非同步采样下电力系统无功和谐波算法研究
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摘要
现有的电能表测量无功的设计原理都是基于正弦周期电压和电流信号的假设,其理论基础是正弦电路功率理论,这类电能表只适用于计量供电电压和电流的波形无畸变下的线性负荷电能。在此情况下正弦电路功率理论逐渐呈现出不适应。论文研究了无功功率测量算法和非同步采样下的谐波算法。
无功测量在电力系统中有着重要的地位和作用。本文分正弦和非正弦两种情况,论述了包括公式法、移相法、改进移相法、积分法等在内的几种主流无功测量方法,对现有方法的精度和误差进行了分析,探讨了各种方法下的误差应对策略。并简要介绍了各种方法的软硬件实现的可行性。
谐波测量重点介绍了加窗插值法和准同步法在电力系统谐波参数估计中的应用。首先分析了非同步采样时FFT算法频谱泄漏的主要原因。然后通过对常用窗函数的特性探讨,给出了基于海宁窗和布莱克曼窗下的幅值和频率估计公式。同时基于准同步法的基本原理,给出了幅值计算公式。
仿真结果表明:综合正弦电路情况下的四种无功测量方法,在电压电流谐波含量较小的情况下,上述四法都能达到比较好的精度。最后结合它们的频率特性和相位特性,对算法的精度和可靠性作了分析。三种谐波测量方法都能显著减少频谱泄漏。最后结合精度、误差频率特性和算法易实现性的比较,对几种算法的实际使用给出了建议。
最后,结合低压无功补偿项目,重点介绍了谐波和无功测量的硬件实现系统,对实际的无功和谐波测量作了一定的介绍。
The design principle of the existing power meter is based on the sinusoid circuit theory, and this kind of power meter is only suitable for the measurement of linear load electric energy of which voltage and current waveform is orthoscopic. However, along with the swift growth of non-linear elements in the power system, the sinusoidal circuit power theory has gradually presented unsuitability. This paper studies the measurement algorithm of the reactive energy and Harmonic analysis by using the quasi-synchronization.
The reactive energy measurement plays an important role in power system. Several prevalent methods such as digital phase shift method, integration method and Hilbert transform method for reactive power measurement are introduced in this paper. The measuring error and the methods of correcting the error are also analyzed. The feasibilities of the hardware and software based on these methods are discussed simply.
The estimation of electrical harmonic parameters by using the quasi-synchronization and interpolated FFT are emphatically introduced in the harmonic measurement. The main factor of spectral leakage is conducted when the sampling is non-synchronous. The computing formulas for the harmonic parameters are given based on the features of Hanning Window and Blackman Window. The computing formulas are given based on the method of quasi-synchronization as well.
The simulation results show that the four measurement methods of reactive power of sinusoidal circuit are more accurate when the harmonic content of voltage and current is small. Finally, the accuracy and reliability of the algorithm are analyzed, combining their frequency characteristics and phase characteristics.
All the three measurement methods will reduce the spectrum leakage significantly. Some suggestion is proposed for the practical use of the algorithms, based on the accuracy, the error characteristics changing with frequency, and the practicability.
Eventually, based on the low-voltage reactive power compensation projects, the hardware system of the harmonic and reactive energy measurement is emphasized on, and the real reactive and harmonic measurement is introduced as well.
无功测量在电力系统中有着重要的地位和作用。本文分正弦和非正弦两种情况,论述了包括公式法、移相法、改进移相法、积分法等在内的几种主流无功测量方法,对现有方法的精度和误差进行了分析,探讨了各种方法下的误差应对策略。并简要介绍了各种方法的软硬件实现的可行性。
谐波测量重点介绍了加窗插值法和准同步法在电力系统谐波参数估计中的应用。首先分析了非同步采样时FFT算法频谱泄漏的主要原因。然后通过对常用窗函数的特性探讨,给出了基于海宁窗和布莱克曼窗下的幅值和频率估计公式。同时基于准同步法的基本原理,给出了幅值计算公式。
仿真结果表明:综合正弦电路情况下的四种无功测量方法,在电压电流谐波含量较小的情况下,上述四法都能达到比较好的精度。最后结合它们的频率特性和相位特性,对算法的精度和可靠性作了分析。三种谐波测量方法都能显著减少频谱泄漏。最后结合精度、误差频率特性和算法易实现性的比较,对几种算法的实际使用给出了建议。
最后,结合低压无功补偿项目,重点介绍了谐波和无功测量的硬件实现系统,对实际的无功和谐波测量作了一定的介绍。
The design principle of the existing power meter is based on the sinusoid circuit theory, and this kind of power meter is only suitable for the measurement of linear load electric energy of which voltage and current waveform is orthoscopic. However, along with the swift growth of non-linear elements in the power system, the sinusoidal circuit power theory has gradually presented unsuitability. This paper studies the measurement algorithm of the reactive energy and Harmonic analysis by using the quasi-synchronization.
