基于变步长原理的改进型高精度数字积分算法
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摘要
为解决电子式电流互感器测量中积分环节中低频噪声、电压漂移及测量精度问题,提高空心线圈电子式电流互感器的工程实用性,依据变步长积分算法的原理,提出一种改进型高精度数字积分算法。算法的频率特性与理想积分的误差相对于一些改进积分算法要小的多,同时该算法具有采样率适中、计算量少、精度高的优点。仿真实验结果表明,所提改进算法性能优良,具有更强的抵抗噪声干扰和电压漂移的能力。
In order to solve the problems of low frequency noise,voltage drift and the measurement accuracy in the integral part of the electronic current transformer measurement and improve the engineering practicability of air-core coil electronic current transformer,an improved high-precision digital integral algorithm is proposed based on the principle of variable step integral algorithm.Compared to some other improved integral transfer functions,the error of the frequency characteristic and the ideal integral is much smaller.Meanwhile,the algorithm has the advantages of moderate sampling rate,less amount of calculation and high precision.The simulation results show that the improved algorithm has good performance and better ability of resisting noise and voltage drift.
In order to solve the problems of low frequency noise,voltage drift and the measurement accuracy in the integral part of the electronic current transformer measurement and improve the engineering practicability of air-core coil electronic current transformer,an improved high-precision digital integral algorithm is proposed based on the principle of variable step integral algorithm.Compared to some other improved integral transfer functions,the error of the frequency characteristic and the ideal integral is much smaller.Meanwhile,the algorithm has the advantages of moderate sampling rate,less amount of calculation and high precision.The simulation results show that the improved algorithm has good performance and better ability of resisting noise and voltage drift.
引文
[1]刘彬,叶国雄,郭克勤,等.基于Rogowski线圈的电子式电流互感器复合误差计算方法[J].高电压技术,2011,37(10):2391-2397.LIU Bin,YE Guoxiong,GUO Keqin,et al.Calculation method of composite error for electronic current transformers based on Rogowski coil[J].High Voltage Engineering,2011,37(10):2391-2397.
[2]姚东晓,吕利娟,倪传坤,等.应用于空心线圈电子式互感器的双环数字积分器设计[J].电力系统自动化,2016,40(6):96-100.DIO:10.7500/AEPS20150520002.YAO Dongxiao,LYU Lijuan,NI Chuankun,et al.Dual loop digital integrator design for Rogowski coil electronic transformer[J].Automation of Electric Power Systems[J].2016,40(6):96-100.DIO:10.7500/AEPS20150520002.
[3]冯宇,王小琪,陈晓明,等.电容式电压互感器电路参数对电网谐波电压测量的影响[J].中国电机工程学报,2014,34(28):4968-4975.FENG Yu,WANG Xiaoqi,CHEN Xiaoming,et al.Influences of circuit parameters of capacitor voltage transformer on grid harmonic voltage measurements[J].Proceedings of the CSEE,2014,34(28):4968-4975.
[4]李振华,胡蔚中,闫苏红,等.隔离开关开合下电子式互感器传导干扰分析及抗干扰方法[J].高电压技术,2016,42(1):233-240.LI Zhenhua,HU Weizhong,YAN Suhong,et al.Conductive interference analysis and anti-interference methods of electronic transformers in disconnector switching test[J].High Voltage Engineering,2016,42(1):233-240.
[5]张鑫,牟龙华.Rogowski线圈用新型积分电路设计[J].电力自动化设备,2010,30(5):115-117.ZHANG Xin,MOU Longhua.Design of integral circuit for Rogowski coil[J].Electric Power Automation Equipment,2010,30(5):115-117.
[6]朱超,梅军,黄灿,等.测量用电子式互感器的延时补偿设计[J].电力系统自动化,2013,37(21):184-189.ZHU Chao,MEI Jun,HUANG Can,et al.Delay compensation design for electronic measuring transformer[J].Automation of Electric Power Systems,2013,37(21):184-189.
[7]李伟,尹项根,陈德树,等.基于Rogowski线圈的电子式电流互感器暂态特性研究[J].电力自动化设备,2008,28(10):34-37.LI Wei,YIN Xianggen,CHEN Deshu,et al.Study on transient characteristics of electronic current transformer based on Rogowski coil[J].Electric Power Automation Equipment,2008,28(10):34-37.
[8]冯宇,万罡,舒开旗,等.电流互感器暂态特性试验用标准信号的参数估计[J].电网技术,2014,38(8):2263-2267.FENG Yu,WAN Gang,SHU Kaiqi,et al.Parameter estimation of standard signals for transient characteristics test of current transformer[J].Power System Technology,2014,38(8):2263-2267.
[9]向珉江,高厚磊,安艳秋,等.一种提高数据同步精度的自适应插值算法[J].电力系统自动化,2012,36(8):77-81.XIANG Mingjiang,GAO Houlei,AN Yanqiu,et al.An adaptive interpolation algorithm to improve data synchronization precision[J].Automation of Electric Power Systems,2012,36(8):77-81.
