直流偏磁条件下电力变压器振动特性研究进展
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摘要
基于电力系统中直流偏磁成因及变压器振动机制的分析,结合演绎铁磁材料本构关系的基础理论,从磁畴理论、现象学理论、热力学关系及弹性力学4个角度对磁致伸缩的建模机理与存在的问题进行了分析。在此基础上,对发生直流偏磁时磁致伸缩的现有计算模型进行对比,并讨论了发生直流偏磁时的硅钢片实验与变压器现场测试等研究中的不足,继而探析变压器振动的实验研究中直流电源的引入方式。综合分析现有研究进展后指出,为了给评估变压器承受直流偏磁能力与指导变压器的设计等提供参考,亟需研究直流偏磁时铁磁材料的磁化特性与磁致伸缩的模型这2个科学问题。
Based on the analysis of the forming reason of DC bias and the vibration mechanism of transformer in power system and combined with the fundamental theory of ferromagnetic material constitutive relation deduction,the modeling mechanism of magnetostriction and corresponding problems are elucidated from aspects of the magnetic domain theory,thermodynamic relationship,phenomenological theory and elasticity.On this basis,the existing computing models of magnetostriction with DC bias are compared,and the inadequacies of silicon steel sheet and onsite transformer tests when DC bias occurs are discussed.Furthermore,the inducing modes of DC power source during the experimental study of transformer vibration are explored and analyzed.According to the comprehensive analysis of the current research progress,it is pointed out that special attention should be paid on science problems such as ferromagnetic material magnetization characteristics and magnetostriction modeling,so as to provide a reference for evaluating the transformer withstand ability of DC bias and guiding the transformer construction design.
Based on the analysis of the forming reason of DC bias and the vibration mechanism of transformer in power system and combined with the fundamental theory of ferromagnetic material constitutive relation deduction,the modeling mechanism of magnetostriction and corresponding problems are elucidated from aspects of the magnetic domain theory,thermodynamic relationship,phenomenological theory and elasticity.On this basis,the existing computing models of magnetostriction with DC bias are compared,and the inadequacies of silicon steel sheet and onsite transformer tests when DC bias occurs are discussed.Furthermore,the inducing modes of DC power source during the experimental study of transformer vibration are explored and analyzed.According to the comprehensive analysis of the current research progress,it is pointed out that special attention should be paid on science problems such as ferromagnetic material magnetization characteristics and magnetostriction modeling,so as to provide a reference for evaluating the transformer withstand ability of DC bias and guiding the transformer construction design.
引文
[1]ALBERTSONV D,BOZOKI B,FEERO W E,et al.Geomagnetic disturbance effects on power systems[J].IEEE Transactions on Power Delivery,1993,8(3):1206-1216.
[2]舒印彪,张文亮.特高压输电若干关键技术研究[J].中国电机工程学报,2007,27(31):3-8.SHU Yinbiao,ZHANG Wenliang.Research of key technologies for UHV transmission[J].Proceedings of the CSEE,2007,27(31):3-8.
[3]刘明军,程臣,赵克江,等.交流电网整流变引起的直流偏磁机理与实验分析[J].电气技术,2016,17(6):93-96,100.LIU Mingjun,CHENG Chen,ZHAO Kejiang,et al.The mechanism and experiment analysis of DC magnetic bias caused by rectifier transformer of AC grid[J].Electrical Engineering,2016,17(6):93-96,100.
[4]WEISERB,PFTZNER H,ANGER J.Relevance of magnetostriction and forces for the generation of audible noise of transformer cores[J].IEEE Transactions on Magnetics,2000,36(5):3759-3777.
[5]曾连生.直流输电接地极电流对电力变压器的影响[J].高电压技术,2005,31(4):57-58,81.ZENG Liansheng.Impact of HVDC ground electrode current on the adjacent power transformers[J].High Voltage Engineering,2005,31(4):57-58,81.
[6]刘连光,王开让,赵春红,等.太阳风暴对电网干扰的日面参数与条件[J].电工技术学报,2013,28(增刊2):360-367.LIU Lianguang,WANG Kairang,ZHAO Chunhong,et al.Solar storm heligraphic parameters and conditions driving the GIC in grid[J].Transactions of China Electrotechnical Society,2013,28(Supplement2):360-367.