The reactive energy measurement plays an important role in power system. Several prevalent methods such as digital phase shift method, integration method and Hilbert transform method for reactive power measurement are introduced in this paper. The measuring error and the methods of correcting the error are also analyzed. The feasibilities of the hardware and software based on these methods are discussed simply.
The estimation of electrical harmonic parameters by using the quasi-synchronization and interpolated FFT are emphatically introduced in the harmonic measurement. The main factor of spectral leakage is conducted when the sampling is non-synchronous. The computing formulas for the harmonic parameters are given based on the features of Hanning Window and Blackman Window. The computing formulas are given based on the method of quasi-synchronization as well.
The simulation results show that the four measurement methods of reactive power of sinusoidal circuit are more accurate when the harmonic content of voltage and current is small. Finally, the accuracy and reliability of the algorithm are analyzed, combining their frequency characteristics and phase characteristics.
All the three measurement methods will reduce the spectrum leakage significantly. Some suggestion is proposed for the practical use of the algorithms, based on the accuracy, the error characteristics changing with frequency, and the practicability.
Eventually, based on the low-voltage reactive power compensation projects, the hardware system of the harmonic and reactive energy measurement is emphasized on, and the real reactive and harmonic measurement is introduced as well.
引文
[1].程浩忠.电力系统无功与电压稳定性[M].北京:中国电力出版社.2004,3.
[2].陆安定.发电厂变电所及电力系统的无功功率[M].北京:中国电力出版社,2003,8.
[3].张有顺,冯井岗.电能计量基础[M].北京:中国计量出版社,1996.
[4].王兆安,杨君,刘进军.谐波抑制和无功功率补偿[M].北京:机械工业出版社,1998.
[5].刘金华,刘永强.非正弦条件下无功功率定义分析与展望[J].电测与仪表,2006,43(3):1-4,59.
[6].张旭俊.非正弦波形下各种无功功率定义的本质[J].电测与仪表,2004,41(1):1-3,9.
[7].赵建国,石岩,丁磊等.电能计量中的谐波分析[J].中国电力,1997,30(12):21-24.
[8].刘桂英,粟时平.无功电能计量理论技术及其发展[J].中国测试技术,2006,32(2):11-14,21.
[9].Etienne Moulin.电能表计量无功功率的方法[J].电测与仪表,2004,41(4):46-48.
[10].肖湘宁,徐永梅.电力系统谐波及其综合治理[J].中国电力,1998,31(4):59-61.
[11].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.
[12].赵玲,王亮.基于瞬时无功功率理论检测谐波的Matlab仿真[J].广西师范大学学报(自然科学版),2005,23(1):46-49.
[13].向东阳,王公宝,马伟明等.基于FFT和神经网络的非整数次谐波检测方法[J].中国电机工程学报,2005,25(9):35-39.
[14].石志强,任震,黄雯莹.基于小波变换检测谐波的新方法(二)理论基础[J].电力系统自动化,1997,21(2):13-17.
[15].曾乃鸿.电子式电能表的发展现状和展望[J].华东电力,2001,(9):24-27.
[16].韩小涛,谢剑峰,李启炎等.嵌入式技术及其在电能计量中的应用[J].电测与仪表,2005.42(8):46-50.
[17].王茂海,刘会金.非正弦及不对称电路中功率现象的探讨[J].电工技术学报,2002,17(3):93-96,20.
[18].张旭俊.非正弦波及不对称下三相功率因数的定义[J].电测与仪表,2004,41(5):1-2,35.