[10]张可畏,王宁,段雄英,等.用于电子式电流互感器的数字积分器[J].中国电机工程学报,2004,24(12):104-107.ZHANG Kewei,WANG Ning,DUAN Xiongying,et al.A digital integrator for electronic current transducer[J].Proceedings of the CSEE,2004,24(12):104-107.
[11]李振华,闫苏红,胡蔚中,等.一种基于改进数字积分的高精度电流互感器在线校验系统[J].电网技术,2016,40(3):978-984.LI Zhenhua,YAN Suhong,HU Weizhong,et al.A high accuracy on-line calibration system for current transformers based on improved digital integrator[J].Power System Technology,2016,40(3):978-984.
[12]宋涛.Rogowski线圈电流互感器中的高精度数字积分器技术研究[J].高电压技术,2015,41(1):237-244.SONG Tao.High precision digital integrator technology research in Rogowski coil current transformer[J].High Voltage Engineering,2015,41(1):237-244.
[13]BIHAN J L.Novel class of digital integrators and differentiators[J].Electronics Letters,1993,29(11):971-973.
[14]TSENG C C.Digital integrator design using Simpson rule and fractional delay filter[J].IEE Proceedings—Vision,Image and Signal Processing,2006,153(1):79-86.
[15]魏毅强,张建国.数值计算方法[M].北京:科学出版社,2004:179-193.
[16]GUPTA M,JAIN M,JAIN N.A new fractional order recursive digital integrator using continued fraction expansion[C]//India International Conference on Power Electronics,2010,New Delhi,India:1-3.
[17]王晓明,周有庆,彭红海,等.基于Rogowski线圈的数字积分器的研究与设计[J].电力自动化设备,2013,33(2):155-159.WANG Xiaoming,ZHOU Youqing,PENG Honghai,et al.Research and design of digital intergrator based on Rogowski coil[J].Electric Power Automation Equipment,2013,33(2):155-159.
[18]TSENG C C,LEE S L.Digital IIR integrator design using recursive Romberg integration rule and fractional sample delay[J].Signal Processing,2008,88(9):2222-2233.
[19]NGO NQ.A new approach for the design of wideband digital integrator and differentiator[J].IEEE Transaction on Circuits SystemsⅡ,2006,53(9):936-940.
[20]TSENG C C.Design of digital feller fractional order integrator[J].Signal Processing,2014,94(102):16-31.
[21]张健,段梅梅,蔡奇新,等.电子式互感器整周波延时检测技术的研究[J].电测与仪表,2015,52(4):66-70.ZHANG Jian,DUAN Meimei,CAI Qixin,et al.Research on the integral cycle delay detection technology of electronic transformer[J].Electronic Measurement&Instrumentation,2015,52(4):66-70.
[22]焦在滨,张梦瑶,何世恩,等.基于频域模型识别的串补线路保护方案[J].中国电机工程学报,2013,33(4):186-193.JIAO Zaibin,ZHANG Mengyao,HE Shien,et al.A distance protection scheme of series compensated lines based on model identification in frequency domain[J].Proceedings of the CSEE,2013,33(4):186-193.
[23]李振华,闫苏红,胡蔚中.光学电压互感器的研究及应用现状分析[J].高电压技术,2016,42(10):3230-3236.LI Zhenhua,YAN Suhong,HU Weizhong.The research and application situation analysis of optical voltage transformers[J].High Voltage Engineering,2016,42(10):3230-3236.
[2]姚东晓,吕利娟,倪传坤,等.应用于空心线圈电子式互感器的双环数字积分器设计[J].电力系统自动化,2016,40(6):96-100.DIO:10.7500/AEPS20150520002.YAO Dongxiao,LYU Lijuan,NI Chuankun,et al.Dual loop digital integrator design for Rogowski coil electronic transformer[J].Automation of Electric Power Systems[J].2016,40(6):96-100.DIO:10.7500/AEPS20150520002.
[3]冯宇,王小琪,陈晓明,等.电容式电压互感器电路参数对电网谐波电压测量的影响[J].中国电机工程学报,2014,34(28):4968-4975.FENG Yu,WANG Xiaoqi,CHEN Xiaoming,et al.Influences of circuit parameters of capacitor voltage transformer on grid harmonic voltage measurements[J].Proceedings of the CSEE,2014,34(28):4968-4975.
[4]李振华,胡蔚中,闫苏红,等.隔离开关开合下电子式互感器传导干扰分析及抗干扰方法[J].高电压技术,2016,42(1):233-240.LI Zhenhua,HU Weizhong,YAN Suhong,et al.Conductive interference analysis and anti-interference methods of electronic transformers in disconnector switching test[J].High Voltage Engineering,2016,42(1):233-240.
[5]张鑫,牟龙华.Rogowski线圈用新型积分电路设计[J].电力自动化设备,2010,30(5):115-117.ZHANG Xin,MOU Longhua.Design of integral circuit for Rogowski coil[J].Electric Power Automation Equipment,2010,30(5):115-117.
