大型电力变压器绕组短路强度与稳定性研究
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摘要
本文围绕辽宁省重大科技攻关项目“超高压大型电力变压器集成设计与仿真分析系统”课题,在总结有关文献的基础上,对大型电力变压器的暂态电磁场、涌流电磁力、绕组短路强度和多次短路冲击等问题进行了深入的研究,建立了绕组的模态分析模型及多次短路冲击累积形变的弹塑性模型,给出了轴向及辐向稳定性判据,计算了多次短路冲击的累积形变,为提高绕组短路能力的设计提供了理论依据。全文主要包括四部分内容：
第一部分用场路耦合的方法对三维暂态电磁场的磁密分布进行研究。根据大容量变压器的结构特点,在ANSYS有限元软件平台上,应用参数化设计语言进行二次开发,建立了大容量变压器在短路及空载工况下的场路耦合有限元模型。应用此模型对电力变压器的故障工况下的暂态电磁场进行研究,给出了变压器的磁密按单元分布规律。
第二部分对变压器空载合闸时,不同磁滞的涌流及绕组涌流应力进行分析和计算。由于变压器铁心磁导率的非线性,变压器空载合闸、次级绕组故障切除重合闸等状态下可能产生与短路电流相比拟的暂态励磁涌流,并由此产生较大的机械力,对变压器绕组的动态稳定性和绕组匝绝缘将造成损坏。所以,建立了空载合闸仿真分析模型,计算了故障工况下绕组的电流,分析了涌流电磁力特点,指出了不同磁滞的涌流和短路电流激励下绕组受力的区别,提出了空载合闸时需要校准稳态载荷的原因及方法。
第三部分对电力变压器绕组的轴向短路电磁力及短路强度、辐向稳定性等问题进行研究。建立了用于绕组轴向动力学分析的试验模态模型,分析了绕组的固有频率和预紧力关系,给出了避免共振的预紧力条件,并结合数值计算方法,计算了轴向短路冲击力作用下的线饼位移,提出了轴向稳定性判据。根据绕组的结构特点、垫块及撑条分布规律、辐向振动和工艺缺陷等复杂因素,建立了辐向振动仿真分析模型,并用于试验模型的辐向稳定性仿真分析,提出了保证绕组辐向短路强度的措施。
第四部分对在多次短路冲击工况下电力变压器绕组的累积形变进行研究。建立了分析多次短路冲击累积形变的层合加筋圆柱壳模型,用大挠度弹塑性理论计算了变压器绕组在多次短路冲击下的累积形变,给出了绕组单元的变形规律及塑性形变的临界载荷,计算结果表明,该模型能够用于绕组多次短路冲击下的弹塑性累积形变分析及稳定性判断。
The dissertation focuses on the study of major scientific and technological project in Liaoning Province "EHV large power transformers Integrated Design and Simulation Analysis System". Based on the summary of relevant literature, the dissertation deals with the transient electromagnetic field in large power transformers, surge electromagnetic force, short-circuit strength of winding and the impact of repeated short-circuit deeply. A winding short-circuit modal analysis model and the impact of the cumulative deformation of the elastic-plastic model is established. A few achievements with values on theory and engineering have been gained, theoretical basis are provided to improve capacity for transformer windings to withstand short-circuit. The full text mainly consists of four parts.
In the first part, the field-circuit coupled problem of three-dimensional transient electromagnetic field of flux density distribution is studied. According to the structural characteristics of large capacity transformer, the application parameters design language of ANSYS software are used for the second development, where field-circuit coupled finite element model of three-dimensional transient electromagnetic field for transformers under short-circuit and no-load conditions is established, By using this model, Many accidental conditions of magnetic field distribution in large transformers are studied, and laws of transient magnetic flux density in per unit are given.
In the second part ,when transformer is switching-on with no-load, inrush current distribution and electromagnetic force is analyzed and calculated. As non-linear of transformer core magnetic permeability, when transformer is switching-on with no-load, outside the fault of secondary winding is removed again, it may have transient inrush which is compared with the short-circuit current. The resulting mechanical force will cause great harm on the transformer winding, changing turn insulation strength and the dynamic stability, so the no-load of switching simulation model is built, the characteristics of surge electromagnetic force is analyzed, where differences between short-circuit current and inrush current are found, That's the reason why homeostasis loads need calibrating.
In the third part, the power transformer windings axial short-circuit electromagnetic force and strengthand and radial stability issues are studied. Axial dynamic analysis model for experimental modal is established, which is used to analyze relations of natural frequency and pro-compression, the conditions of pre-compression are given to avoid resonance, combined with numerical methods to calculate disk unit displacements by impacting of axial short-circuit. The axial stability criterion is proposed. According to the structural characteristics of windings, distribution of spacer and strip, radial vibration process defects and other complex factors, the radial vibration simulation model is established, which is used to analyze stability of test model, measures are provided to guarantee radial short-circuit strength.
In the fourth part, the power transformer winding deformation cumulative impact of multiple short-circuit are carefully dealt with. The cumulative impact of repeated short-circuit deformation of laminated cylindrical shell with stiffeners model is built, the impact of accumulated deformation of repeated short-circuit of transformer winding is calculated with large deformation elastic-plastic theory. Displacement distribution of the impact on repeate short-circuit of the winding and plastic deformation of the load are given, the simulation results show that paper of the model and the theoretical formula have great significance, which is for power transformer windings of the elastic-plastic deformation analysis and the stability judgement of winding.
