基于Gauss算法的高精度数字积分器
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摘要
为使空心线圈电子式电流互感器更适应于工程现场,使其积分环节具备一定的抗干扰能力是必要的。为此研究了不同数字积分算法的特性,分析了采样频率、谐波、噪声干扰、频率波动等因素对积分环节的影响,在此基础上设计了一种高精度数字积分器。理论与仿真结果都表明:在计算正弦波信号时,相对于梯形与辛普森积分算法,Gauss算法的复合误差更小,具有较好的抵抗上述干扰因素的能力。同时,对于保护用电子式电流互感器可以降低采样点数,以减少运算量的方式起到提高速动性的作用。仿真实验表明:对基于Gauss算法设计的数字积分器,存在13次以下谐波源时,复合误差≤0.13%。频率波动范围±0.5 Hz时,复合误差<8×10~(-5)%。存在幅值比10%的白噪声时,6.4 kHz采样频率下基波幅值比差为0.077%。
In order to make the Rogowski coil electronic current transformer more suitable for the project, the anti-interference ability for integral part is necessary. We researched the characteristics of different digital integration algorithm, analyzed the effects of sampling frequency, harmonics, the interference of noise, frequency fluctuations and other factors on the electronic transformer used for measurement and protection, and thereby designed a high-precision digital integrator. The critical and experimental results show that the composite error and ratio error of the Gauss Algorithm are smaller and the Gauss Algorithm possesses a good ability to resist the above disturbance factors in the process of calculating sine wave signal, compared with the trapezoidal and Simpson integration algorithm. Meanwhile, the electronic current transformer used for protection can reduce the sampling points and play the role in improving its high-speed tripping to reduce the amount of calculation. Simulation results show that the design of digital integrator's composite error is less than 0.13% under the 13 times harmonic based on the Gauss algorithm. The composite error is less than 8×10~(-5)% when the frequency fluctuation range is ±0.5 Hz. The relative error is 0.077% if there is 10% white noise amplitude ratio.
In order to make the Rogowski coil electronic current transformer more suitable for the project, the anti-interference ability for integral part is necessary. We researched the characteristics of different digital integration algorithm, analyzed the effects of sampling frequency, harmonics, the interference of noise, frequency fluctuations and other factors on the electronic transformer used for measurement and protection, and thereby designed a high-precision digital integrator. The critical and experimental results show that the composite error and ratio error of the Gauss Algorithm are smaller and the Gauss Algorithm possesses a good ability to resist the above disturbance factors in the process of calculating sine wave signal, compared with the trapezoidal and Simpson integration algorithm. Meanwhile, the electronic current transformer used for protection can reduce the sampling points and play the role in improving its high-speed tripping to reduce the amount of calculation. Simulation results show that the design of digital integrator's composite error is less than 0.13% under the 13 times harmonic based on the Gauss algorithm. The composite error is less than 8×10~(-5)% when the frequency fluctuation range is ±0.5 Hz. The relative error is 0.077% if there is 10% white noise amplitude ratio.
引文
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[8]余瑜,刘开培,陈俊,等.基于调制理论的高压直流输电系统混合谐振型谐波不稳定判据[J].高电压技术,2014,40(5):1582-1589.YU Yu,LIU Kaipei,CHEN Jun,et al.Modulation theory based criterion on composite resonant harmonic instability in HVDC transmission system[J].High Voltage Engineering,2014,40(5):1582-1589.
[9]王果,周末,常文寰.适于电气化铁路的三相四开关型有源滤波器选择性谐波补偿的控制策略研究[J].高电压技术,2016,39(1):1-8.WANG Guo,ZHOU Mo,CHANG Wenhuan.Selective harmonic current control strategy for three-phase four-switch active power filter in electrification railway[J].High Voltage Engineering,2016,39(1):1-8.
[10]互感器第8部分:电子式电流互感器:GB/T 20480.8—2007[S],2007.Instrument transformers,part 8:electronic current transformers:GB/T20480.8—2007[S],2007.
[11]周强,何为,李松浓,等.单极电容式电压互感器的试验研究[J].高电压技术,2016,42(6):1781-1789.ZHOU Qiang,HE Wei,LI Songnong,et al.Experimental research of unipolar capacitive voltage transformer[J].High Voltage Engineering,2016,42(6):1781-1789.