[19].杨本渤.谐波对电能计量仪器的影响[J].电测与仪表,1993,(11):32-35
[20].闫华光,宗建华,杨林.非正弦情况下无功功率定义的分析[J].电测与仪表,2003,40(2):5-7,30.
[21].张文生,刘耀年,聂宏展.非正弦和三相不对称系统中功率的实用计算[J].电测与仪表,2002,39(7):19-22.
[22].宋光清,雷惠博.跨相接线无功电度表的方法误差[J].电测与仪表,2001,38(12):14-17.
[23].富致超,田春雨,耿心志等.数字移相法测量无功功率的频率误差补偿[J].2004,41(10):9-11.
[24].富致超,王伦展,耿心志.积分法测量无功功率的原理初探[J].电测与仪表.2004,41(3):1-2.
[25].富致超,赵志华,王伦展等.对“积分法移相测无功功率”的进一步研究[J].电测与仪表,2005,42(10):5-7.
[26].薛蕙,杨仁刚.基于FFT的高精度谐波检测算法[J].中国电机工程学报,2002.22(12):106-110.
[27].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.
[28].杜广宇,陈小桥,万中田.锁相倍频和准同步采样法在谐波测量中的应用[J].武汉大学学报(工学版).2001,34(5):39-44.
[29].俎云霄,庞浩,李东霞等.一种基于Hilbert数字滤波的无功功率测量方法[J].电力系统自动化,2003,27(16):50-52,70.
[30].杨桦,任震,唐卓尧.基于小波变换检测谐波的新方法[J].电力系统自动化,1997,21(10):39-42.
[31].金雄飞,乐秀璠.电网谐波测量方法评述[J].继电器,2003,31(8):11-14.
[32].潘文,钱俞淘,周鄂.基于加窗插值FFT的电力谐波测量理论(Ⅰ)窗函数研究[J].电工技术学报,1994,(1):50-54.
[33].潘文,钱俞寿,周鹗.基于加窗差值FFT的电力谐波测量理论(Ⅱ)双插值FFT理论[J].电工技术学报,1994,(2):53-56.
[34].赵文春,马伟明,胡安.电机测试中谐波分析的高精度FFT算法[J].中国电 机工程学报,2001,21(12):83-87,92.
[35].戴先中.准同步采样及其在非正弦功率测量中的应用[J].仪器仪表学报,1984,5(4):390-396.
[36].戴先中.准同步采样应用中的若干问题[J].电测与仪表,1988(2):2-7
[37].邓春,杨学昌,戚庆成等.非线性供电系统中电能准确计量的研究[J].仪器仪表学报,1997,18(4):337-342.
[38].李君凯,丁化成.一种新的电力系统谐波分析仪采样计算方法[J].电测与仪表.2000(10):1-3
[39].何一浩,王树民.TSC动态无功补偿技术述评[J].中国电力2004,37(10):22-26
[40].刘黎明,刘涤尘,史进,刘慧环.DSP无功补偿控制器的研究[J].电工技术,2003(1):5-6.
[41].王丹,张波,丘东元,袁光明.基于DSP的TSC综合型动态无功补偿装置闭[J].电气应用 2005,24(6):57-60
[2].陆安定.发电厂变电所及电力系统的无功功率[M].北京:中国电力出版社,2003,8.
[3].张有顺,冯井岗.电能计量基础[M].北京:中国计量出版社,1996.
[4].王兆安,杨君,刘进军.谐波抑制和无功功率补偿[M].北京:机械工业出版社,1998.
[5].刘金华,刘永强.非正弦条件下无功功率定义分析与展望[J].电测与仪表,2006,43(3):1-4,59.
[6].张旭俊.非正弦波形下各种无功功率定义的本质[J].电测与仪表,2004,41(1):1-3,9.
[7].赵建国,石岩,丁磊等.电能计量中的谐波分析[J].中国电力,1997,30(12):21-24.
[8].刘桂英,粟时平.无功电能计量理论技术及其发展[J].中国测试技术,2006,32(2):11-14,21.
[9].Etienne Moulin.电能表计量无功功率的方法[J].电测与仪表,2004,41(4):46-48.
[10].肖湘宁,徐永梅.电力系统谐波及其综合治理[J].中国电力,1998,31(4):59-61.
