基于曲梁理论输电线舞动及防舞有限元分析
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摘要
输电导线覆冰后,受到稳态风荷载作用,可能会产生低频、大幅度的自激振动,即舞动。输电线舞动会造成相间闪络、短路、损害金具、断线倒塔等事故,造成重大经济损失。目前对输电线舞动数值分析大都基于索单元理论,这一理论不考虑抗弯刚度,与实际输电线存在抗弯刚度不符。论文基于全面考虑抗拉刚度、抗弯刚度、抗扭刚度的曲梁理论,对输电线进行舞动及防舞有限元分析。主要研究内容有:
①覆冰单导线曲梁模型及分析。基于曲梁理论,建立结点6自由度的单导线曲梁模型,根据虚功原理推导动力学方程。采用Matlab编制单导线的非线性分析程序。算例分析表明曲梁模型计算单导线是可行的,比索单元模型精度更高。
②覆冰分裂导线曲梁模型及抗扭刚度分析。假定间隔棒为刚性体,根据位移协调条件,建立分裂导线的曲梁模型;根据虚功原理推导分裂导线的动力学方程;采用Matlab编制分裂导线的非线性分析程序。算例分析表明基于曲梁理论的分裂导线模型同样具有可行性与优越性。在此基础上,采用曲梁模型计算分裂导线抗扭刚度,计算结果分别与试验值、理论公式解对比。间隔棒、分裂间距、垂度等分裂导线参数分析表明,间隔棒数目越多,抗扭刚度越大;分裂间距越大,抗扭刚度越大;垂度越大,抗扭刚度越大;离塔-线连接点越近,抗扭刚度越大。
③输电线舞动有限元分析。采用已建立的单导线、分裂导线的曲梁模型及动力学方程,编制Matlab程序,进行输电线舞动时程分析。算例分析进一步验证曲梁模型是合理且优越的。档距、初始张力、抗弯刚度、分裂间距等因素对舞动振幅影响的分析结果表明,档距越大,舞动振幅越大;导线初始张力越大,竖向振幅越小,转角越大;考虑导线抗弯刚度,舞动竖向振幅增大,转角变小;分裂导线舞动的竖向振幅比单导线大的多,转角振幅比单导线小的多。
④输电线防舞有限元分析。推导了失谐摆的质量矩阵、刚度矩阵,对安装失谐摆的导线进行了舞动时程分析,分析了失谐摆防舞效果。算例分析表明失谐摆防舞只适用于Nigol的舞动,对DenHartog的舞动反而会增大舞动竖向振幅。最后,采用稳定性理论求解输电线舞动临界风速,分析了档距、张力、失谐摆等因素对舞动临界风速的影响。分析表明舞动临界风速随着档距增大而减小,随着张力增大而增大;失谐摆摆长对舞动临界风速的影响不大,锤重对舞动临界风速的影响较大,锤重越重,临界风速越大。
Under the stable wind, the iced transmission conductor will appear low frequency and large amplitude vibration which is usually called as galloping. The galloping of transmission conductor will cause electric accident, such as flashover, short circuit, hardware damage and so on, creating enormous economic loss. At the present time, the finite element analysis of galloping of transmission line is mainly based on cable element theory that neglects the bending rigidity and is discrepant with bending rigidity of transmission line. Based on curved beam theory considering tensile stiffness, bending stiffness and torsional stiffness, this paper does some research on galloping and anti-galloping of transmission line.
①The analysis of curved beam mode of iced single line. Based on curved beam theory, the curved beam model of 6-DOF node single line is established and the kinetic equation is derived with the principle of virtual work. Nonlinear of single line is analyzed through Matlab programming. The results of examples show that the curved beam model of single line is more accurate than cable element modle.
②The analysis of curved beam mode and torsional stiffness of iced bundle lines. Firstly, the spacer was assumed as rigid body. The curved beam model of bundle lines was formulated according to the displacement compatibility conditions. Moreover, the kinetic equation is derived through virtual work principle. Secondly, nonlinear property of bundle lines is analyzed through Matlab programming. The results of examples turn out that the model of bundle lines based on curved beam theory is feasible and advantageous. Based on this, the curved beam model is used to calculate torsional stiffness of bundle lines. The results of bundle lines’parameter analysis show: the more spacers there are, the greater torsional stiffness is; the greater the space is, the greater the torsional stiffness is; the greater the sag is, the greater the torsional stiffness is; the closer it is away from the tower- line connection point, the greater the torsional stiffness is.
③The finite element analysis of transmission line galloping. According to the curved beam model and kinetic equation of single line and bundle lines, the time history of galloping of transmission line is analyzed through Matlab programming. The results of examples further prove that the curved beam model of transmission line is accurate and advantageous. Analyse of the wind speed, span, tension and other factors’effects on the initial amplitude of galloping show: the greater the span is, the greater the amplitude is; the greater the initial tension is, the smaller the vertical amplitude is; the greater the initial tension is, the bigger the torsional angle is; Consider wire bending rigidity, vertical amplitude and lateral vertical amplitude will increase, torsional angle will decline; galloping vertical amplitude of bundle lines is much bigger than the single line, and torsional angle of bundle lines is much smaller than the single line.