[12]MANJURE D P,MAKRAM E B.Investigation of distribution factors for bilateral contract assessment[J].Electric Power Systems Research,2003,66(3):205-214.
[13]魏毅强,张建国.数值计算方法[M].北京:科学出版社,2004:179-193.WEI Yiqiang,ZHANG Jianguo.Numerical calculation method[M].Beijing,China:Science Press,2004:179-193.
[14]陈辉,陈卫,李伟.基于Rogowski线圈的数字积分器仿真及研究[J].电力系统保护与控制,2009,37(2):43-47.CHEN Hui,CHEN Wei,LI Wei.The simulation and research based on the digital integrator of the Rogowski coil[J].Power System Protection and Control,2009,37(2):43-47.
[15]常非,王一,王一振,等.基于模块化多电平变换器的高压直流输电故障特性与控制保护[J].高电压技术,2015,41(7):2428-2434.CHANG Fei,WANG Yi,WANG Yizhen,et al.Faults feature analysis and control protection strategies of modular multilevel converter based high voltage direct current[J].High Voltage Engineering,2015,41(7):2428-2434.
[16]陈晓明,王晓琪,郭克勤,等.互感器二次负荷调查统计与分析[J].高压电器,2015,50(5):63-68.CHEN Xiaoming,WANG Xiaoqi,GUO Keqin,et al.Statistics and analysis of secondary load in instrument transformer[J].High Voltage Apparatus,2015,50(5):63-68.
[17]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):108-111.ZHANG Kewei,WANG Ning,DUAN Xiongying,et al.A digital integrator for electronic current transducer[J].Proceeding of the CSEE,2004,24(12):108-111.
[18]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.
[19]李谦,邵建康,张波,等.基于无线传输相位差比较的变电站接地网地线分流向量及接地阻抗准确测量[J].高电压技术,2014,40(8):2271-2278.LI Qian,SHAO Jiankang,ZHANG Bo,et al.Accurate measurement of ground wires current division vectors and ground impedance in substation based on phase comparison of wireless transmission[J].High Voltage Engineering,2014,40(8):2271-2278.
[20]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 integrator based on Rogowski coil[J].Electric Power Automation Equipment,2013,33(2):155-159.
[21]刘益青,高伟聪,王成友,等.基于差电流半周积分特征的电流互感器饱和识别方法[J].电网技术,2016,40(9):2889-2896.LIU Yiqing,GAO Weicong,WANG Chengyou,et al.Detection method for current transformer saturation based on characteristic of differential current by half-cycle integral algorithm[J].Power System technology,2016,40(9):2889-2896.
[2]童悦,张勤,叶国雄,等.电子式互感器电磁兼容性能分析[J].高电压技术,2013,39(11):2829-2835.TONG Yue,ZHANG Qin,YE Guoxiong,et al.Electromagnetic compatibility performance of electronic transformers[J].High Voltage Engineering,2013,39(11):2829-2835.
[3]王黎明,杜镇安.用于高压输电线路现场带电校验的开口式双气隙铁芯结构电子式电流互感器[J].高电压技术,2015,41(1):106-114.WANG Liming,DU Zhen’an.Double air-gap current transformer applied to high voltage transmission line on-site mobile comparison system[J].High Voltage Engineering,2015,41(1):106-114.
[4]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 Rowgowski coil[J].High Voltage Engineering,2011,37(10):2391-2397.
[5]何瑞文,吕梦丽,蔡泽祥.适应继电保护暂态传变的空心线圈电流互感器积分技术研究[J].电测与仪表,2015,52(13):48-55.HE Ruiwen,LüMengli,CAI Zexiang,et al.Research on the integral technology of the air-core current transformer applicable to relay protection transient transmission[J].Electrical Measurement&Instrumentation,2015,52(13):48-55.
[6]彭庆华,陈龙,康文斌,等.电容式电压互感器谐波测量误差分析[J].高电压技术,2015,41(5):956-962.PENG Qinghua,CHEN Long,KANG Wenbin,et al.Analysis of harmonic measurement error using capacitive voltage transformer[J].High Voltage Engineering,2015,41(5):956-962.