[6]朱超,梅军,黄灿,等.测量用电子式互感器的延时补偿设计[J].电力系统自动化,2013,37(21):184-189.ZHU Chao,MEI Jun,HUANG Can,et al.Delay compensation design for electronic measuring transformer[J].Automation of Electric Power Systems,2013,37(21):184-189.
[7]李伟,尹项根,陈德树,等.基于Rogowski线圈的电子式电流互感器暂态特性研究[J].电力自动化设备,2008,28(10):34-37.LI Wei,YIN Xianggen,CHEN Deshu,et al.Study on transient characteristics of electronic current transformer based on Rogowski coil[J].Electric Power Automation Equipment,2008,28(10):34-37.
[8]冯宇,万罡,舒开旗,等.电流互感器暂态特性试验用标准信号的参数估计[J].电网技术,2014,38(8):2263-2267.FENG Yu,WAN Gang,SHU Kaiqi,et al.Parameter estimation of standard signals for transient characteristics test of current transformer[J].Power System Technology,2014,38(8):2263-2267.
[9]向珉江,高厚磊,安艳秋,等.一种提高数据同步精度的自适应插值算法[J].电力系统自动化,2012,36(8):77-81.XIANG Mingjiang,GAO Houlei,AN Yanqiu,et al.An adaptive interpolation algorithm to improve data synchronization precision[J].Automation of Electric Power Systems,2012,36(8):77-81.
[10]张可畏,王宁,段雄英,等.用于电子式电流互感器的数字积分器[J].中国电机工程学报,2004,24(12):104-107.ZHANG Kewei,WANG Ning,DUAN Xiongying,et al.A digital integrator for electronic current transducer[J].Proceedings of the CSEE,2004,24(12):104-107.
[11]李振华,闫苏红,胡蔚中,等.一种基于改进数字积分的高精度电流互感器在线校验系统[J].电网技术,2016,40(3):978-984.LI Zhenhua,YAN Suhong,HU Weizhong,et al.A high accuracy on-line calibration system for current transformers based on improved digital integrator[J].Power System Technology,2016,40(3):978-984.
[12]宋涛.Rogowski线圈电流互感器中的高精度数字积分器技术研究[J].高电压技术,2015,41(1):237-244.SONG Tao.High precision digital integrator technology research in Rogowski coil current transformer[J].High Voltage Engineering,2015,41(1):237-244.
[13]BIHAN J L.Novel class of digital integrators and differentiators[J].Electronics Letters,1993,29(11):971-973.
[14]TSENG C C.Digital integrator design using Simpson rule and fractional delay filter[J].IEE Proceedings—Vision,Image and Signal Processing,2006,153(1):79-86.
[15]魏毅强,张建国.数值计算方法[M].北京:科学出版社,2004:179-193.
[16]GUPTA M,JAIN M,JAIN N.A new fractional order recursive digital integrator using continued fraction expansion[C]//India International Conference on Power Electronics,2010,New Delhi,India:1-3.
[17]王晓明,周有庆,彭红海,等.基于Rogowski线圈的数字积分器的研究与设计[J].电力自动化设备,2013,33(2):155-159.WANG Xiaoming,ZHOU Youqing,PENG Honghai,et al.Research and design of digital intergrator based on Rogowski coil[J].Electric Power Automation Equipment,2013,33(2):155-159.
[18]TSENG C C,LEE S L.Digital IIR integrator design using recursive Romberg integration rule and fractional sample delay[J].Signal Processing,2008,88(9):2222-2233.
[19]NGO NQ.A new approach for the design of wideband digital integrator and differentiator[J].IEEE Transaction on Circuits SystemsⅡ,2006,53(9):936-940.
[20]TSENG C C.Design of digital feller fractional order integrator[J].Signal Processing,2014,94(102):16-31.
[21]张健,段梅梅,蔡奇新,等.电子式互感器整周波延时检测技术的研究[J].电测与仪表,2015,52(4):66-70.ZHANG Jian,DUAN Meimei,CAI Qixin,et al.Research on the integral cycle delay detection technology of electronic transformer[J].Electronic Measurement&Instrumentation,2015,52(4):66-70.
[22]焦在滨,张梦瑶,何世恩,等.基于频域模型识别的串补线路保护方案[J].中国电机工程学报,2013,33(4):186-193.JIAO Zaibin,ZHANG Mengyao,HE Shien,et al.A distance protection scheme of series compensated lines based on model identification in frequency domain[J].Proceedings of the CSEE,2013,33(4):186-193.
[23]李振华,闫苏红,胡蔚中.光学电压互感器的研究及应用现状分析[J].高电压技术,2016,42(10):3230-3236.LI Zhenhua,YAN Suhong,HU Weizhong.The research and application situation analysis of optical voltage transformers[J].High Voltage Engineering,2016,42(10):3230-3236.