[7]刘林玉,谢学武.500 k V主变压器异常声音分析[J].高电压技术,2005,31(4):85-88.LIU Linyu,XIE Xuewu.Analysis of increase of noise of 500 k V transformer[J].High Voltage Engineering,2005,31(4):85-88.
[8]VIJAYRAGHAVAN P,KRISHNAN R.Noise in electrical machines:a review[J].IEEE Transactions on Industry and Applications,1999,35(5):1007-1013.
[9]汲胜昌,刘味果,李彦明,等.振动法用于在线监测电力变压器绕组及铁心状况的可行性研究[J].高压电器,2001,37(5):4-7.JI Shengchang,LIU Weiguo,LI Yanming,et al.Feasibility of vibration analysis method in application to on-line monitoring of the core and the winding of power transformer[J].High Voltage Apparatus,2001,37(5):4-7.
[10]陈青恒,马宏彬,何金良.直流偏磁引起的500 k V电力变压器振动和噪声的现场测量与分析[J].高压电器,2009,45(3):93-96.CHEN Qingheng,MA Hongbin,HE Jinliang.Field monitoring and analysis on vibration and noise of 500 k V electrical transformer under DC current biasing[J].High Voltage Apparatus,2009,45(3):93-96.
[11]郭洁,黄海,唐昕,等.500 k V电力变压器偏磁振动分析[J].电网技术,2012,36(3):70-75.GUO Jie,HUANG Hai,TANG Xin,et al.Analysis on 500 k V power transformer vibration under DC magnetic biasing[J].Power System Technology,2012,36(3):70-75.
[12]ZHANG Y,WANG J,SUN X,et al.Measurement and modeling of anisotropic magnetostriction characteristic of grain-oriented silicon steel sheet under DC bias[J].IEEE Transactions on Magnetics,2014,50(2):361-364.
[13]赵凯华,陈熙谋.电磁学[M].北京:高等教育出版社,1985:238-276.
[14]姚缨英.大型电力变压器直流偏磁现象的研究[D].沈阳:沈阳工业大学,2000.YAO Yingying.Research on the DC bias phenomena of large power transformers[D].Shenyang:Shenyang University of Technology,2000.
[15]WEISER B,HASENZAGL A,BOOTH T,et al.Mechanisms of noise generation of model transformer cores[J].Journal of Magnetism and Magnetic Materials,1996,160(1996):207-209.
[16]WEISER B,PFTZNER H,ANGER J.Relevance of magnetostriction and forces for the generation of audible noise of transformer cores[J].IEEE Transactions on Magnetics,2000,36(5):3759-3777.
[17]HILGERT T,VANDEVELDE L,MELKEBEEK J.Comparison of magnetostriction models for use in calculations of vibrations in magnetic cores[J].IEEE Transactions on Magnetics,2008,44(6):874-877.
[18]DELACHEISSERIE E D T.Magneto-striction:theory and applications of magnetoelasticity[M].Boca Ratyon,USA:CRC Press,1993:122-136.
[19]JILESD C.Theory of the magnetomechanical effect[J].Journal of Physics D Applied Physics,1995,28(8):1537-1546.
[20]SABLIKM J,JILES D C.Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis[J].IEEE Transactions on Magnetics,1993,29(3):2113-2123.
[21]HRISTOFOROU E.Magnetostrictive delay lines:engineering theory and sensing applications[J].Measurement Science&Technology,2003,14(2):R15-R47.
[22]ADLYA A,MAYERGOYZ I D,BERGQVIST A.Preisach modeling of magnetostrictive hysteresis[J].Journal of Applied Physics,1991,69(8):5777-5779.
[23]周浩淼.铁磁材料非线性磁弹性耦合理论及其在超磁致伸缩智能材料中的应用[D].兰州:兰州大学,2004.ZHOU Haomiao.Nonlinear coupled magneto-elastic theory in ferromagnetic materials and the application in giant magnetostrictive smart material[D].Lanzhou:Lanzhou University,2004.
