Analysis of Aeolian Vibrations of Transmission Line Conductors and Extraction of Damper Optimal Placement with a Comprehensive Methodology


Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran


Energy balance method is an effective and simple method which is used in the amplitude calculation of Aeolian vibration in transmission lines with Stockbridge damper. However, the accuracy of the results obtained by this method, heavily depends on the assumed mode shapes of the conductor vibration. In this study, by considering an appropriate model for the conductor vibration, a comprehensive methodology is presented to calculate the steady-state vibration amplitude of a conductor with arbitrary number of dampers. In this proposed method, the effects of traveling waves, variations of amplitude and phase, boundary conditions (finite length of the conductor), as well as the effect of number, location and impedance of the dampers are taken into account. Natural frequencies, damping rates and complex mode shapes are also obtained from forming and solving the nonlinear eigenvalue problem. Using this method, the effects of the damper placement on the vibration amplitude and bending strain are examined to achieve an optimum damper location. The comparison of the obtained values shows that considering the above parameters has a significant effect on the accuracy of the results.


1.     Kiessling, F., Nefzger, P., Nolasco, J., and Kaintzyk, U., Overhead power lines: planning, design, construction, Springer Science & Business Media, (2014).
2.     Chan, J., Havard, D., Rawlins, C., Diana, G., and Cloutier, L., EPRI Transmission Line Reference Book: wind-induced Conductor Motion, Electric Power Research Institute (EPRI), (2009).
3.     Bayliss, C., Bayliss, C., and Hardy, B., Transmission and distribution electrical engineering, Elsevier, (2012).
4.     Hartmann, G.K.D., and Kern, G.G., Wind Induced Vibrations on High Voltage Overhead Lines, Mosdorfer, Austria, (1994).
5.     Emamgholizadeh, M.J., Gharabaghi, A.M., Abedi, K., and Sedaaghi, M., “Experimental investigation of the effect of splitter plate angle on the under-scouring of submarine pipeline due to steady current and clear water condition”, International Journal of Engineering-Transactions C: Aspects,  Vol. 28, No. 3, (2014), 368–377.
6.     Dulhunty, P., “Vibration dampers on AAC and AAAC conductors”, In 22nd International Conference and Exhibition on Electricity Distribution (CIRED 2013), Institution of Engineering and Technology, Stockholm, (2013), 1–4.
7.     Liu, S., Sun, N., Yin, Q., Qi, Y., Cao, D., and Zhang, L., “Study of New Vibration Suppression Devices for Application to EHV Transmission Line Groundwires”, Energy Procedia,  Vol. 12, (2011), 313–319.
8.     Krispin, H.J., Fuchs, S., and Hagedorn, P., “Optimization of the Efficiency of Aeolian Vibration Dampers”, In IEEE Power Engineering Society Conference and Exposition in Africa - PowerAfrica, IEEE, (2007), 1–3.
9.     Varney, T., “Notes on the vibration of transmission-line conductors”, Journal of the American Institute of Electrical Engineers (AIEE),  Vol. 45, No. 10, (1926), 953–957.
10.   Claren, R., and Diana, G., “Mathematical Analysis of Transmission Line Vibration”, IEEE Transactions on Power Apparatus and Systems,  Vol. PAS-88, No. 12, (1969), 1741–1771.
11.   Dhotarad, M.S., Ganesan, N., and Rao, B.V.A., “Transmission line vibrations”, Journal of Sound and Vibration,  Vol. 60, No. 2, (1978), 217–237.
12.   Li L., De-yi K., Xiao-hong L., and Zheng-ping L., “Analysis of Aeolian Transmission Conductor with Dampers by the Finite Element Method”, High Voltage Engineering,  Vol. 34, No. 2, (2008), 324–328.
13.   Li, L., De-Yi, K., Xiao-Hong, L., and Zheng-ping, L., “Numerical simulation of aeolian vibrations transmission lines by CFD”, Engineering Mechanics,  Vol. 26, No. S2, (2009), 235–240.
14.   Vecchiarelli, J., “Aeolian vibration of a conductor with a Stockbridge-type damper”, Doctoral dissertation, University of Toronto, (1998).
