10th International Conference on Harmonics and Quality of Power, vol.1: 195～200
[56] 卢涛．交流瞬时采样的频率跟踪．电测与仪表，1997，34(3)：25～27
[57] 刘卓夫，彭侠夫，等．FPGA在高速多通道数据采集中的应用．电测与仪表，2002，39(10)：42～44
[58] 蒋亚坚，沈桂明．FPGA在雷达信号处理器中的应用研究．雷达与对抗，1999(2)：57～63
[59] 沙征东，宋光爱．一种数字信号处理算法的现场可编程门阵列实现．武汉水利电力大学学报，2000，33(4)：104～107
[2] Dugan R C, McGranaghan M F, Beaty H W. Electrical Power Systems Quality. New York: McGraw-Hill, 1996
[3] Emanuel A E, Orr J A, Gulachenski E M. A Survey of Harmonic Voltages and Currents at the Customer's Bus. IEEE Trans on Power Delivery, 1993, 8(1)
[4] 胡铭，等．电能质量及其分析方法综述．电网技术，2000，24(3)：36～38
[5] 肖湘宁，徐永海．电能质量问题剖析．电网技术，2001，25(3)：65～69
[6] 潘贞存，陈青，王慧，等．电能质量及其检测方法的研究．山东电力技术，1997(5)：55～58
[7] 俞宁，李泰光，黄道基．电力谐波在线测量方法与监测系统设计．电测与仪表，1999(9)：12～15
[8] 王宾，潘贞存，赵建国，等．电能质量监测数据的同步处理与装置设计．电力系统自动化，2002，26(11)：45～49
[9] 郭茂，彭白杨，冯旭．电力系统实时相角测量新方法．电测与仪表，2000，37(11)：21～22
[10] 肖永清，郭自坤，雷惠博．电力系统无功功率实时测量方法评析．电测与仪表，2000，37(11)：8～12
[11] 朱晓华，王建新，是湘全．基于DSP算法的谐波功率测量仪的研究．电测与仪表，2001，38(10)：12～15
[12] 李君凯，丁化成．一种新的电力系统谐波分析仪表采样计算方法．电测与仪表，2000，37(10)：5～7
[13] 廖泽龙．电能质量综合测试系统的设计．电网技术，2000，24(2)：42～44
[14] 李宗华，徐欣，卢启中，周一宁．信号处理中高速计算器的设计与FPGA实现．电子技术应用，1999(11)：67～68
[15] 吴道虎，李玉华，康巍晶．新型多功能电能质量监测仪的研制．电测与仪表，1997，34(6)：27～29
[16] 王小平，杨维翰，王绍兰．便携式电能质量分析仪的研制．电测与仪表，2000，37(3)：19～21
[17] 王宝安，蒋平，等．基于DSP技术的电能质量监测仪的研制．国际电能质量研讨会：244～247
[18] 王宾，潘贞存．电能质量监测系统硬件平台的特点与设计．国际电能质量研讨会：36～39
[19] 陈隆道，等．电能质量监测中的周期域分析．国际电能质量研讨会：258～262
[20] 陈隆道，陈云．电能质量监测中一种减小频谱泄漏的算法．国际电能质量研讨会：253～257
[21] A．V．奥本海姆(A．V．oppenheim)，R．W．谢弗(R．W．Sehafer)．数字信号处理．北京：科出版社，1980
[22] E．O．布赖姆(E．O．Brigham)．快速傅立叶变换．上海：上海科学技术出版社，1979
[23] Ferrero A, Ortobomi R. High-accuracy Fourier Analysis Based on Synchronous Sampling Techniques. IEEE Trans on IM, 1992, 41(6): 380～386
[24] Harris FJ. On the use of windows for Harmonic analysis with the discrete Fourier transform. Proc. IEEE, 1978, 66(1): 51～83
[25] Nara K, Hasegawa Oyama T, et, al. Forwarding to Future Power Delivery System. In: Proceeding of IEEE ICHOP IX. Orlando(USA): 2000,8～18
[26] 吕润余．电力系统高次谐波．北京：中国电力出版社，1998
[27] 段晓明．DZJ-1F型电能质量监测仪的研制．华北电力技术，1998(4)
[28] 孙树勤．电压波动与闪变．北京：中国电力出版社，1999
[29] Mancao R T. Power Quality Monitoring of a Distribution System. IEEE Trans on Power Delivery, 1994, 9(2): 1136～1140
[30] M.T.Bishop, A.V.Do, S.R.Mendis. Voltage Flicker Measurement and Analysis System. IEEE CompterApplications in Power. 1994, 7(2): 34～38
[31] HANOCH Lev-Ari, Senior Member, et al. Application of Staggered Undersampling to Power Quality Monitoring. IEEE Transactions on Power Delivery. 2000, 15(3): 864～869