[24]LI Q,WANG X,ZHANG L,et al.Modelling methodology for transformer core vibrations based on the magnetostrictive properties[J].IET Electric Power Applications,2012,6(9):604-610.
[25]张黎,王国政,董攀婷,等.基于磁致伸缩本征特性的晶粒取向性变压器铁心振动模型[J].中国电机工程学报,2016,36(14):3990-4000.ZHANG Li,WANG Guozheng,DONG Panting,et al.Study on the vibration of grain-oriented transformer core based on the magnetostrictive intrinsic characteristics[J].Proceedings of the CSEE,2016,36(14):3990-4000.
[26]顾晓安.电磁场诱发铁磁材料电磁振动机理研究及其应用[D].上海:复旦大学,2003.GU Xiaoan.Study on mechanism of mechanical behavior of ferromagnetic materials under sinusoidal magnetization and its applications[D].Shanghai:Fudan University,2003.
[27]FOSTERS L,REIPLINGER E.Characteristics and control of transformer sound[J].IEEE Transactions on Power Apparatus and Sys-tems,1981,100(3):1072-1077.
[28]祝丽花,杨庆新,闫荣格,等.考虑磁致伸缩效应电力变压器振动噪声的研究[J].电工技术学报,2013,28(4):1-7.ZHU Lihua,YANG Qingxin,YAN Rongge,et al.Research on vibration and noise of power transformer cores including magnetostriction effects[J].Transactions of China Electrotechnical Society,2013,28(4):1-7.
[29]董攀婷.基于硅钢片磁致伸缩本质模型的变压器铁芯振动问题研究[D].济南:山东大学,2015.DONG Panting.Study on the vibration of transformer core based on the magnetostrictive intrinsic model of grain-oriented electrical steel sheet[D].Ji'nan:Shandong University,2015.
[30]张剑.直流偏磁条件下变压器振动噪声的多物理场耦合研究[D].沈阳:沈阳工业大学,2013.ZHANG Jian.Research of multi-physics coupling in transformer's vibration and noise inder DC bias conditions[D].Shenyang:Shenyang University of Technology,2013.
[31]高沛,王丰华,苏磊,等.直流偏磁下电力变压器的振动特性[J].电网技术,2014,38(6):1536-1541.GAO Pei,WANG Fenghua,SU Lei,et al.Analysis on vibration characteristics of power transformer under DC bias[J].Power System Technology,2014,38(6):1536-1541.
[32]李长云,刘亚魁.直流偏磁时变压器铁心的力学特性分析[J].电力自动化设备,2015,35(12):122-125.LI Changyun,LIU Yakui.Analysis on the mechanical characteristics of the transformer iron-core with DC bias[J].Elecric Power Automation Equipment,2015,35(12):122-125.
[33]王佳音,白保东,刘宏亮,等.直流偏磁对变压器振动噪声的影响[J].电工技术学报,2015,30(8):56-61.WANG Jiayin,BAI Baodong,LIU Hongliang,et al.Research on vibration and noise of transformers under DC bias[J].Transactions of China Electrotechnical Society,2015,30(8):56-61.
[34]张艳丽,王佳音,白保东,等.直流偏磁磁场对硅钢片磁致伸缩特性的影响分析[J].中国电机工程学报,2016,36(15):4299-4306.ZHANG Yanli,WANG Jiayin,BAI Baodong,et al.Influence analysis of DC biased magnetic field on magnetostrictive characteristics of silicon steel sheet[J].Proceedings of the CSEE,2016,36(15):4299-4306.
[35]ZHANG Y,WANG J,SUN X,et al.Measurement and modeling of anisotropic magnetostriction characteristic of grain-oriented silicon steel sheet under DC bias[J].IEEE Transactions on Magnetics,2014,50(2):361-364.
[36]BAGULEYC A,MADAWALA U K,CARSTEN B.The impact of vibration due to magnetostriction on the core losses of ferrite toroidals under DC bias[J].IEEE Transactions on Magnetics,2011,47(8):2022-2028.