第一部分用场路耦合的方法对三维暂态电磁场的磁密分布进行研究。根据大容量变压器的结构特点,在ANSYS有限元软件平台上,应用参数化设计语言进行二次开发,建立了大容量变压器在短路及空载工况下的场路耦合有限元模型。应用此模型对电力变压器的故障工况下的暂态电磁场进行研究,给出了变压器的磁密按单元分布规律。
第二部分对变压器空载合闸时,不同磁滞的涌流及绕组涌流应力进行分析和计算。由于变压器铁心磁导率的非线性,变压器空载合闸、次级绕组故障切除重合闸等状态下可能产生与短路电流相比拟的暂态励磁涌流,并由此产生较大的机械力,对变压器绕组的动态稳定性和绕组匝绝缘将造成损坏。所以,建立了空载合闸仿真分析模型,计算了故障工况下绕组的电流,分析了涌流电磁力特点,指出了不同磁滞的涌流和短路电流激励下绕组受力的区别,提出了空载合闸时需要校准稳态载荷的原因及方法。
第三部分对电力变压器绕组的轴向短路电磁力及短路强度、辐向稳定性等问题进行研究。建立了用于绕组轴向动力学分析的试验模态模型,分析了绕组的固有频率和预紧力关系,给出了避免共振的预紧力条件,并结合数值计算方法,计算了轴向短路冲击力作用下的线饼位移,提出了轴向稳定性判据。根据绕组的结构特点、垫块及撑条分布规律、辐向振动和工艺缺陷等复杂因素,建立了辐向振动仿真分析模型,并用于试验模型的辐向稳定性仿真分析,提出了保证绕组辐向短路强度的措施。
第四部分对在多次短路冲击工况下电力变压器绕组的累积形变进行研究。建立了分析多次短路冲击累积形变的层合加筋圆柱壳模型,用大挠度弹塑性理论计算了变压器绕组在多次短路冲击下的累积形变,给出了绕组单元的变形规律及塑性形变的临界载荷,计算结果表明,该模型能够用于绕组多次短路冲击下的弹塑性累积形变分析及稳定性判断。
The dissertation focuses on the study of major scientific and technological project in Liaoning Province "EHV large power transformers Integrated Design and Simulation Analysis System". Based on the summary of relevant literature, the dissertation deals with the transient electromagnetic field in large power transformers, surge electromagnetic force, short-circuit strength of winding and the impact of repeated short-circuit deeply. A winding short-circuit modal analysis model and the impact of the cumulative deformation of the elastic-plastic model is established. A few achievements with values on theory and engineering have been gained, theoretical basis are provided to improve capacity for transformer windings to withstand short-circuit. The full text mainly consists of four parts.
In the first part, the field-circuit coupled problem of three-dimensional transient electromagnetic field of flux density distribution is studied. According to the structural characteristics of large capacity transformer, the application parameters design language of ANSYS software are used for the second development, where field-circuit coupled finite element model of three-dimensional transient electromagnetic field for transformers under short-circuit and no-load conditions is established, By using this model, Many accidental conditions of magnetic field distribution in large transformers are studied, and laws of transient magnetic flux density in per unit are given.
In the second part ,when transformer is switching-on with no-load, inrush current distribution and electromagnetic force is analyzed and calculated. As non-linear of transformer core magnetic permeability, when transformer is switching-on with no-load, outside the fault of secondary winding is removed again, it may have transient inrush which is compared with the short-circuit current. The resulting mechanical force will cause great harm on the transformer winding, changing turn insulation strength and the dynamic stability, so the no-load of switching simulation model is built, the characteristics of surge electromagnetic force is analyzed, where differences between short-circuit current and inrush current are found, That's the reason why homeostasis loads need calibrating.
In the third part, the power transformer windings axial short-circuit electromagnetic force and strengthand and radial stability issues are studied. Axial dynamic analysis model for experimental modal is established, which is used to analyze relations of natural frequency and pro-compression, the conditions of pre-compression are given to avoid resonance, combined with numerical methods to calculate disk unit displacements by impacting of axial short-circuit. The axial stability criterion is proposed. According to the structural characteristics of windings, distribution of spacer and strip, radial vibration process defects and other complex factors, the radial vibration simulation model is established, which is used to analyze stability of test model, measures are provided to guarantee radial short-circuit strength.
In the fourth part, the power transformer winding deformation cumulative impact of multiple short-circuit are carefully dealt with. The cumulative impact of repeated short-circuit deformation of laminated cylindrical shell with stiffeners model is built, the impact of accumulated deformation of repeated short-circuit of transformer winding is calculated with large deformation elastic-plastic theory. Displacement distribution of the impact on repeate short-circuit of the winding and plastic deformation of the load are given, the simulation results show that paper of the model and the theoretical formula have great significance, which is for power transformer windings of the elastic-plastic deformation analysis and the stability judgement of winding.
引文
[1]王梦云.2004年度110kV及以上变压器事故统计分析.电力设备,2005,6(11)：31-37.
