基于卡尔曼滤波的电力变压器主保护的研究
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摘要
随着电力工业的迅速发展，大型变压器得到了广泛的应用。大型变压器一旦发生故障，影响范围很大。因此大型变压器的继电保护十分重要。
差动保护是变压器的主保护。如何提高大型变压器差动保护的灵敏性和可靠性，是倍受关注和十分重要的领域。
本文旨在讨论现代大型变压器的主保护装置的设计。
文中系统的介绍了变压器保护装置的历史发展及其现状；具体分析励磁涌流产生的原因及常规的辨别励磁涌流的方法；采用11状态卡尔曼滤波算法作为提取基波及高次谐波的方法；分析、比较傅氏算法、卡尔曼滤波算法等算法在信号处理中的优劣；构建主保护装置的硬件电路。
文中对变压器保护中遇到的和应涌流现象提出思考，以期能够引起同行的注意，找到一个合适的解决方案。
With the development of electrical industry, more large power transformers will be widely used in power system. As the failure of them damages the power system normal operation seriously, the protection performance for the large power transformer must be improved.
Differential relay is the key protection for power transformer. It is notable to improve the sensitivity and reliability of differential relay.
The purpose of this paper is a discussion about how to design a sensitive protection device.
The paper systematically discussed the developments and present situation of transformer protection. The paper has introduced and analyzed the principles of discriminating the magnetizing inrush and fault current, which had been developed in resent decades. A set of eleven-state Kalman filters is used to estimate the fundamental and up to fifth harmonic components of the transformer current signals. Here the calculation method for signals including aperiodic component based on the algorithms such as the Fourier algorithm and Kalman filter algorithm and so on are given. The paper presents the design and real-time implementation of a Kalman filter based digital percentage differential and ground fault protection scheme for three phase power transformers. The paper introduced the partly hardware used in the device.
The paper also points out another question of surge inrush.
差动保护是变压器的主保护。如何提高大型变压器差动保护的灵敏性和可靠性，是倍受关注和十分重要的领域。
本文旨在讨论现代大型变压器的主保护装置的设计。
文中系统的介绍了变压器保护装置的历史发展及其现状；具体分析励磁涌流产生的原因及常规的辨别励磁涌流的方法；采用11状态卡尔曼滤波算法作为提取基波及高次谐波的方法；分析、比较傅氏算法、卡尔曼滤波算法等算法在信号处理中的优劣；构建主保护装置的硬件电路。
文中对变压器保护中遇到的和应涌流现象提出思考，以期能够引起同行的注意，找到一个合适的解决方案。
With the development of electrical industry, more large power transformers will be widely used in power system. As the failure of them damages the power system normal operation seriously, the protection performance for the large power transformer must be improved.
Differential relay is the key protection for power transformer. It is notable to improve the sensitivity and reliability of differential relay.
The purpose of this paper is a discussion about how to design a sensitive protection device.
The paper systematically discussed the developments and present situation of transformer protection. The paper has introduced and analyzed the principles of discriminating the magnetizing inrush and fault current, which had been developed in resent decades. A set of eleven-state Kalman filters is used to estimate the fundamental and up to fifth harmonic components of the transformer current signals. Here the calculation method for signals including aperiodic component based on the algorithms such as the Fourier algorithm and Kalman filter algorithm and so on are given. The paper presents the design and real-time implementation of a Kalman filter based digital percentage differential and ground fault protection scheme for three phase power transformers. The paper introduced the partly hardware used in the device.
The paper also points out another question of surge inrush.