[37]YOU Y,FUCHS E F,LIN D,et al.Reactive power demand of transformers with DC bias[J].IEEE Industry Application Magazine,1996,2(4):45-52.
[38]李慧奇,崔翔,候永亮,等.直流偏磁下变压器励磁电流的实验研究及计算[J].华北电力大学学报,2007,34(4):1-6.LI Huiqi,CUI Xiang,HOU Yongliang,et al.Experimental studies and calculations of the exciting current in the transformer under DC bias magnetization[J].Journal of North China Electric Power University,2007,34(4):1-6.
[39]孔剑虹,何湘宁,钱照明,等.功率变换器电感在直流偏置或矩形波激励时磁损问题研究[J].电工技术学报,2005,20(5):13-19,29.KONG Jianhong,HE Xiangning,QIAN Zhaoming,et al.Core losses of magnetic components in power converter topologies[J].Transactions of China Electrotechnical Society,2005,20(5):13-19,29.
[40]STONER E C,WOHLFARTH E P.A mechanism of magnetic hysteresis in heterogeneous alloys[J].Philosophical Transactions of the Royal Society of London,1948,24(A):599-642.
[41]GLOBUS A,DUPLEX P,GUYOT M.Determination of initial magnetization curve from crystallites size and effective anisotropy field[J].IEEE Transactions on Magnetics,1971,7(3):617-622.
[42]JILES D C,ATHERTON D L.Theory of ferromagnetic hysteresis[J].Journal of Applied Physics,1984,55(6):2115-2120.
[43]LIORZOU F,PHELPS B,ATHERTON D L.Macroscopic models of magnetization[J].IEEE Transactions on Magnetics,2000,36(2):418-427.
[44]郭满生,梅桂华,刘东升,等.直流偏磁条件下电力变压器铁心B-H曲线及非对称励磁电流[J].电工技术学报,2009,24(5):46-51,59.GUO Mansheng,MEI Guihua,LIU Dongsheng,et al.B-H curve based on core and asymmetric magnetizing current in DC-biased transformers[J].Transactions of China Electrotechnical Society,2009,24(5):46-51,59.
[45]曹林,何金良,张波.直流偏磁状态下电力变压器铁心动态磁滞损耗模型及验证[J].中国电机工程学报,2008,28(24):141-146.CAO Lin,HE Jinliang,ZHANG Bo.Dynamic hysteresis loss model of power transformer under DC current biasing and its verification[J].Proceedings of the CSEE,2008,28(24):141-146.
[46]BOTERR D H.Geomagnetically induced currents:present knowledge and future research[J].IEEE Transactions on Power Delivery,1994,9(1):50-58.
[47]电力行业电力规划设计标准化技术委员会.高压直流输电大地返回运行系统设计技术规定:D/L5224—2005[S].北京:中国电力出版社,2005.
[48]刘曲,郑健超,潘文,等.变压器铁心承受直流能力的仿真和分析[J].变压器,2006,43(9):5-10.LIU Qu,ZHENG Jianchao,PAN Wen,et al.Analysis and simulation of direct current withstand ability of transformer core[J].Transformer,2006,43(9):5-10.
[49]李长云,李庆民,李贞,等.电能质量约束下变压器承受直流偏磁能力的分析[J].高电压技术,2010,36(12):3112-3118.LI Changyun,LI Qingmin,LI Zhen,et al.Analysis on the with-standing ability of power transformer to DC bias under power quality constraint[J].High Voltage Engineering,2010,36(12):3112-3118.
[2]舒印彪,张文亮.特高压输电若干关键技术研究[J].中国电机工程学报,2007,27(31):3-8.SHU Yinbiao,ZHANG Wenliang.Research of key technologies for UHV transmission[J].Proceedings of the CSEE,2007,27(31):3-8.
[3]刘明军,程臣,赵克江,等.交流电网整流变引起的直流偏磁机理与实验分析[J].电气技术,2016,17(6):93-96,100.LIU Mingjun,CHENG Chen,ZHAO Kejiang,et al.The mechanism and experiment analysis of DC magnetic bias caused by rectifier transformer of AC grid[J].Electrical Engineering,2016,17(6):93-96,100.