15.   Vecchiarelli, J., Currie, I.G., and Havard, D.G., “Computational analysis of aeolian conductor vibration with a stockbridge-type damper”, Journal of Fluids and Structures,  Vol. 14, No. 4, (2000), 489–509.
16.   Langlois, S., and Legeron, F., “Prediction of Aeolian Vibration on Transmission-Line Conductors Using a Nonlinear Time History Model—Part I: Damper Model”, IEEE Transactions on Power Delivery,  Vol. 29, No. 3, (2014), 1168–1175.
17.   Guerard, S., Godard, B., and Lilien, J.L., “Aeolian Vibrations on Power-Line Conductors, Evaluation of Actual Self Damping”, IEEE Transactions on Power Delivery,  Vol. 26, No. 4, (2011), 2118–2122.
18.   Godard, B., Guerard, S., and Lilien, J.L., “Original Real-Time Observations of Aeolian Vibrations on Power-Line Conductors”, IEEE Transactions on Power Delivery,  Vol. 26, No. 4, (2011), 2111–2117.
19.   Hagedorn, P., “Ein einfaches Rechenmodell zur Berechnung winderregter Schwingungen an Hochspannungsleitungen mit Dampfern”, Ingenieur-Archiv,  Vol. 49, No. 3–4, (1980), 161–177.
20.   Hagedorn, P., “On the computation of damped wind-excited vibrations of overhead transmission lines”, Journal of Sound and Vibration,  Vol. 83, No. 2, (1982), 253–271.
21.   Wolf, H., Adum, B., Semenski, D., and Pustaić, D., “Using the Energy Balance Method in the Estimation of Overhead Transmission Line Aeolian Vibrations”, Strojarstvo,  Vol. 50, No. 5, (2008), 269–276.
22.   Kasap, H., “Investigation of Stockbridge dampers for vibration control of overhead transmission lines”, Doctoral dissertation, Middle East Technical University, (2012).
23.   Sadeghi, S.M., and Rezaei, A., “Extending of ‘Energy Balance Method’ for Calculating of Cable Vibration with Arbitrary Number of Dampers and their Optimal Placement”, Modares Mechanical Engineering,  Vol. 15, No. 8, (2015), 438–448.
24.   Rezaei, A., and Sadeghi, M.H., “Aeolian Vibrations of Transmission Line Conductors with More than One Damper”, International Journal of Engineering-Transactions A: Basics,  Vol. 28, No. 10, (2015), 1515–1524.
25.   Langlois, S., Legeron, F., and Levesque, F., “Time History Modeling of Vibrations on Overhead Conductors With Variable Bending Stiffness”, IEEE Transactions on Power Delivery,  Vol. 29, No. 2, (2014), 607–614.
26.   Levesque, F., Goudreau, S., Langlois, S., and Legeron, F., “Experimental Study of Dynamic Bending Stiffness of ACSR Overhead Conductors”, IEEE Transactions on Power Delivery,  Vol. 30, No. 5, (2015), 2252–2259.
27.   Braga, G.E., Nakamura, R., and Furtado, T.A., “Aeolian vibration of overhead transmission line cables: endurance limits”, In IEEE/PES Transmision and Distribution Conference and Exposition: Latin America, IEEE, (2004), 487–492.
28.   Kraus, M., and Hagedorn, P., “Aeolian vibrations: wind energy input evaluated from measurements on an energized transmission line”, IEEE Transactions on Power Delivery,  Vol. 6, No. 3, (1991), 1264–1270.
29.   Hagedorn, P., “Wind-excited vibrations of transmission lines: A comparison of different mathematical models”, Mathematical Modelling,  Vol. 8, (1987), 352–358.
30.   Diana, G., and Falco, M., “On the forces transmitted to a vibrating cylinder by a blowing fluid”, Meccanica,  Vol. 6, No. 1, (1971), 9–22.
31.   IEEE Standards, “IEEE Std. 563- IEEE Guide on Conductor Self Damping Measurements”, IEEE Power & Energy Society, New York, U. S. A., (1978).
32.   Guérard, S., “Power line conductors, a contribution to the analysis of their dynamic behaviour”, Doctoral dissertation, Université de Liège, Belgique, (2011).
33.   Noiseux, D.U., “Similarity laws of the internal damping of stranded cables in transverse vibrations”, In Proceedings of the 1991 IEEE Power Engineering Society Transmission and Distribution Conference, IEEE, 817–823.
34.   IEC Standards, “IEC Std 61897- Requirements and tests for Stockbridge type Aeolian vibration dampers”, International Electro technical Commission, Switzerland, (1998).
35.   Dimarogonas, A.D., Vibration for Engineers, Prentice Hall, (1996).