[2]樊明武,颜威利.电磁场积分方程法.北京：机械工业出版社,1988.
[3]周克定等著.工程电磁场数值计算的理论方法及应用.北京：高等教育出版社,1994.
[4]谢德馨,汤蕴璆,徐子宏.变压器三维涡流问题的有限元解.哈尔滨电工学院学报,1986,9(2)：91-104.
[5]乔静秋,汤蕴璆.三相突然短路时变压器电磁力的数值计算.哈尔滨电工学院学报,1989,12(2)：127-135.
[6]Tang Y Q, Qiao J Q,Xu Z H. Numerical calculation of short-circuit electromagnetic forces on the transformer winding. IEEE Transactions on Magmetics,1990,26(2):1039-1041.
[7]Tang R Y, Yang J Y, Wu Z X, et al. Computation of eddy current losses by heavy current leads and winding in large transformer using IEM coupled with improved R-ψ method, IEEE Transactions on Magmetics,1990,26(2):452-455.
[8]陈家平.电磁场有限元计算方法及变压器线圈电磁力与振动的研究：(博士学位论文).武汉：华中理工大学,1993.
[9]李岩.大型电力变压器线圈电磁力和局部过热问题研究：(博士学位论文).沈阳：沈阳工业大学,1995.
[10]林鹤云,周鹗.有限元分析三维涡流场的A,V—Ψ方法.中国电机工程学报,1993,13(5)：42-49.
[11]王胜辉.大型变压器场路耦合瞬态涡流场及螺旋线圈轴向电流效应研究：(博士学位论文).沈阳：沈阳工业大学,1999.
[12]胡岩.大型电力变压器磁分路及低压引线电流漏磁效应和局部过热的研究：(博士学位论文).沈阳：沈阳工业大学,2001.
[13]梁振光.大型电力变压器场路耦合三维瞬态涡流场和绕组短路强度的研究：(博士学位论文).沈阳：沈阳工业大学,2001.
[14]Turneer P J. Finite-element simulation of turbine generator terminal and application to machine parameter prediction. IEEE Transactions on Energy Conversion,1987,12(1):1905-1909.
[15]Belforte P, Chiampi M,Tartaglia M. A finite element computation procedure for electromagnetic fields under different supply condition. IEEE Transactions on Magmetics, 1985,21(6):2284-2287.
[16]Strangas E. Coupling the circuit equations to the nonlinear time dependent field solution in inverter driven induction motors. IEEE Transactions on Magmetics,1985,21(6):2408-2411.
[17]Vassent E, Meunier G, Foggia A. Simulation of induction machines using complex magnetodynamic finite element method coupled with the circuit Equations. IEEE Transactions on Magmetics,1991,27(5):4246-4249.
[18]Tsukerman I A, Konrad A, Lavers J D. A method for circuit connections in time-dependent eddy current problems. IEEE Transactions on Magmetics,1992,28(2):1299-1302.
[19]Piriou F,Razek A. A non-linear coupled 3D model for magnetic field and electric circuit equations. IEEE Transactions on Magmetics,1992,28(2):1295-1298.
[20]Dreher T,Meunier G. 3D modeling of electromagnets fed by alternating voltage sources. IEEE Transactions on Magmetics,1993,29(2):1341-1344.
[21]Bouissou S,Piriou F. Numerical simulation of a power transformer using 3D finite element method coupled to circuit equation. IEEE Transactions on Magmetics,1994,30(5):3224-3227.
[22]Benali B,Francis P. Hybrid formulation A-Ω with finite element method to model in 3D electromagnetic systems. IEEE Transactions on Magmetics,1996,32(6):659-662.
[23]Meunier G,Luong H T,Marechal Y. Computation of coupled of 3D Eddy current and electrical circuit by using T0-T-Ω formulation. IEEE Transactions on Magmetics,1998,34(5):3074-3077.
[24]周小泸,李小庆,纪志成.基于MATLAB的仿真建模及特性分析.变压器,2004,40(7)：12-16.
[25]Brunke J H,Frohlich K J. Elimination of transformer inrush currents by controlled switching, part one:Theoretical considerations,IEEE transactions on Power Delivery,2001,16(2):276-280.
[26]林湘宁,刘沛,刘世明等.变压器有载合闸的超饱和现象及对变压器差动保护的影响.中国电机工程学报,2002,33(3)：22-25.
[27]李明武,梁冠安.基于控制策略的变压器励磁涌流分析.高电压技术,2004,30(6)：25-28.
[28]Koen J,Gaunt C T. Disturbances in the south african power network due to geomagnetically induced currents. Cigre session,2002,(8):36-206.
[29]黄绍平,李永坚.基于MATLAB的变压器空载合闸瞬变过程仿真研究.继电器,2004,32(8)：33-36.
[30]Swihart D O,Wright D V. Dynamic stiffness and damping of transformer pressdoard during axial short-circuit vibration. IEEE Transactions on Power Apparatus and Systems,1976,95(2):721-730.
[31]瓦修京斯基.变压器的理论与计算.北京：机械工业出版社,1983.
[32][日]变压器专业委员会.变压器线圈短路时的机械强度(上).国外变压器,1980,(4)：1-12.
