输电线路舞动有限元分析
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摘要
输电导线舞动对线路的安全运行极具威胁性,给整个输电线路造成损坏,造成重大经济损失;但由于输电线路舞动特性的复杂性,人们对舞动机制还没有完全认识清楚,很难在实践中做好防治工作。为了保证输电线路在覆冰作用下的安全可靠运行,必须对输电线路舞动进行深入的研究。本文从单自由度、两自由度模型建立、三自由度非线性有限元公式推导及模型的建立、增量谐波平衡法在舞动上的应用等几方面对输电线覆冰舞动进行了研究。主要研究内容有:
1)建立单自由度和两自由度力学模型,分析了输电线舞动规律。采用简化力模型,由D'Alembert原理建立微元的运动平衡方程,分别推导出单自由度和两自由度动力学方程,并自编mathematics程序验证准确性。分析表明,舞动以垂直运动为主,对于扭转刚度较小的舞动,垂直方向计算结果偏大;扭转刚度较大的,计算结果相对较为准确。
2)推导了三节点索单元三维有限元模型。首先将空间中的输电线路用三结点索单元离散化,根据Hamilton原理和变分原理,推导三自由度舞动模型的位移关系,并给出输电线舞动的有限元模型的具体表达格式。最后指出传统索单元刚度矩阵比本文推导刚度矩阵偏大,造成对输电塔拉力计算值偏小。最后通过编制Matlab程序,用时间积分算法对非线性舞动方程进行求解,证明本模型的准确性。
3)利用增量谐波平衡法(IHB)分析输电线路舞动问题,然后利用增量谐波平衡法求解该数学模型。首先利用增量谐波平衡法分析索在简谐荷载线性和非线性的特性,然后分析舞动问题。从计算结果可知,最终不平衡力趋于零。经分析一阶谐波值明显偏小,两阶谐波即可满足分析精度要求。
增量谐波平衡法(IHB)能有效解决舞动非线性问题,分析极限环等非线性现象,与数值结果相比具有较高的精度;并能得出锁定频率区间,可分析参数变化对振动特性的影响。
The galloping threatens the safe of the transmission lines, and it can lead to severe disruptions in the electrical power supply, and resulting in major economic loss. However, The galloping characteristics are complex, so it’s difficult to prevent and cure the galloping in practice. In order to guarantee the safety and reliability of electrical network,the galloping phenomenon of power transmission lines must be in-depth study. In this paper, a single degree of freedom, two degrees of freedom model, three degrees of freedom, incremental harmonic balance method in galloping on the application of several aspects of ice dancing power lines has been studied . The main contents are:
A single degree of freedom and two degrees of freedom mechanical model is established,and the transmission line dancing rules is analyzed. Simplified force model is used, established by the D'Alembert principle of infinitesimal movement, and equilibrium equation derived single degree of freedom and two degrees of freedom dynamic equations, and verify the accuracy of self mathematics program. Analysis showed that the vertical movement is the main in galloping. To the smaller torsional stiffness, the results are relatively large vertical direction. When torsional stiffness is relatively large, results is relatively accurate.
The three-degree-of-freedom model for galloping is derived three nodes . Forst of all, the space of the transmission line cable is discreted with three node element, and according to Hamilton principle and the variational principle, the general method for establishing galloping finite element model is provided. Finite element model of transmission line dancing specific expression forma is given. Finally pointed out that traditional cable element stiffness matrix than this article derivation stiffness matrix too big, cause tension on the transmission tower small calculated values. Finally by crafting a Matlab program, using the time integral algorithm on nonlinear equations to prove the accuracy of this model.
Using incremental harmonic balance method (IHB) of transmission line dancing issues, and then use incremental harmonic balance method for calculating the mathematical model. Firstly, harmonic load is used to analyse the characteristics of the cable, then to analyse the problems of galloping. The calculation results show that the ultimate unbalanced force tends to zero, shows that the method used in the field is rational. The analysis was that first-order harmonic is significantly smaller, the two-order harmonic analysis can meet the accuracy requirements.
Incremental harmonic balance method (IHB) can effectively solve the nonlinear problem of galloping to analyze nonlinear phenomena such as limit cycle, and compared with the numerical results with high accuracy. The frequency interval that can be locked, you can analysis parameters change on vibration characteristics.