引文
[1]周玉兰．1990～1999年220kV及以上变压器保护运行情况[J]．电力自动化设备2001，(5)：51～54．
[2]安徽省电力调度中心．安徽省220kV系统继电保护及自动装置统计分析年报[J]．1991～2000．
[3]傅翔华，贾长朱．微机变压器保护装置现状分析及改进建议[J]．电力系统自动化．1997，(21)：8．
[4]贺家李．电力系统继电保护技术的现状与发展．中国电力[J]．1999，(10)：32
[5]史世文．元件保护国内外发展综述．电力系统自动化[J]．1996，(4)
[6]杨奇逊．微型机继电保护基础[M]．北京：水利水电出版社．1988
[7]陈德树主编．计算机继电保护原理与技术[M]．北京：水利电力出版社．1992．11。
[8]王祖光．电力系统主设备保护论文集[M]．南京：南京自动化研究院．1990
[9]陈增田编．电力变压器保护(第二版)[M]．北京：水利电力出版社．1992．11
[10]华中工学院编．电力系统继电保护原理与运行．北京：水利电力出版社．1981
[11]徐进亮等．WBZ～500型微机变压器保护[J]．1994．8(3)：51～59
[12]蒋豪贤．电机学[M]．华南理工大学出版社，广州：1997年3月
[13]周鹗．电机学[M]．水利水电出版社．北京：1995
[14]王维俭．发电机变压器继电保护应用[M]．北京：中国电力出版社，1998年3月第一版
[15]王维俭，侯炳蕴．大型机组继电保护理论基础．北京：水利电力出版社[M]，1989年第二版
[16]史世文．大机组继电保护[M]．北京：水利电力出版社．1992
[17]胡玉峰，陈德树．微机变压器保护中几种谐波制动比计算的比较[J]．继电器．2000．7
[18]董洁，于莉萍等．变压器差动保护涌流原理的研究[J]．电力系统自动化．1997．12
[19]王祖光．间断角原理的变压器差动保护[J]．电力系统自动化．1979．(1)
[20]Thorp J S. Phadke A G. A Microprocessor Based Voltage Restrained Three Phase Transformer Differential Relay[J].Proceeding of the South Eastern Symposium on System Theory. 1982.4: 312～316
[21]Inagaki K et al. Digital Protection Method for Power Transformers Based on and Equivalent Circuit Composed of Inductance[J].IEEE Trans on Power
Delivery. 1988.10.3(4)
[22]王维俭译．考虑励磁特性的保护新技术[J]．(日)电气计算．49(5)
[23]郭勇．大型变压器微机继电保护的研究．华中理工大学硕士论文．1987
[24]Phadke A G. Trop J S.A New Computer～based Flux Restrained Current Differential Relay for Power Transformer Protection[J].IEEE Trans on Power Apparatus and System. 1983.102(11): 3624～3629
[25]孙志杰，陈云仑．波形对称原理的变压器差动保护[J]．电力系统自动化1996．4：42～46
[26]M.A.Rahman and B.Jeyasurya.A State～of～the～Art Review of Transformer Protection Algorithms[J].IEEE PES Winter Meeting. 1987.2:1～6
[27]O.P.Malik, EK.Dash and G.S.Hope. Digital protection of power transformor. IEEE PES Winter Meeting.1976.1 : 1～7
[28]M.A.Rahman and P.K.Dash. Fast algorithm for digital protection of power transformers.IEE Vol.129, PartC.1982.3:79～85
[29]D.B.Fakruddin et al. Application of Haar functions for transmission line and transformer differential protection. Int. J. Electr Power and Energy System.1984.7(6): 169～180
[30]B.Jeyasurya and M.A.Rahman. Application of Walsh functions for Microprocessor Based transformer protection. IEEE Trans. on Electromagnetic compatibility. 1985(4): 221～225
[31]A.J. Degens. Algorithm for a digital transformer differential protection based on a least～fitting. Proceedings IEE, Vol.128, Part C, No.3.1981:155～161
[32]M.S.Sachdev and D.V.Shah. Transformer differential and restricted earth fault protection using a digital processor. Transactions of the Canadian Electrial Association, Vol.20, Part4.1981:1～11
[33]M.A.Rahman, P.K.Dash and E.R.Downton .Digital protection of power transformer based on weighted least square algorithm. IEEE Trans. On Power Apparatus and Systems , Vol.PAS～101, No.11, 1982:4204～4209