[33][日]变压器专业委员会.变压器线圈短路时的机械强度(下).国外变压器,1980,(5)：1-15.
[34]陈阆琪.变压器线圈短路强度计算综述.变压器,1974,21(5)：1-19.
[35]路长柏,朱英浩,张怀灵等.电力变压器计算.哈尔滨：黑龙江科学出版社,1986.
[36]Kurita K,Kuriyama T,Hiraishi K. Mechnical strength of transformer windings under short-circuit conditions. IEEE Transactions on Power Apparatus and Systems,1969,99(2):222-230.
[37]王璋奇,王孟.电力变压器绕组轴向振动稳定性分析.中国电机工程学报,2002,22(7)：24-28.
[38]Hori Y,Okuyama K. Axial vibration analysis of transformer windings under short circuit condition. IEEE Transactions on Power Apparatus and Systems,1980,99(2):443-451.
[39]Tamaki E, Kishi A, Itoh K. The coil mechanical behavior under short circuit. cigre transformer colloquium in Budapest,1999,2(11):313-317.
[40]Kawanishi K, Suzuki T, Kosaka M H, et al. Axial behavior of transformer windings on short-circuit (Part2), Proceedings of Tech Annual Conference of Power&Energy Society. IEEE of Japan,1999, B(480):423-426.
[41]Uchiyama N,Saito S,Kashiwakura M A,et al. Axial vibration analysis of transformer windings with hysteresis of stress-and-Strain characteristic of insulating materials, IEEE Power Engineering Society Summer Meeting,2000,(2):2428-2433.
[42]王世山,汲胜昌,李彦明.电缆绕组变压器短路时线圈轴向稳定性的研究.中国电机工程学报,2004,24(2)：166-169.
[43]王洪方,王乃庆,李同生.大型电力变压器绕组轴向非线性振动研究.电网技术,2000,24(3)： 42-45.
[44]Toshikazu N,Kyohei H,Seiji I,et al. Estimation on on-load vibration of transformer windings. IEEE Power Engineering Society Winter Meeting,2002, (2):1378-1382.
[45]邵宇鹰,饶柱石,谢坡岸等.预紧力对变压器绕组固有频率的影响.噪声与振动控制,2006,23(6)：51-53.
[46]王洪方,王乃庆,李同生.短路条件下电力变压器绕组轴向振动等效单自由度分析.电工技术学报,2000,15(5)：39-42.
[47]Quinney D A. Dynamic response of a power-transformer winding under axial short-circuit conditions. IEE Proceedings-Electric Power Applications,1981,128(2):114-118.
[48]陈振茂,徐建学.大型电力变压器线圈轴向非线性振动研究.应用力学学报,1990,7(1)：21-29.
[49]Hong K X, Pan Z P, Vibration model of power transformer under short-circuit condition. International Conference on Electrical Machines and Systems, Tokyo,2009:115-120.
[50]陈振茂,徐健学,徐子宏.考虑铁窗影响时变压器绕组短路轴向非线性振动的研究.西安交大学报,1991,25(1)：17-26.
[51]Madin A B, Eng B, Whitaker J D, et al. The dynamic behaviour of a transformer winding under axial short-circuit forces. Proceedings of IEEE,1963,11(3):535-550.
[52]詹琼华译.变压器线圈在短路条件下动态特性的研究.CIGRE,第十九届会议,143号报告.
[53]Bose A K. Dynamic response of windings under short-circuit. CIGRE,1972:Report12-03.
[54]李文海.变压器短路强度研究成果简介.变压器,1997,34(10)：18-22.
[55]谢毓城等.电力变压器手册.北京：机械工业出版社,2003.
[56]变压器制造技术丛书编审委员会编.变压器绕组制造工业.北京：机械工业出版社,1998.
[57]Steel R B, Johnson W M, Narus J J, et al. Dynamic measurements in power transformers under short-circuit conditions. CIGRE,1972:Report 12-01.
[58]周纪卿,徐健学,张培真.变压器内线圈径向动力稳定性研究.西安交大学报,1986,20(4)：102-111.
[59]Hiroyuki K J,Hiroshi M Y, Shigeru S, et al. Buckling strength analysis of large power transformer windings subjected to electromagnetic force under short circuit. IEEE Transactions on Power Apparatus and Systems,1980,99(3):1288-1297.
[60]曹志军,胡家炘,巨建民等.大容量变压器线圈短路状态下非线性稳定性与动力稳定性.大连铁道学院学报,2003,24(2)：31-35.
[61]田立坚,岳军,张瑛.大型变压器线圈短路电磁力的数值计算.东北电力技术,2000,12(2)：3-5.
[62]朱维璐,刘振永,甄然.浅谈短路电流对变压器轴向稳定性的危害.变压器,2002,39(3)：22-24.
[63]尹克宁.变压器设计原理.北京：中国电力出版社,2003.
[64]电力变压器换位导线内线圈短路动稳定性分析.75-50-05-01
[65]Hugh A,Thompson. The dynamic response of low power voltage high current disk type transformer windings to through fault loads. IEEE Transactions on Power Apparatus and Systems,1979, 98(3):1091-1098.
[66]Koen J,Gaunt C T. Disturbances in the southern african power network due to geomagnetically induced currents. Cigre Session,2002, (8):198-206.