1)建立单自由度和两自由度力学模型,分析了输电线舞动规律。采用简化力模型,由D'Alembert原理建立微元的运动平衡方程,分别推导出单自由度和两自由度动力学方程,并自编mathematics程序验证准确性。分析表明,舞动以垂直运动为主,对于扭转刚度较小的舞动,垂直方向计算结果偏大;扭转刚度较大的,计算结果相对较为准确。
2)推导了三节点索单元三维有限元模型。首先将空间中的输电线路用三结点索单元离散化,根据Hamilton原理和变分原理,推导三自由度舞动模型的位移关系,并给出输电线舞动的有限元模型的具体表达格式。最后指出传统索单元刚度矩阵比本文推导刚度矩阵偏大,造成对输电塔拉力计算值偏小。最后通过编制Matlab程序,用时间积分算法对非线性舞动方程进行求解,证明本模型的准确性。
3)利用增量谐波平衡法(IHB)分析输电线路舞动问题,然后利用增量谐波平衡法求解该数学模型。首先利用增量谐波平衡法分析索在简谐荷载线性和非线性的特性,然后分析舞动问题。从计算结果可知,最终不平衡力趋于零。经分析一阶谐波值明显偏小,两阶谐波即可满足分析精度要求。
增量谐波平衡法(IHB)能有效解决舞动非线性问题,分析极限环等非线性现象,与数值结果相比具有较高的精度;并能得出锁定频率区间,可分析参数变化对振动特性的影响。
The galloping threatens the safe of the transmission lines, and it can lead to severe disruptions in the electrical power supply, and resulting in major economic loss. However, The galloping characteristics are complex, so it’s difficult to prevent and cure the galloping in practice. In order to guarantee the safety and reliability of electrical network,the galloping phenomenon of power transmission lines must be in-depth study. In this paper, a single degree of freedom, two degrees of freedom model, three degrees of freedom, incremental harmonic balance method in galloping on the application of several aspects of ice dancing power lines has been studied . The main contents are:
A single degree of freedom and two degrees of freedom mechanical model is established,and the transmission line dancing rules is analyzed. Simplified force model is used, established by the D'Alembert principle of infinitesimal movement, and equilibrium equation derived single degree of freedom and two degrees of freedom dynamic equations, and verify the accuracy of self mathematics program. Analysis showed that the vertical movement is the main in galloping. To the smaller torsional stiffness, the results are relatively large vertical direction. When torsional stiffness is relatively large, results is relatively accurate.
The three-degree-of-freedom model for galloping is derived three nodes . Forst of all, the space of the transmission line cable is discreted with three node element, and according to Hamilton principle and the variational principle, the general method for establishing galloping finite element model is provided. Finite element model of transmission line dancing specific expression forma is given. Finally pointed out that traditional cable element stiffness matrix than this article derivation stiffness matrix too big, cause tension on the transmission tower small calculated values. Finally by crafting a Matlab program, using the time integral algorithm on nonlinear equations to prove the accuracy of this model.
Using incremental harmonic balance method (IHB) of transmission line dancing issues, and then use incremental harmonic balance method for calculating the mathematical model. Firstly, harmonic load is used to analyse the characteristics of the cable, then to analyse the problems of galloping. The calculation results show that the ultimate unbalanced force tends to zero, shows that the method used in the field is rational. The analysis was that first-order harmonic is significantly smaller, the two-order harmonic analysis can meet the accuracy requirements.
Incremental harmonic balance method (IHB) can effectively solve the nonlinear problem of galloping to analyze nonlinear phenomena such as limit cycle, and compared with the numerical results with high accuracy. The frequency interval that can be locked, you can analysis parameters change on vibration characteristics.
引文
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[2]郭应龙,李国兴,尤传永.输电线路舞动[M].北京:中国电力出版社, 2003.
[3]巫世晶,向农.神经网络在输电导线舞动监测诊断系统中的应用.华北电力技术, 19(9): 1-4.
[4]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.
[5]何隆华.高压输电线路导线舞动.贵州电力技术. 1993, (1):26~36.
[6]蒋兴良,易辉.输电线路覆冰及防护[M].北京:中国电力出版社, 2002.
[7]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.
[8]马俊,蒋兴良,张志劲,胡建林,舒立春.交流电场对绝缘子覆冰形成的影响机理[J].电网技术, 2008(5):7-11.
[9]常浩,石岩,殷威扬,张民.交直流线路融冰技术研究[J].电网技术, 2008, 32(5):1-6.
[10]李光辉.电力系统防冻融冰问题的分析及对策[J].大众用电, 2007, (1): 33-34.