[32] Heydt G T, Fjeld P S, Liu C C, et al. Application of the Windows FFT to Electric Power Quality Assessment. IEEE Transon Power Delivery, 1999, 14(4): 1411～1416
[33] Bollen M H J. Understanding power quality problems, voltage sags and interruptions. IEEE PRESS, Piscataway, New Jersey, 2000
[34] 陈振晖，蔡灿勇等．锁相环倍频软件实现及在电力谐波参数检测系统中应用．电子测
量技术，2001(3)
[35] 李树森，江帆．电力系统在线谐波测量中的误差分析．电测与仪表，1991(4)
[36] 徐震，陈山林，孙成明．谐波分析仪中采样截断误差的分析及抑制．电测与仪表，1990(2)
[37] 陈隆道．过程信号周期域分析域应用的研究．浙江大学博士学位论文．杭州，1998．8
[38] Jiangtao Xi, J F Chicharo. A New Algrithm for Improving the Accuracy of Periodic Signal Analysis. IEEE Trans. IM.1996. 45(4): 827～831
[39] Dan Sabin. A Systems Approach to Power Quality Monitoring for Performance Assessment, Mark McGranaghan-Electrotek Concepts, Knoxville, Tennessee, Ashok Sundaram-Electric Power Research Institue
[40] 陈隆道，钱照明，张圣训．周期域分析中非同步取样数据的同步化．电子学报，2001，29(7)：950～953
[41] X.Z.Dai. Quasi-synchronous sampling algorithm and its applications. IEEE Trans., 1993,IM-43(2): 204～209
[42] H.C.Lin, C.S.Lee. Enhanced FFT-based parametric algorithm for simultaneous multiple harmonics analysis. IEEProc., 2001, GTD-148(3): 209～214
[43] Jiangtao Xi, Chicharo, J.F., A New Algorithm for Improving the Accuracy of Periodic Signal Analysis. IEEETrans., 1996, IM-45(4): 827～831
[44] 王念旭，等．DSP基础与应用系统设计．北京：北京航空航天大学出版社，2001
[45] 诸振勇，翁木云．FPGA设计及应用．西安：西安电子科技大学出版社，2002
[46] 刘凌，胡永生．数字信号处理的FPGA实现．北京：清华大学出版社，2003
[47] 黄正道，徐坚，等．CPLD系统设计技术入门与应用．北京：电子工业出版社，2002
[48] 柳义利，刘海霞，周涓．高速连续频率测量．电子测量技术，1999(7)：19～22
[49] 张伏生，耿中行，葛耀中．电力系统谐波分析的高精度FFT算法．中国电机工程学报，1999，19(3)：63～66
[50] 于海生，潘松峰．基于复序列FFT和锁相原理的电参数测量．电网技术，2000(3)
[51] Andria, G., Savino, M., Trotta. A Windows and Interpolation Algorithms to Improve Electical Measurement Accuracy. IEEE Trans., 1989, IM-38(4): 856～863
[52] Fusheng Zhang, Zhongxing Geng, Wei Yuan. The Algorithm of Interpolating Windowed FFT for Harmonic Analysis of Electric Power System. IEEE Trans on Power Delivery, 2001, 16(2): 160～164
[53] 马小斌，金连文，尹俊勋．利用DSP和CPLD增加数据采集的可扩展性．电子技术应用，2003(3)：78～80
[54] 赵晨，吉安，刘军成．电能质量的SCADA系统及其应用．电能质量国际研讨会：27～30
[55] N.Kagan, E.L.Ferrari, et al. A Methodology for Monitoring Harmonic Distortions in Electric Power Distribution Systems. 10th International Conference on Harmonics and Quality of Power, vol.1: 195～200
[56] 卢涛．交流瞬时采样的频率跟踪．电测与仪表，1997，34(3)：25～27
[57] 刘卓夫，彭侠夫，等．FPGA在高速多通道数据采集中的应用．电测与仪表，2002，39(10)：42～44
[58] 蒋亚坚，沈桂明．FPGA在雷达信号处理器中的应用研究．雷达与对抗，1999(2)：57～63
[59] 沙征东，宋光爱．一种数字信号处理算法的现场可编程门阵列实现．武汉水利电力大学学报，2000，33(4)：104～107