[67]Moser H P, Dahinden V等著.朱英浩,赵育文译.变压器绝缘纸板.沈阳：辽宁科学技术出版社,1997.
[68]孙定华,许宪中.论材料特性与变压器的抗短路能力—写在新世纪到来之际.变压器,2000, 37(2)：15-20.
[69]Timoshenko S,Young DH,Weaver Jr W. Vibration problems in engineering. John Wiley & Sons,Inc,1974.
[70]王宏.110kv变压器短路故障分析.电力设备,2004,5(12)：45-47.
[7l]徐达明.变压器短路后的综合诊断.高电压技术,2002,28(7)：96-100.
[72]金文龙,陈建华,李光范等.全国110kV及以上等级电力变压器短路损坏事故统计分析.电力设备,1999,23(6)：70-75.
[73]Porkar S,Gharehpetian G B, Feser K. A disk-to-disk breakdown and arc modeling method for fault diagnosis of power transformers during impulse testing.Electrical Engineering,2004,8(6):261-265.
[74]朱建军,黄国泉,王中等.突发短路造成110KV主变压器损坏的原因分析.高电压技术,2004,30(8)：58-59.
[75]赵海燕,史耀武.用有限元法分析焊接变压器的三维磁场.机械工程学报,2001,37(2)：74-78.
[76]魏春华.变压器制造技术丛书.北京：机械工业出版社,2008.
[77]朱维璐,刘振永,甄然.浅谈短路电流对变压器轴向稳定性的危害.变压器,2002,39(3)：22-24.
[78]Karimifard P,Gharehpetan G B. A new algorithm for localization of radial deformation and determination of deformation extent in transformer windings. Electric Power Systems Research, 2008,78(10):1701-1711.
[79]Najdenkoski k, Manov D. Electromagnetic forces calculation on power transformer windings under short circuit. The International Symposium on Electromagnetic Fields in Electrical Engineering Conference,1997:25-27.
[80]哈尔滨工业大学,沈阳变压器研究所.大容量变压器短路强度研究.85-303-01-01-3A.
[81]李英,懂振华,詹凤顺等.特大容量变压器短路径向稳定性的模型模拟实验.变压器,2003,40(11)：1-7.
[82]孟庆民,李文海,洛君婷等.大容量变压器内绕组辐向失稳特性的模拟研究.变压器,2010,47(4)：32-40.
[83]Philip R,Price. Geomagtically induced current effects on transformer.IEEE Transactions on Power Delivery,2002,17(4):1002-1008.
[84]Wang H,K L Butler. Finite element anaysls of internal winding faults in distribution transformers. IEEE Trans on Power Delivery,2001,16(3):422-428.
[85]Wang H, Butler K L. Modeling transformers with internal incipient faults. IEEE Transactions on Power Delivery,2002,17(2):500-509.
[86]Juan A M, Bruce A M. Transformer modeling for low-and-mid-frequency transients-Review. IEEE Transaction on Power Delivery,2005,4(2):1625-1632.
[87]项晨,陈浩然,郭兆璞.复合材料加筋结构的流固耦合振动及动响应分析.复合材料学报,1996,13(3)：100-104.
[88]刘人怀,王墦.复合材料层合扁球壳的非线性强迫振动.力学学报,1997,29(2)：236-241.
[89]张雨,向锦武.复合材料层合厚圆柱壳高阶理论的改进及其应用.复合材料学报,2002,19(4)：87-91.
[90]唐文勇,陈铁云.迭层复合材料圆柱曲板的非线性动力响应分析.上海交通大学学报,1998,32(7)：128-131.
[91]Lam K Y,Loy C T. Analysis of rotating laminated cylindrical shells by different thin shell theories. Journal of Sound and Vibration.1995,196(1):23-35.
[92]Sallam S,Simitsesd G L. Delamination buckling of laminated cylindrical shells under axial compression. Composite Structures,1987,7(2):83-101.
[93]Kardomates G A.Cheng C B. Thin film modeling of delamination buckling in pressure loaded laminated cylindrical shell. AIAA Journal.1992,30(8):2119-2123.
[94]陈铁云,沈惠申.结构的屈曲.上海：上海科学技术文献出版社.1993.
[95]沈惠申,陈铁云.圆柱薄壳在外压作用下屈曲的边界层理论.应用数学和力学,1988,9(6)：515-527.
[96]Larsson R A. A discontinuous shell-interface element for delamination analysis of laminated composite structures. Methods in Applied Mechanics Engineering,2004,193(23):3173-3194.
[97]刘怀恒.结构及弹塑性力学有限元法.西安：西北工业大学出版设,2007.
[98]谢贻权,何福保.弹性和塑性力学中的有限元法.北京：机械工业出版社,1981.
[99]Bisagni C, Cordisco P. Post-buckling and collapse experiments of stiffened composite cylindrical shells subjected to axial loading and torque. Composite Structures.2006,73(19):138-149.
[100]张慧玲.复合筒结构中的周向导波：(博士学位论文).南京：南京理工大学,2008.
[101]邱吉宝等.计算结构动力学.北京：中国科学技术大学出版社,2009.
[102]张朝晖.ANSYS11.0结构分析工程应用实例解析.北京：机械工业出版社,2008.