[11]张忠河,王藏柱.舞动研究现状及发展趋势.电力情报, 1998, (4)6-8.
[12]夏正春.特压输电线的覆冰舞动及脱冰跳跃研究. [D].华中科技大学, 2008. 10.
[13]郭应龙.输电导线舞动[M].武汉:武汉水利电力大学出版社, 1998.
[14]石吉汉,吴继云.导线舞动的防治.电力建设, 2005 12(26):39-42.
[15]刘纯,陆佳政,陈红冬.湖南500 kV输电线路覆冰倒塔原因分析[J].湖南电力, 2005, 25(5):1-4.
[16] Liu Chun, Lu Jiazheng, Chen Hongdong. Cause analysis of tower falling down and ice accretion in Hunan 500kV power transmission line[J]. Hunan Electric Power, 2005, 25(5):1-4(in Chinese).
[17]李万平,黄河,何锃.特大覆冰导线气动力特性测试.华中科技大学学报, 2001, 29(8):84-86.
[18]刘文杰.架空输电导线舞动动态仿真与扰流防舞器的研究.武汉大学: [D]. , 2005.
[19] M. I. Kazakevich, A. G. Vasilenko. Closed Analytical Solution for Galloping Aeroelastic Self- oscillations. Journal of Wind Engineering and industrial Aerodynamics, 1996, 65(1-3): 353-360
[20] O. Nigol, P. G. Buchan. Conductor Galloping. 1. Den Hartog Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2):699-707.
[21] O. Nigol, P. G. Buchan. Conductor Galloping. 2. Torsional Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2):708-720.
[22] P. Yu, Y. M. Desai, A. H. Shah et al. 3-degree-of-freedom Model for Galloping. 1. Formulation. Journal of Engineering Mechanics-ASCE, 1993, 119(12):2404-2425.
[23] P. Yu, Y. M. Desai, N. Popplewell et al. 3-degree-of-freedom Model for Galloping. 2. Solutions. Journal of Engineering Mechanics-ASCE, 1993, 119(12):2426-2448.
[24] Q. Zhang, N. Popplewell, A. H. Shah. Galloping of Bundle Conductor. Journal of Sound and Vibration, 2000, 234(1):115-134.
[25] Den Hartog J P. Mechanical vibration[M]. New York:Mcgraw-Hill, 1956.
[26] Den Hartog J P. Transmission line vibration due to sleet[J]. AIEE Transactions, 1932, 51(12): 1074-1086.
[27]李文蕴.覆冰分裂导线舞动数值模拟方法研究[D].重庆:重庆大学, 2009. 5.
[28] P. Yu, A. H. Shah, N. Popplewell. Inertially coupled galloping of iced conductors [J] . Journal ofApplied Mechanics-transactions of the ASME, 1992, 59(1):140-145.
[29] P. Yu, N. Popplewell, A. H. Shah. Instability trends of inertially coupled galloping. 2. periodic vibrations [J] . Journal of Sound and Vibration, 1995183(4):679-691.
[30] Y. M. Desai, P. Yu, N. Popplewell et al. Finite-element Modeling of Transmission-line Galloping. Computers&Structures, 1995, 57(3):407-420.
[31] Y. M. Desai, P. Yu, A. H. Shah et al. Perturbation-based Finite Element Analysesof Transmission Line Galloping. Journal of Sound and Vibration, 1996, 191(4):469-489.
[32]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.
[33]蔡廷湘.输电线舞动新机理研究[J].中国电力, 1998(10):62-66.
[34] Kathleen F. Jones. Coupled vertical and horizontal galloping. [J] Journal of Engineering Mechanics, 1992, 118(1):92-107.
[35] R. D. Blevins, W. D. Iwan. The Galloping Response of a 2-degree-of-freedom system. Journal of Applied Mechanics-ASME, 1974, 41:1113-1118.
[36] Y. M. Desai, A. H. Shah, N. Popplewell. Galloping Analysis for2-degree-of-freedom Oscillator. Journal of Engineering Mechanics-ASCE, 1990, 116(12):2583-2602.
[37] G. S. Byun, R. I. Egbert. 2-degree-of-freedom Analysis of Power-line Gallopingby Describing Function Methods. Electric Power Systems Research, 1991, 21(3):187-193.
[38] T. I. Haaker, Van der Burgh Ahp. Rotational Galloping of Two Coupled Oscillators. Meccanica, 1998, 33(3):219-227.
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