④The finite element analysis of anti-galloping of transmission line. Detuning pendulum mass matrix and stiffness matrix are derived to analyze the anti-galloping of the detuning pendulum. The results show that detuning pendulum only decreses the galloping of Nigol but increases the vertical galloping amplitude of Den Hartog. Finally, the critical wind speed of galloping of transmission line is solved by stability theory. Moreover, effects of span, tension and detuning pendulum on the critical wind speed are analyzed. The results of analysis show: the critical wind speed declines as the span and the initial tension increase; the gravity of hammer of detuning pendulum has little effect on critical wind speed but pendulum length plays great effect on critical wind speed.
①覆冰单导线曲梁模型及分析。基于曲梁理论,建立结点6自由度的单导线曲梁模型,根据虚功原理推导动力学方程。采用Matlab编制单导线的非线性分析程序。算例分析表明曲梁模型计算单导线是可行的,比索单元模型精度更高。
②覆冰分裂导线曲梁模型及抗扭刚度分析。假定间隔棒为刚性体,根据位移协调条件,建立分裂导线的曲梁模型;根据虚功原理推导分裂导线的动力学方程;采用Matlab编制分裂导线的非线性分析程序。算例分析表明基于曲梁理论的分裂导线模型同样具有可行性与优越性。在此基础上,采用曲梁模型计算分裂导线抗扭刚度,计算结果分别与试验值、理论公式解对比。间隔棒、分裂间距、垂度等分裂导线参数分析表明,间隔棒数目越多,抗扭刚度越大;分裂间距越大,抗扭刚度越大;垂度越大,抗扭刚度越大;离塔-线连接点越近,抗扭刚度越大。
③输电线舞动有限元分析。采用已建立的单导线、分裂导线的曲梁模型及动力学方程,编制Matlab程序,进行输电线舞动时程分析。算例分析进一步验证曲梁模型是合理且优越的。档距、初始张力、抗弯刚度、分裂间距等因素对舞动振幅影响的分析结果表明,档距越大,舞动振幅越大;导线初始张力越大,竖向振幅越小,转角越大;考虑导线抗弯刚度,舞动竖向振幅增大,转角变小;分裂导线舞动的竖向振幅比单导线大的多,转角振幅比单导线小的多。
④输电线防舞有限元分析。推导了失谐摆的质量矩阵、刚度矩阵,对安装失谐摆的导线进行了舞动时程分析,分析了失谐摆防舞效果。算例分析表明失谐摆防舞只适用于Nigol的舞动,对DenHartog的舞动反而会增大舞动竖向振幅。最后,采用稳定性理论求解输电线舞动临界风速,分析了档距、张力、失谐摆等因素对舞动临界风速的影响。分析表明舞动临界风速随着档距增大而减小,随着张力增大而增大;失谐摆摆长对舞动临界风速的影响不大,锤重对舞动临界风速的影响较大,锤重越重,临界风速越大。
Under the stable wind, the iced transmission conductor will appear low frequency and large amplitude vibration which is usually called as galloping. The galloping of transmission conductor will cause electric accident, such as flashover, short circuit, hardware damage and so on, creating enormous economic loss. At the present time, the finite element analysis of galloping of transmission line is mainly based on cable element theory that neglects the bending rigidity and is discrepant with bending rigidity of transmission line. Based on curved beam theory considering tensile stiffness, bending stiffness and torsional stiffness, this paper does some research on galloping and anti-galloping of transmission line.
①The analysis of curved beam mode of iced single line. Based on curved beam theory, the curved beam model of 6-DOF node single line is established and the kinetic equation is derived with the principle of virtual work. Nonlinear of single line is analyzed through Matlab programming. The results of examples show that the curved beam model of single line is more accurate than cable element modle.
②The analysis of curved beam mode and torsional stiffness of iced bundle lines. Firstly, the spacer was assumed as rigid body. The curved beam model of bundle lines was formulated according to the displacement compatibility conditions. Moreover, the kinetic equation is derived through virtual work principle. Secondly, nonlinear property of bundle lines is analyzed through Matlab programming. The results of examples turn out that the model of bundle lines based on curved beam theory is feasible and advantageous. Based on this, the curved beam model is used to calculate torsional stiffness of bundle lines. The results of bundle lines’parameter analysis show: the more spacers there are, the greater torsional stiffness is; the greater the space is, the greater the torsional stiffness is; the greater the sag is, the greater the torsional stiffness is; the closer it is away from the tower- line connection point, the greater the torsional stiffness is.
③The finite element analysis of transmission line galloping. According to the curved beam model and kinetic equation of single line and bundle lines, the time history of galloping of transmission line is analyzed through Matlab programming. The results of examples further prove that the curved beam model of transmission line is accurate and advantageous. Analyse of the wind speed, span, tension and other factors’effects on the initial amplitude of galloping show: the greater the span is, the greater the amplitude is; the greater the initial tension is, the smaller the vertical amplitude is; the greater the initial tension is, the bigger the torsional angle is; Consider wire bending rigidity, vertical amplitude and lateral vertical amplitude will increase, torsional angle will decline; galloping vertical amplitude of bundle lines is much bigger than the single line, and torsional angle of bundle lines is much smaller than the single line.