[2]樊明武,颜威利.电磁场积分方程法.北京：机械工业出版社,1988.
[3]周克定等著.工程电磁场数值计算的理论方法及应用.北京：高等教育出版社,1994.
[4]谢德馨,汤蕴璆,徐子宏.变压器三维涡流问题的有限元解.哈尔滨电工学院学报,1986,9(2)：91-104.
[5]乔静秋,汤蕴璆.三相突然短路时变压器电磁力的数值计算.哈尔滨电工学院学报,1989,12(2)：127-135.
[6]Tang Y Q, Qiao J Q,Xu Z H. Numerical calculation of short-circuit electromagnetic forces on the transformer winding. IEEE Transactions on Magmetics,1990,26(2):1039-1041.
[7]Tang R Y, Yang J Y, Wu Z X, et al. Computation of eddy current losses by heavy current leads and winding in large transformer using IEM coupled with improved R-ψ method, IEEE Transactions on Magmetics,1990,26(2):452-455.
[8]陈家平.电磁场有限元计算方法及变压器线圈电磁力与振动的研究：(博士学位论文).武汉：华中理工大学,1993.
[9]李岩.大型电力变压器线圈电磁力和局部过热问题研究：(博士学位论文).沈阳：沈阳工业大学,1995.
[10]林鹤云,周鹗.有限元分析三维涡流场的A,V—Ψ方法.中国电机工程学报,1993,13(5)：42-49.
[11]王胜辉.大型变压器场路耦合瞬态涡流场及螺旋线圈轴向电流效应研究：(博士学位论文).沈阳：沈阳工业大学,1999.
[12]胡岩.大型电力变压器磁分路及低压引线电流漏磁效应和局部过热的研究：(博士学位论文).沈阳：沈阳工业大学,2001.
[13]梁振光.大型电力变压器场路耦合三维瞬态涡流场和绕组短路强度的研究：(博士学位论文).沈阳：沈阳工业大学,2001.
[14]Turneer P J. Finite-element simulation of turbine generator terminal and application to machine parameter prediction. IEEE Transactions on Energy Conversion,1987,12(1):1905-1909.
[15]Belforte P, Chiampi M,Tartaglia M. A finite element computation procedure for electromagnetic fields under different supply condition. IEEE Transactions on Magmetics, 1985,21(6):2284-2287.
[16]Strangas E. Coupling the circuit equations to the nonlinear time dependent field solution in inverter driven induction motors. IEEE Transactions on Magmetics,1985,21(6):2408-2411.
[17]Vassent E, Meunier G, Foggia A. Simulation of induction machines using complex magnetodynamic finite element method coupled with the circuit Equations. IEEE Transactions on Magmetics,1991,27(5):4246-4249.
[18]Tsukerman I A, Konrad A, Lavers J D. A method for circuit connections in time-dependent eddy current problems. IEEE Transactions on Magmetics,1992,28(2):1299-1302.
[19]Piriou F,Razek A. A non-linear coupled 3D model for magnetic field and electric circuit equations. IEEE Transactions on Magmetics,1992,28(2):1295-1298.
[20]Dreher T,Meunier G. 3D modeling of electromagnets fed by alternating voltage sources. IEEE Transactions on Magmetics,1993,29(2):1341-1344.
[21]Bouissou S,Piriou F. Numerical simulation of a power transformer using 3D finite element method coupled to circuit equation. IEEE Transactions on Magmetics,1994,30(5):3224-3227.
[22]Benali B,Francis P. Hybrid formulation A-Ω with finite element method to model in 3D electromagnetic systems. IEEE Transactions on Magmetics,1996,32(6):659-662.
[23]Meunier G,Luong H T,Marechal Y. Computation of coupled of 3D Eddy current and electrical circuit by using T0-T-Ω formulation. IEEE Transactions on Magmetics,1998,34(5):3074-3077.
[24]周小泸,李小庆,纪志成.基于MATLAB的仿真建模及特性分析.变压器,2004,40(7)：12-16.
[25]Brunke J H,Frohlich K J. Elimination of transformer inrush currents by controlled switching, part one:Theoretical considerations,IEEE transactions on Power Delivery,2001,16(2):276-280.
[26]林湘宁,刘沛,刘世明等.变压器有载合闸的超饱和现象及对变压器差动保护的影响.中国电机工程学报,2002,33(3)：22-25.
[27]李明武,梁冠安.基于控制策略的变压器励磁涌流分析.高电压技术,2004,30(6)：25-28.
[28]Koen J,Gaunt C T. Disturbances in the south african power network due to geomagnetically induced currents. Cigre session,2002,(8):36-206.
[29]黄绍平,李永坚.基于MATLAB的变压器空载合闸瞬变过程仿真研究.继电器,2004,32(8)：33-36.
[30]Swihart D O,Wright D V. Dynamic stiffness and damping of transformer pressdoard during axial short-circuit vibration. IEEE Transactions on Power Apparatus and Systems,1976,95(2):721-730.
[31]瓦修京斯基.变压器的理论与计算.北京：机械工业出版社,1983.
[32][日]变压器专业委员会.变压器线圈短路时的机械强度(上).国外变压器,1980,(4)：1-12.