[4]WEISERB,PFTZNER H,ANGER J.Relevance of magnetostriction and forces for the generation of audible noise of transformer cores[J].IEEE Transactions on Magnetics,2000,36(5):3759-3777.
[5]曾连生.直流输电接地极电流对电力变压器的影响[J].高电压技术,2005,31(4):57-58,81.ZENG Liansheng.Impact of HVDC ground electrode current on the adjacent power transformers[J].High Voltage Engineering,2005,31(4):57-58,81.
[6]刘连光,王开让,赵春红,等.太阳风暴对电网干扰的日面参数与条件[J].电工技术学报,2013,28(增刊2):360-367.LIU Lianguang,WANG Kairang,ZHAO Chunhong,et al.Solar storm heligraphic parameters and conditions driving the GIC in grid[J].Transactions of China Electrotechnical Society,2013,28(Supplement2):360-367.
[7]刘林玉,谢学武.500 k V主变压器异常声音分析[J].高电压技术,2005,31(4):85-88.LIU Linyu,XIE Xuewu.Analysis of increase of noise of 500 k V transformer[J].High Voltage Engineering,2005,31(4):85-88.
[8]VIJAYRAGHAVAN P,KRISHNAN R.Noise in electrical machines:a review[J].IEEE Transactions on Industry and Applications,1999,35(5):1007-1013.
[9]汲胜昌,刘味果,李彦明,等.振动法用于在线监测电力变压器绕组及铁心状况的可行性研究[J].高压电器,2001,37(5):4-7.JI Shengchang,LIU Weiguo,LI Yanming,et al.Feasibility of vibration analysis method in application to on-line monitoring of the core and the winding of power transformer[J].High Voltage Apparatus,2001,37(5):4-7.
[10]陈青恒,马宏彬,何金良.直流偏磁引起的500 k V电力变压器振动和噪声的现场测量与分析[J].高压电器,2009,45(3):93-96.CHEN Qingheng,MA Hongbin,HE Jinliang.Field monitoring and analysis on vibration and noise of 500 k V electrical transformer under DC current biasing[J].High Voltage Apparatus,2009,45(3):93-96.
[11]郭洁,黄海,唐昕,等.500 k V电力变压器偏磁振动分析[J].电网技术,2012,36(3):70-75.GUO Jie,HUANG Hai,TANG Xin,et al.Analysis on 500 k V power transformer vibration under DC magnetic biasing[J].Power System Technology,2012,36(3):70-75.
[12]ZHANG Y,WANG J,SUN X,et al.Measurement and modeling of anisotropic magnetostriction characteristic of grain-oriented silicon steel sheet under DC bias[J].IEEE Transactions on Magnetics,2014,50(2):361-364.
[13]赵凯华,陈熙谋.电磁学[M].北京:高等教育出版社,1985:238-276.
[14]姚缨英.大型电力变压器直流偏磁现象的研究[D].沈阳:沈阳工业大学,2000.YAO Yingying.Research on the DC bias phenomena of large power transformers[D].Shenyang:Shenyang University of Technology,2000.
[15]WEISER B,HASENZAGL A,BOOTH T,et al.Mechanisms of noise generation of model transformer cores[J].Journal of Magnetism and Magnetic Materials,1996,160(1996):207-209.
[16]WEISER B,PFTZNER H,ANGER J.Relevance of magnetostriction and forces for the generation of audible noise of transformer cores[J].IEEE Transactions on Magnetics,2000,36(5):3759-3777.
[17]HILGERT T,VANDEVELDE L,MELKEBEEK J.Comparison of magnetostriction models for use in calculations of vibrations in magnetic cores[J].IEEE Transactions on Magnetics,2008,44(6):874-877.
[18]DELACHEISSERIE E D T.Magneto-striction:theory and applications of magnetoelasticity[M].Boca Ratyon,USA:CRC Press,1993:122-136.
[19]JILESD C.Theory of the magnetomechanical effect[J].Journal of Physics D Applied Physics,1995,28(8):1537-1546.
[20]SABLIKM J,JILES D C.Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis[J].IEEE Transactions on Magnetics,1993,29(3):2113-2123.