[11].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.
[12].赵玲,王亮.基于瞬时无功功率理论检测谐波的Matlab仿真[J].广西师范大学学报(自然科学版),2005,23(1):46-49.
[13].向东阳,王公宝,马伟明等.基于FFT和神经网络的非整数次谐波检测方法[J].中国电机工程学报,2005,25(9):35-39.
[14].石志强,任震,黄雯莹.基于小波变换检测谐波的新方法(二)理论基础[J].电力系统自动化,1997,21(2):13-17.
[15].曾乃鸿.电子式电能表的发展现状和展望[J].华东电力,2001,(9):24-27.
[16].韩小涛,谢剑峰,李启炎等.嵌入式技术及其在电能计量中的应用[J].电测与仪表,2005.42(8):46-50.
[17].王茂海,刘会金.非正弦及不对称电路中功率现象的探讨[J].电工技术学报,2002,17(3):93-96,20.
[18].张旭俊.非正弦波及不对称下三相功率因数的定义[J].电测与仪表,2004,41(5):1-2,35.
[19].杨本渤.谐波对电能计量仪器的影响[J].电测与仪表,1993,(11):32-35
[20].闫华光,宗建华,杨林.非正弦情况下无功功率定义的分析[J].电测与仪表,2003,40(2):5-7,30.
[21].张文生,刘耀年,聂宏展.非正弦和三相不对称系统中功率的实用计算[J].电测与仪表,2002,39(7):19-22.
[22].宋光清,雷惠博.跨相接线无功电度表的方法误差[J].电测与仪表,2001,38(12):14-17.
[23].富致超,田春雨,耿心志等.数字移相法测量无功功率的频率误差补偿[J].2004,41(10):9-11.
[24].富致超,王伦展,耿心志.积分法测量无功功率的原理初探[J].电测与仪表.2004,41(3):1-2.
[25].富致超,赵志华,王伦展等.对“积分法移相测无功功率”的进一步研究[J].电测与仪表,2005,42(10):5-7.
[26].薛蕙,杨仁刚.基于FFT的高精度谐波检测算法[J].中国电机工程学报,2002.22(12):106-110.
[27].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.
[28].杜广宇,陈小桥,万中田.锁相倍频和准同步采样法在谐波测量中的应用[J].武汉大学学报(工学版).2001,34(5):39-44.
[29].俎云霄,庞浩,李东霞等.一种基于Hilbert数字滤波的无功功率测量方法[J].电力系统自动化,2003,27(16):50-52,70.
[30].杨桦,任震,唐卓尧.基于小波变换检测谐波的新方法[J].电力系统自动化,1997,21(10):39-42.
[31].金雄飞,乐秀璠.电网谐波测量方法评述[J].继电器,2003,31(8):11-14.
[32].潘文,钱俞淘,周鄂.基于加窗插值FFT的电力谐波测量理论(Ⅰ)窗函数研究[J].电工技术学报,1994,(1):50-54.
[33].潘文,钱俞寿,周鹗.基于加窗差值FFT的电力谐波测量理论(Ⅱ)双插值FFT理论[J].电工技术学报,1994,(2):53-56.
[34].赵文春,马伟明,胡安.电机测试中谐波分析的高精度FFT算法[J].中国电 机工程学报,2001,21(12):83-87,92.
[35].戴先中.准同步采样及其在非正弦功率测量中的应用[J].仪器仪表学报,1984,5(4):390-396.
[36].戴先中.准同步采样应用中的若干问题[J].电测与仪表,1988(2):2-7
[37].邓春,杨学昌,戚庆成等.非线性供电系统中电能准确计量的研究[J].仪器仪表学报,1997,18(4):337-342.
[38].李君凯,丁化成.一种新的电力系统谐波分析仪采样计算方法[J].电测与仪表.2000(10):1-3
[39].何一浩,王树民.TSC动态无功补偿技术述评[J].中国电力2004,37(10):22-26
[40].刘黎明,刘涤尘,史进,刘慧环.DSP无功补偿控制器的研究[J].电工技术,2003(1):5-6.
[41].王丹,张波,丘东元,袁光明.基于DSP的TSC综合型动态无功补偿装置闭[J].电气应用 2005,24(6):57-60