[33][日]变压器专业委员会.变压器线圈短路时的机械强度(下).国外变压器,1980,(5)：1-15.
[34]陈阆琪.变压器线圈短路强度计算综述.变压器,1974,21(5)：1-19.
[35]路长柏,朱英浩,张怀灵等.电力变压器计算.哈尔滨：黑龙江科学出版社,1986.
[36]Kurita K,Kuriyama T,Hiraishi K. Mechnical strength of transformer windings under short-circuit conditions. IEEE Transactions on Power Apparatus and Systems,1969,99(2):222-230.
[37]王璋奇,王孟.电力变压器绕组轴向振动稳定性分析.中国电机工程学报,2002,22(7)：24-28.
[38]Hori Y,Okuyama K. Axial vibration analysis of transformer windings under short circuit condition. IEEE Transactions on Power Apparatus and Systems,1980,99(2):443-451.
[39]Tamaki E, Kishi A, Itoh K. The coil mechanical behavior under short circuit. cigre transformer colloquium in Budapest,1999,2(11):313-317.
[40]Kawanishi K, Suzuki T, Kosaka M H, et al. Axial behavior of transformer windings on short-circuit (Part2), Proceedings of Tech Annual Conference of Power&Energy Society. IEEE of Japan,1999, B(480):423-426.
[41]Uchiyama N,Saito S,Kashiwakura M A,et al. Axial vibration analysis of transformer windings with hysteresis of stress-and-Strain characteristic of insulating materials, IEEE Power Engineering Society Summer Meeting,2000,(2):2428-2433.
[42]王世山,汲胜昌,李彦明.电缆绕组变压器短路时线圈轴向稳定性的研究.中国电机工程学报,2004,24(2)：166-169.
[43]王洪方,王乃庆,李同生.大型电力变压器绕组轴向非线性振动研究.电网技术,2000,24(3)： 42-45.
[44]Toshikazu N,Kyohei H,Seiji I,et al. Estimation on on-load vibration of transformer windings. IEEE Power Engineering Society Winter Meeting,2002, (2):1378-1382.
[45]邵宇鹰,饶柱石,谢坡岸等.预紧力对变压器绕组固有频率的影响.噪声与振动控制,2006,23(6)：51-53.
[46]王洪方,王乃庆,李同生.短路条件下电力变压器绕组轴向振动等效单自由度分析.电工技术学报,2000,15(5)：39-42.
[47]Quinney D A. Dynamic response of a power-transformer winding under axial short-circuit conditions. IEE Proceedings-Electric Power Applications,1981,128(2):114-118.
[48]陈振茂,徐建学.大型电力变压器线圈轴向非线性振动研究.应用力学学报,1990,7(1)：21-29.
[49]Hong K X, Pan Z P, Vibration model of power transformer under short-circuit condition. International Conference on Electrical Machines and Systems, Tokyo,2009:115-120.
[50]陈振茂,徐健学,徐子宏.考虑铁窗影响时变压器绕组短路轴向非线性振动的研究.西安交大学报,1991,25(1)：17-26.
[51]Madin A B, Eng B, Whitaker J D, et al. The dynamic behaviour of a transformer winding under axial short-circuit forces. Proceedings of IEEE,1963,11(3):535-550.
[52]詹琼华译.变压器线圈在短路条件下动态特性的研究.CIGRE,第十九届会议,143号报告.
[53]Bose A K. Dynamic response of windings under short-circuit. CIGRE,1972:Report12-03.
[54]李文海.变压器短路强度研究成果简介.变压器,1997,34(10)：18-22.
[55]谢毓城等.电力变压器手册.北京：机械工业出版社,2003.
[56]变压器制造技术丛书编审委员会编.变压器绕组制造工业.北京：机械工业出版社,1998.
[57]Steel R B, Johnson W M, Narus J J, et al. Dynamic measurements in power transformers under short-circuit conditions. CIGRE,1972:Report 12-01.
[58]周纪卿,徐健学,张培真.变压器内线圈径向动力稳定性研究.西安交大学报,1986,20(4)：102-111.
[59]Hiroyuki K J,Hiroshi M Y, Shigeru S, et al. Buckling strength analysis of large power transformer windings subjected to electromagnetic force under short circuit. IEEE Transactions on Power Apparatus and Systems,1980,99(3):1288-1297.
[60]曹志军,胡家炘,巨建民等.大容量变压器线圈短路状态下非线性稳定性与动力稳定性.大连铁道学院学报,2003,24(2)：31-35.
[61]田立坚,岳军,张瑛.大型变压器线圈短路电磁力的数值计算.东北电力技术,2000,12(2)：3-5.
[62]朱维璐,刘振永,甄然.浅谈短路电流对变压器轴向稳定性的危害.变压器,2002,39(3)：22-24.
[63]尹克宁.变压器设计原理.北京：中国电力出版社,2003.
[64]电力变压器换位导线内线圈短路动稳定性分析.75-50-05-01
[65]Hugh A,Thompson. The dynamic response of low power voltage high current disk type transformer windings to through fault loads. IEEE Transactions on Power Apparatus and Systems,1979, 98(3):1091-1098.
[66]Koen J,Gaunt C T. Disturbances in the southern african power network due to geomagnetically induced currents. Cigre Session,2002, (8):198-206.