[34]Y.V.V.S.Murty and W.J.Smolinski.Design and implementation of a digital differential relay for a 3～phase power transformer based on Kalman filtering theory.IEEE PES Winter meeting 1987.2.1～6
[35]姚天任，孙洪．现代数字信号处理[M]．武汉：华中科技大学出版社．1999．6
[36]申鼎煊 应用随机过程．武汉：华中理工大学出版社．1994
[37]丁书文，张承学等．半波傅氏算法的改进[J]．电力系统自动化．1999．23(5)：18～20
[38]孙雅明，张兆宁等．电力系统故障暂态信号中提取基波分量的短窗积分法[J]．电力系统自动化．2000．24(1)：30～33
[39]贾贵玺，王克昌等．关于推广的傅氏算法滤除衰减直流分量方法的探讨[J]．电力系统自动化．1992．16(2)：14～17．
[40]张志竞，王汉忠．傅里叶算法和微分方程算法的改进[J]．电力系统自动化．1983．7(5)：20～30．
[41]田立军，陆于平等．一种新的微机保护快速算法[J]．电力系统自动化．1997，21(、3)：21～23
[42]朱声石．高压电网继电保护原理与技术[M]．北京：中国电力出版社．1995
[43]Bomard P, Bastide J.C. A prototype of multiprocessor based distance relay[J].IEEE Trans PAS, 101(2): 491～498
[44]张哲，陈德树．递推最小二乘算法在距离保护中的应用研究[J]．电网技术．1991．(4)：31～40
[45]汪亚南，TMS320系列高速单片计算机原理与应用[M]．西安：电子科技大学出版社．1991．3
[46]TMS320C3X Users Guide.Texas Instrument.2000
[47]TMSS320C3X General Purpose Applications.Texas Instrument.2000
[48]张雄伟．DSP芯片的原理与开发应用．北京：电子工业出版社．2000．9
[49]王念旭．DSP基础与应用系统设计．北京：北京航空航天大学出版社．2001．8
[50]赵勇．DSP应用系统设计．北京：电子工业出版社．2002．10
[51]戴逸民．基于DSP的现代电子系统设计．北京：电子工业出版社．2002．5
[52]TMS320C3X Assembly Language Tools.Texas Instrument.2000
[53]传感器变送器测控仪表大全[M]．北京：机械工业出版社．1998．5
[54]刘乐善．微型计算机接口技术及应用[M]．武汉：华中科技大学出版社．2000．4
[55]沈红卫．单片机应用系统设计实例与分析[M]．北京：北京航空航天大学出版社．2003．1
[56]何立民．单片机应用系统设计[M]．北京：北京航空航天大学出版社．1990．1
[2]安徽省电力调度中心．安徽省220kV系统继电保护及自动装置统计分析年报[J]．1991～2000．
[3]傅翔华，贾长朱．微机变压器保护装置现状分析及改进建议[J]．电力系统自动化．1997，(21)：8．
[4]贺家李．电力系统继电保护技术的现状与发展．中国电力[J]．1999，(10)：32
[5]史世文．元件保护国内外发展综述．电力系统自动化[J]．1996，(4)
[6]杨奇逊．微型机继电保护基础[M]．北京：水利水电出版社．1988
[7]陈德树主编．计算机继电保护原理与技术[M]．北京：水利电力出版社．1992．11。
[8]王祖光．电力系统主设备保护论文集[M]．南京：南京自动化研究院．1990
[9]陈增田编．电力变压器保护(第二版)[M]．北京：水利电力出版社．1992．11
[10]华中工学院编．电力系统继电保护原理与运行．北京：水利电力出版社．1981
[11]徐进亮等．WBZ～500型微机变压器保护[J]．1994．8(3)：51～59
[12]蒋豪贤．电机学[M]．华南理工大学出版社，广州：1997年3月
[13]周鹗．电机学[M]．水利水电出版社．北京：1995
[14]王维俭．发电机变压器继电保护应用[M]．北京：中国电力出版社，1998年3月第一版
[15]王维俭，侯炳蕴．大型机组继电保护理论基础．北京：水利电力出版社[M]，1989年第二版
[16]史世文．大机组继电保护[M]．北京：水利电力出版社．1992
[17]胡玉峰，陈德树．微机变压器保护中几种谐波制动比计算的比较[J]．继电器．2000．7
[18]董洁，于莉萍等．变压器差动保护涌流原理的研究[J]．电力系统自动化．1997．12
[19]王祖光．间断角原理的变压器差动保护[J]．电力系统自动化．1979．(1)
[20]Thorp J S. Phadke A G. A Microprocessor Based Voltage Restrained Three Phase Transformer Differential Relay[J].Proceeding of the South Eastern Symposium on System Theory. 1982.4: 312～316
[21]Inagaki K et al. Digital Protection Method for Power Transformers Based on and Equivalent Circuit Composed of Inductance[J].IEEE Trans on Power
Delivery. 1988.10.3(4)
[22]王维俭译．考虑励磁特性的保护新技术[J]．(日)电气计算．49(5)
[23]郭勇．大型变压器微机继电保护的研究．华中理工大学硕士论文．1987
[24]Phadke A G. Trop J S.A New Computer～based Flux Restrained Current Differential Relay for Power Transformer Protection[J].IEEE Trans on Power Apparatus and System. 1983.102(11): 3624～3629