④The finite element analysis of anti-galloping of transmission line. Detuning pendulum mass matrix and stiffness matrix are derived to analyze the anti-galloping of the detuning pendulum. The results show that detuning pendulum only decreses the galloping of Nigol but increases the vertical galloping amplitude of Den Hartog. Finally, the critical wind speed of galloping of transmission line is solved by stability theory. Moreover, effects of span, tension and detuning pendulum on the critical wind speed are analyzed. The results of analysis show: the critical wind speed declines as the span and the initial tension increase; the gravity of hammer of detuning pendulum has little effect on critical wind speed but pendulum length plays great effect on critical wind speed.
引文
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[5]卢明良,尤传永.架空输电线路分裂导线舞动的非线性分析[J].电力建设, 1994, 15 (13): 26-31.
[6]张明升.架空输电线路单导线舞动与分裂导线舞动的异同[J].河北电力技术, 1990, (1): 29-33.
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[9] Nigol, P. G. Buchan. Conductor galloping. 2. Torsional Mechanism[J]. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2):708-720.
[10] P. Yu, Y. M. Desai, A. H. Shah et al. 3-degree-of-freedom model for galloping. 1.formulation[J]. Journal of Engineering Mechanics-ASCE, 1993, 119(12):2404-2425.
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[2]蒋兴良,马俊,王少华等.输电线路冰害事故及原因分析[J].中国电力, 2005, (11):27-30.
[3]刘连睿.我国高压架空线路导线舞动情况及分析[J].华北电力技术, 1989, (9):40-43.
[4]黄经亚.架空送电线路导线舞动的分析研究[J].中国电力, 1995, (12):21-26.
[5]卢明良,尤传永.架空输电线路分裂导线舞动的非线性分析[J].电力建设, 1994, 15 (13): 26-31.
[6]张明升.架空输电线路单导线舞动与分裂导线舞动的异同[J].河北电力技术, 1990, (1): 29-33.
[7]赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究[D].华中科技大学, 2005. 5.
[8] Nigol, P. G. Buchan. Conductor galloping. 1. Den Hartog Mechanism[J]. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2):699-707.
[9] Nigol, P. G. Buchan. Conductor galloping. 2. Torsional Mechanism[J]. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2):708-720.
[10] P. Yu, Y. M. Desai, A. H. Shah et al. 3-degree-of-freedom model for galloping. 1.formulation[J]. Journal of Engineering Mechanics-ASCE, 1993, 119(12):2404-2425.
[11] P. Yu, Y. M. Desai, N. Popplewell et al. 3-degree-of-freedom model for galloping. 2.solutions[J]. Journal of Engineering Mechanics-ASCE, 1993, 119(12):2426-2448.
[12] Haaker. T. I, Vanoudheusden B W. One-degree-of-freedom rotational galloping under strong wind conditions[J]. International Journal of Non-linear Mechanics, 1997, 32(5):803-814.
[13] Parkinson. G. Phenomena and modeling of flow-indeced vibrations of bluff bodies[J]. Progress in Aerospace Science 1989, 26, 169-224.
[14] R. D. Blevins and Wdiwan. The galloping response of a tow-degree-of-freedom system[J]. ASME, 1974, 96(3), 1113-1118.
[15] P. YU, A. H. Shah, N. Popplewell, Inertially coupled galloping of iced conductors [J]. Journal of ApplieMechanics-transactions of the ASME, 1992, 59(1):140-145.
[16] Y. M Desai, A.H.SHAN and N.Popplewell. Galloping analysis for tow-degree-of-freedom oscillator [J]. Journal of Engineering Mechanics, American Society of CivilEngineers, 1990, 116(12), 583-2602.
[17] Luongo, Gpiccardo. Non-linear galloping of sagged cables in 1:2 internal resonance[J]. J.Sound Vib, 1998, 214(5):915-94.
[18] K.F Jones.Coupled vertical and horizontal galloping[J].Engra.Mech.ASCE,1992,118(1),92-107.
[19] Y.M.Desai, P.Yu, N. Popplewell et al.Finite-element modeling of transmission-line galloping. Computers&Structures, 1995, 57(3):407-420.
[20] Wang.J.W, Lilien.J.L. Overhead electrical transmission line galloping- a full multi-span 3-DOF model some application and design recommendations [J]. IEEE Transaction on Power Delivery, 1998, 13(3):909~915
[21] Jianwei Wang, Lilien JeanLouis. A new theory for torsional stiffness of multi-span bundle overhead transmission lines [J]. IEEE Transaction on Power Delivery, 1998, 13(4):1405~1411
[22] Zhang Q, Popplewell N, Shah AH. Galloping of bundle conductor [J]. Journal of Sound and Vibration, 2000, 234(1):115-134
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