[67]Moser H P, Dahinden V等著.朱英浩,赵育文译.变压器绝缘纸板.沈阳：辽宁科学技术出版社,1997.
[68]孙定华,许宪中.论材料特性与变压器的抗短路能力—写在新世纪到来之际.变压器,2000, 37(2)：15-20.
[69]Timoshenko S,Young DH,Weaver Jr W. Vibration problems in engineering. John Wiley & Sons,Inc,1974.
[70]王宏.110kv变压器短路故障分析.电力设备,2004,5(12)：45-47.
[7l]徐达明.变压器短路后的综合诊断.高电压技术,2002,28(7)：96-100.
[72]金文龙,陈建华,李光范等.全国110kV及以上等级电力变压器短路损坏事故统计分析.电力设备,1999,23(6)：70-75.
[73]Porkar S,Gharehpetian G B, Feser K. A disk-to-disk breakdown and arc modeling method for fault diagnosis of power transformers during impulse testing.Electrical Engineering,2004,8(6):261-265.
[74]朱建军,黄国泉,王中等.突发短路造成110KV主变压器损坏的原因分析.高电压技术,2004,30(8)：58-59.
[75]赵海燕,史耀武.用有限元法分析焊接变压器的三维磁场.机械工程学报,2001,37(2)：74-78.
[76]魏春华.变压器制造技术丛书.北京：机械工业出版社,2008.
[77]朱维璐,刘振永,甄然.浅谈短路电流对变压器轴向稳定性的危害.变压器,2002,39(3)：22-24.
[78]Karimifard P,Gharehpetan G B. A new algorithm for localization of radial deformation and determination of deformation extent in transformer windings. Electric Power Systems Research, 2008,78(10):1701-1711.
[79]Najdenkoski k, Manov D. Electromagnetic forces calculation on power transformer windings under short circuit. The International Symposium on Electromagnetic Fields in Electrical Engineering Conference,1997:25-27.
[80]哈尔滨工业大学,沈阳变压器研究所.大容量变压器短路强度研究.85-303-01-01-3A.
[81]李英,懂振华,詹凤顺等.特大容量变压器短路径向稳定性的模型模拟实验.变压器,2003,40(11)：1-7.
[82]孟庆民,李文海,洛君婷等.大容量变压器内绕组辐向失稳特性的模拟研究.变压器,2010,47(4)：32-40.
[83]Philip R,Price. Geomagtically induced current effects on transformer.IEEE Transactions on Power Delivery,2002,17(4):1002-1008.
[84]Wang H,K L Butler. Finite element anaysls of internal winding faults in distribution transformers. IEEE Trans on Power Delivery,2001,16(3):422-428.
[85]Wang H, Butler K L. Modeling transformers with internal incipient faults. IEEE Transactions on Power Delivery,2002,17(2):500-509.
[86]Juan A M, Bruce A M. Transformer modeling for low-and-mid-frequency transients-Review. IEEE Transaction on Power Delivery,2005,4(2):1625-1632.
[87]项晨,陈浩然,郭兆璞.复合材料加筋结构的流固耦合振动及动响应分析.复合材料学报,1996,13(3)：100-104.
[88]刘人怀,王墦.复合材料层合扁球壳的非线性强迫振动.力学学报,1997,29(2)：236-241.
[89]张雨,向锦武.复合材料层合厚圆柱壳高阶理论的改进及其应用.复合材料学报,2002,19(4)：87-91.
[90]唐文勇,陈铁云.迭层复合材料圆柱曲板的非线性动力响应分析.上海交通大学学报,1998,32(7)：128-131.
[91]Lam K Y,Loy C T. Analysis of rotating laminated cylindrical shells by different thin shell theories. Journal of Sound and Vibration.1995,196(1):23-35.
[92]Sallam S,Simitsesd G L. Delamination buckling of laminated cylindrical shells under axial compression. Composite Structures,1987,7(2):83-101.
[93]Kardomates G A.Cheng C B. Thin film modeling of delamination buckling in pressure loaded laminated cylindrical shell. AIAA Journal.1992,30(8):2119-2123.
[94]陈铁云,沈惠申.结构的屈曲.上海：上海科学技术文献出版社.1993.
[95]沈惠申,陈铁云.圆柱薄壳在外压作用下屈曲的边界层理论.应用数学和力学,1988,9(6)：515-527.
[96]Larsson R A. A discontinuous shell-interface element for delamination analysis of laminated composite structures. Methods in Applied Mechanics Engineering,2004,193(23):3173-3194.
[97]刘怀恒.结构及弹塑性力学有限元法.西安：西北工业大学出版设,2007.
[98]谢贻权,何福保.弹性和塑性力学中的有限元法.北京：机械工业出版社,1981.
[99]Bisagni C, Cordisco P. Post-buckling and collapse experiments of stiffened composite cylindrical shells subjected to axial loading and torque. Composite Structures.2006,73(19):138-149.
[100]张慧玲.复合筒结构中的周向导波：(博士学位论文).南京：南京理工大学,2008.
[101]邱吉宝等.计算结构动力学.北京：中国科学技术大学出版社,2009.
[102]张朝晖.ANSYS11.0结构分析工程应用实例解析.北京：机械工业出版社,2008.