[21]HRISTOFOROU E.Magnetostrictive delay lines:engineering theory and sensing applications[J].Measurement Science&Technology,2003,14(2):R15-R47.
[22]ADLYA A,MAYERGOYZ I D,BERGQVIST A.Preisach modeling of magnetostrictive hysteresis[J].Journal of Applied Physics,1991,69(8):5777-5779.
[23]周浩淼.铁磁材料非线性磁弹性耦合理论及其在超磁致伸缩智能材料中的应用[D].兰州:兰州大学,2004.ZHOU Haomiao.Nonlinear coupled magneto-elastic theory in ferromagnetic materials and the application in giant magnetostrictive smart material[D].Lanzhou:Lanzhou University,2004.
[24]LI Q,WANG X,ZHANG L,et al.Modelling methodology for transformer core vibrations based on the magnetostrictive properties[J].IET Electric Power Applications,2012,6(9):604-610.
[25]张黎,王国政,董攀婷,等.基于磁致伸缩本征特性的晶粒取向性变压器铁心振动模型[J].中国电机工程学报,2016,36(14):3990-4000.ZHANG Li,WANG Guozheng,DONG Panting,et al.Study on the vibration of grain-oriented transformer core based on the magnetostrictive intrinsic characteristics[J].Proceedings of the CSEE,2016,36(14):3990-4000.
[26]顾晓安.电磁场诱发铁磁材料电磁振动机理研究及其应用[D].上海:复旦大学,2003.GU Xiaoan.Study on mechanism of mechanical behavior of ferromagnetic materials under sinusoidal magnetization and its applications[D].Shanghai:Fudan University,2003.
[27]FOSTERS L,REIPLINGER E.Characteristics and control of transformer sound[J].IEEE Transactions on Power Apparatus and Sys-tems,1981,100(3):1072-1077.
[28]祝丽花,杨庆新,闫荣格,等.考虑磁致伸缩效应电力变压器振动噪声的研究[J].电工技术学报,2013,28(4):1-7.ZHU Lihua,YANG Qingxin,YAN Rongge,et al.Research on vibration and noise of power transformer cores including magnetostriction effects[J].Transactions of China Electrotechnical Society,2013,28(4):1-7.
[29]董攀婷.基于硅钢片磁致伸缩本质模型的变压器铁芯振动问题研究[D].济南:山东大学,2015.DONG Panting.Study on the vibration of transformer core based on the magnetostrictive intrinsic model of grain-oriented electrical steel sheet[D].Ji'nan:Shandong University,2015.
[30]张剑.直流偏磁条件下变压器振动噪声的多物理场耦合研究[D].沈阳:沈阳工业大学,2013.ZHANG Jian.Research of multi-physics coupling in transformer's vibration and noise inder DC bias conditions[D].Shenyang:Shenyang University of Technology,2013.
[31]高沛,王丰华,苏磊,等.直流偏磁下电力变压器的振动特性[J].电网技术,2014,38(6):1536-1541.GAO Pei,WANG Fenghua,SU Lei,et al.Analysis on vibration characteristics of power transformer under DC bias[J].Power System Technology,2014,38(6):1536-1541.
[32]李长云,刘亚魁.直流偏磁时变压器铁心的力学特性分析[J].电力自动化设备,2015,35(12):122-125.LI Changyun,LIU Yakui.Analysis on the mechanical characteristics of the transformer iron-core with DC bias[J].Elecric Power Automation Equipment,2015,35(12):122-125.
[33]王佳音,白保东,刘宏亮,等.直流偏磁对变压器振动噪声的影响[J].电工技术学报,2015,30(8):56-61.WANG Jiayin,BAI Baodong,LIU Hongliang,et al.Research on vibration and noise of transformers under DC bias[J].Transactions of China Electrotechnical Society,2015,30(8):56-61.
[34]张艳丽,王佳音,白保东,等.直流偏磁磁场对硅钢片磁致伸缩特性的影响分析[J].中国电机工程学报,2016,36(15):4299-4306.ZHANG Yanli,WANG Jiayin,BAI Baodong,et al.Influence analysis of DC biased magnetic field on magnetostrictive characteristics of silicon steel sheet[J].Proceedings of the CSEE,2016,36(15):4299-4306.