[25]孙志杰，陈云仑．波形对称原理的变压器差动保护[J]．电力系统自动化1996．4：42～46
[26]M.A.Rahman and B.Jeyasurya.A State～of～the～Art Review of Transformer Protection Algorithms[J].IEEE PES Winter Meeting. 1987.2:1～6
[27]O.P.Malik, EK.Dash and G.S.Hope. Digital protection of power transformor. IEEE PES Winter Meeting.1976.1 : 1～7
[28]M.A.Rahman and P.K.Dash. Fast algorithm for digital protection of power transformers.IEE Vol.129, PartC.1982.3:79～85
[29]D.B.Fakruddin et al. Application of Haar functions for transmission line and transformer differential protection. Int. J. Electr Power and Energy System.1984.7(6): 169～180
[30]B.Jeyasurya and M.A.Rahman. Application of Walsh functions for Microprocessor Based transformer protection. IEEE Trans. on Electromagnetic compatibility. 1985(4): 221～225
[31]A.J. Degens. Algorithm for a digital transformer differential protection based on a least～fitting. Proceedings IEE, Vol.128, Part C, No.3.1981:155～161
[32]M.S.Sachdev and D.V.Shah. Transformer differential and restricted earth fault protection using a digital processor. Transactions of the Canadian Electrial Association, Vol.20, Part4.1981:1～11
[33]M.A.Rahman, P.K.Dash and E.R.Downton .Digital protection of power transformer based on weighted least square algorithm. IEEE Trans. On Power Apparatus and Systems , Vol.PAS～101, No.11, 1982:4204～4209
[34]Y.V.V.S.Murty and W.J.Smolinski.Design and implementation of a digital differential relay for a 3～phase power transformer based on Kalman filtering theory.IEEE PES Winter meeting 1987.2.1～6
[35]姚天任，孙洪．现代数字信号处理[M]．武汉：华中科技大学出版社．1999．6
[36]申鼎煊 应用随机过程．武汉：华中理工大学出版社．1994
[37]丁书文，张承学等．半波傅氏算法的改进[J]．电力系统自动化．1999．23(5)：18～20
[38]孙雅明，张兆宁等．电力系统故障暂态信号中提取基波分量的短窗积分法[J]．电力系统自动化．2000．24(1)：30～33
[39]贾贵玺，王克昌等．关于推广的傅氏算法滤除衰减直流分量方法的探讨[J]．电力系统自动化．1992．16(2)：14～17．
[40]张志竞，王汉忠．傅里叶算法和微分方程算法的改进[J]．电力系统自动化．1983．7(5)：20～30．
[41]田立军，陆于平等．一种新的微机保护快速算法[J]．电力系统自动化．1997，21(、3)：21～23
[42]朱声石．高压电网继电保护原理与技术[M]．北京：中国电力出版社．1995
[43]Bomard P, Bastide J.C. A prototype of multiprocessor based distance relay[J].IEEE Trans PAS, 101(2): 491～498
[44]张哲，陈德树．递推最小二乘算法在距离保护中的应用研究[J]．电网技术．1991．(4)：31～40
[45]汪亚南，TMS320系列高速单片计算机原理与应用[M]．西安：电子科技大学出版社．1991．3
[46]TMS320C3X Users Guide.Texas Instrument.2000
[47]TMSS320C3X General Purpose Applications.Texas Instrument.2000
[48]张雄伟．DSP芯片的原理与开发应用．北京：电子工业出版社．2000．9
[49]王念旭．DSP基础与应用系统设计．北京：北京航空航天大学出版社．2001．8
[50]赵勇．DSP应用系统设计．北京：电子工业出版社．2002．10
[51]戴逸民．基于DSP的现代电子系统设计．北京：电子工业出版社．2002．5
[52]TMS320C3X Assembly Language Tools.Texas Instrument.2000
[53]传感器变送器测控仪表大全[M]．北京：机械工业出版社．1998．5
[54]刘乐善．微型计算机接口技术及应用[M]．武汉：华中科技大学出版社．2000．4
[55]沈红卫．单片机应用系统设计实例与分析[M]．北京：北京航空航天大学出版社．2003．1
[56]何立民．单片机应用系统设计[M]．北京：北京航空航天大学出版社．1990．1