[7]汲胜昌,李金宇,伍小生,等.换流站交流滤波电容器振动与噪声研究综述[J].高电压技术,2016,42(4):1159-1167.JI Shengchang,LI Jinyu,WU Xiaosheng,et al.Review of vibration and audible noise of AC filter capacitors in converter stations[J].High Voltage Engineering,2016,42(4):1159-1167.
[8]余瑜,刘开培,陈俊,等.基于调制理论的高压直流输电系统混合谐振型谐波不稳定判据[J].高电压技术,2014,40(5):1582-1589.YU Yu,LIU Kaipei,CHEN Jun,et al.Modulation theory based criterion on composite resonant harmonic instability in HVDC transmission system[J].High Voltage Engineering,2014,40(5):1582-1589.
[9]王果,周末,常文寰.适于电气化铁路的三相四开关型有源滤波器选择性谐波补偿的控制策略研究[J].高电压技术,2016,39(1):1-8.WANG Guo,ZHOU Mo,CHANG Wenhuan.Selective harmonic current control strategy for three-phase four-switch active power filter in electrification railway[J].High Voltage Engineering,2016,39(1):1-8.
[10]互感器第8部分:电子式电流互感器:GB/T 20480.8—2007[S],2007.Instrument transformers,part 8:electronic current transformers:GB/T20480.8—2007[S],2007.
[11]周强,何为,李松浓,等.单极电容式电压互感器的试验研究[J].高电压技术,2016,42(6):1781-1789.ZHOU Qiang,HE Wei,LI Songnong,et al.Experimental research of unipolar capacitive voltage transformer[J].High Voltage Engineering,2016,42(6):1781-1789.
[12]MANJURE D P,MAKRAM E B.Investigation of distribution factors for bilateral contract assessment[J].Electric Power Systems Research,2003,66(3):205-214.
[13]魏毅强,张建国.数值计算方法[M].北京:科学出版社,2004:179-193.WEI Yiqiang,ZHANG Jianguo.Numerical calculation method[M].Beijing,China:Science Press,2004:179-193.
[14]陈辉,陈卫,李伟.基于Rogowski线圈的数字积分器仿真及研究[J].电力系统保护与控制,2009,37(2):43-47.CHEN Hui,CHEN Wei,LI Wei.The simulation and research based on the digital integrator of the Rogowski coil[J].Power System Protection and Control,2009,37(2):43-47.
[15]常非,王一,王一振,等.基于模块化多电平变换器的高压直流输电故障特性与控制保护[J].高电压技术,2015,41(7):2428-2434.CHANG Fei,WANG Yi,WANG Yizhen,et al.Faults feature analysis and control protection strategies of modular multilevel converter based high voltage direct current[J].High Voltage Engineering,2015,41(7):2428-2434.
[16]陈晓明,王晓琪,郭克勤,等.互感器二次负荷调查统计与分析[J].高压电器,2015,50(5):63-68.CHEN Xiaoming,WANG Xiaoqi,GUO Keqin,et al.Statistics and analysis of secondary load in instrument transformer[J].High Voltage Apparatus,2015,50(5):63-68.
[17]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):108-111.ZHANG Kewei,WANG Ning,DUAN Xiongying,et al.A digital integrator for electronic current transducer[J].Proceeding of the CSEE,2004,24(12):108-111.
[18]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.
[19]李谦,邵建康,张波,等.基于无线传输相位差比较的变电站接地网地线分流向量及接地阻抗准确测量[J].高电压技术,2014,40(8):2271-2278.LI Qian,SHAO Jiankang,ZHANG Bo,et al.Accurate measurement of ground wires current division vectors and ground impedance in substation based on phase comparison of wireless transmission[J].High Voltage Engineering,2014,40(8):2271-2278.
[20]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 integrator based on Rogowski coil[J].Electric Power Automation Equipment,2013,33(2):155-159.
[21]刘益青,高伟聪,王成友,等.基于差电流半周积分特征的电流互感器饱和识别方法[J].电网技术,2016,40(9):2889-2896.LIU Yiqing,GAO Weicong,WANG Chengyou,et al.Detection method for current transformer saturation based on characteristic of differential current by half-cycle integral algorithm[J].Power System technology,2016,40(9):2889-2896.