[35]ZHANG Y,WANG J,SUN X,et al.Measurement and modeling of anisotropic magnetostriction characteristic of grain-oriented silicon steel sheet under DC bias[J].IEEE Transactions on Magnetics,2014,50(2):361-364.
[36]BAGULEYC A,MADAWALA U K,CARSTEN B.The impact of vibration due to magnetostriction on the core losses of ferrite toroidals under DC bias[J].IEEE Transactions on Magnetics,2011,47(8):2022-2028.
[37]YOU Y,FUCHS E F,LIN D,et al.Reactive power demand of transformers with DC bias[J].IEEE Industry Application Magazine,1996,2(4):45-52.
[38]李慧奇,崔翔,候永亮,等.直流偏磁下变压器励磁电流的实验研究及计算[J].华北电力大学学报,2007,34(4):1-6.LI Huiqi,CUI Xiang,HOU Yongliang,et al.Experimental studies and calculations of the exciting current in the transformer under DC bias magnetization[J].Journal of North China Electric Power University,2007,34(4):1-6.
[39]孔剑虹,何湘宁,钱照明,等.功率变换器电感在直流偏置或矩形波激励时磁损问题研究[J].电工技术学报,2005,20(5):13-19,29.KONG Jianhong,HE Xiangning,QIAN Zhaoming,et al.Core losses of magnetic components in power converter topologies[J].Transactions of China Electrotechnical Society,2005,20(5):13-19,29.
[40]STONER E C,WOHLFARTH E P.A mechanism of magnetic hysteresis in heterogeneous alloys[J].Philosophical Transactions of the Royal Society of London,1948,24(A):599-642.
[41]GLOBUS A,DUPLEX P,GUYOT M.Determination of initial magnetization curve from crystallites size and effective anisotropy field[J].IEEE Transactions on Magnetics,1971,7(3):617-622.
[42]JILES D C,ATHERTON D L.Theory of ferromagnetic hysteresis[J].Journal of Applied Physics,1984,55(6):2115-2120.
[43]LIORZOU F,PHELPS B,ATHERTON D L.Macroscopic models of magnetization[J].IEEE Transactions on Magnetics,2000,36(2):418-427.
[44]郭满生,梅桂华,刘东升,等.直流偏磁条件下电力变压器铁心B-H曲线及非对称励磁电流[J].电工技术学报,2009,24(5):46-51,59.GUO Mansheng,MEI Guihua,LIU Dongsheng,et al.B-H curve based on core and asymmetric magnetizing current in DC-biased transformers[J].Transactions of China Electrotechnical Society,2009,24(5):46-51,59.
[45]曹林,何金良,张波.直流偏磁状态下电力变压器铁心动态磁滞损耗模型及验证[J].中国电机工程学报,2008,28(24):141-146.CAO Lin,HE Jinliang,ZHANG Bo.Dynamic hysteresis loss model of power transformer under DC current biasing and its verification[J].Proceedings of the CSEE,2008,28(24):141-146.
[46]BOTERR D H.Geomagnetically induced currents:present knowledge and future research[J].IEEE Transactions on Power Delivery,1994,9(1):50-58.
[47]电力行业电力规划设计标准化技术委员会.高压直流输电大地返回运行系统设计技术规定:D/L5224—2005[S].北京:中国电力出版社,2005.
[48]刘曲,郑健超,潘文,等.变压器铁心承受直流能力的仿真和分析[J].变压器,2006,43(9):5-10.LIU Qu,ZHENG Jianchao,PAN Wen,et al.Analysis and simulation of direct current withstand ability of transformer core[J].Transformer,2006,43(9):5-10.
[49]李长云,李庆民,李贞,等.电能质量约束下变压器承受直流偏磁能力的分析[J].高电压技术,2010,36(12):3112-3118.LI Changyun,LI Qingmin,LI Zhen,et al.Analysis on the with-standing ability of power transformer to DC bias under power quality constraint[J].High Voltage Engineering,2010,36(12):3112-3118.