IJE TRANSACTIONS A: Basics Vol. 31, No. 10 (October 2018) 1325-1333   

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A. Rezaei and M. Sadeghi
( Received: February 26, 2018 – Accepted: April 26, 2018 )

Abstract    Energy Balance Method is an effective and simple method which is used in amplitude calculation of Aeolian vibration in transmission lines with Stock Bridge 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 wave, 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 significant effect on the accuracy of the results.


Keywords    Aeolian Vibration, Transmission Line, Energy Balance Method, Stock-bridge Damper, Optimum location


چکیده    تعیین دامنه ارتعاشاتِ «آولین» رساناهای خطوط انتقال برق دارای میراگر «استاک­بریج»، به دلیل پیچیدگی رفتار رسانای رشته­ای، از روش «تعادل انرژی» انجام می‌شود. دقت نتایج بدست آمده از این روش، به شدت به شکل مود فرض شده برای ارتعاش رسانا وابسته است. در تحقیق حاضر با در نظر گرفتن یک مدل مناسب برای ارتعاش رسانا، روش جامعی برای محاسبه­ی دامنه ارتعاش پایای رسانای دارای تعداد دلخواه میراگر ارایه می­شود. در این روش، اثرات روندگی موج، تغییر دامنه و فاز نسبت به زمان، شرایط مرزی دو انتها (طول محدود رسانا) و همچنین تاثیر تعداد، محل نصب و امپدانس میراگر در شکل مود ارتعاشی لحاظ می­شود و فرکانس­های طبیعی، نرخ میرایی و شکل مودهای مختلط از تشکیل و حل مساله مقدار ویژه غیرخطی مربوطه بدست آورده می­شود. همچنین با استفاده از این روش اثر محل نصب میراگر بر روی دامنه ارتعاش و کرنش خمشی رسانا بررسی شده و محل نصب بهینه استخراج می­شود. مقادیر بدست آمده نشان می­دهند در نظر گرفتن پارامترهای فوق اثر قابل ملاحظه­ای بر دقت نتایج دارد.

References    [1] Kiessling, F., Nefzger, P., Nolasco, J. F., Kaintzyk, U., “Overhead Power Lines”, Springer, (2003), 320-350. [2] Chan, J., Havard, D., Rawlins, C., Diana, G., Cloutier, L., Lilien, J. L., Hardy, C., Wang, J., Goel, A., “EPRI Transmission Line Reference Book, Wind Induced Conductor Motion”, Electric Power Research Institute, Palo Alto, California, U.S.A., (2009). [3] Bayliss, C. R., “Transmission and Distribution Electrical Engineering”, Elsevier, (2012), 619-665. [4] Hartman, D., Kern, G., “Wind Induced Vibrations on High Voltage Overhead Lines”, Mosdorfer, Austria, (1994). [5] Emamgholizadeh, M., 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", IJE -Transactions C: Aspects, Vol. 28, No. 3, (2014), 368. [6] Dulhunty, P., “Vibration dampers on AAC and AAAC conductors”, 22nd International Conference and Exhibition on Electricity Distribution, Stockholm, (2013), [7]- Krispin, H. J., Fuchs, S., Hagedorn, P., “Optimization of Efficiency of Aeolian Vibration Dampers”, IEEE Power Africa Conference and Exposition, South Africa, (2007). [8] Varney, T., “Notes on the Vibration of Transmission Line Conductors”, Regional Meeting of District, AIEEE, No. 1 (1926), 791-795. [9] Claren, R., Diana, G., “Mathematical Analysis of Transmission Line Vibration”, IEEE Transactions on Power Apparatus and Systems, No. 12, (1969), 1741-1771. [10] Langlois, S.; Legeron, F., “Prediction of Aeolian Vibration on Transmission-Line Conductors Using a Nonlinear Time History Model- Conductor and Damper Model”, IEEE Transactions on Power Delivery, 29(3), (2014), 1168-1183. [11] Godard, B.; Guerard, S.; Lilien, J.-L., “Original Real-Time Observations of Aeolian Vibrations on Power-Line Conductors”, IEEE Transactions on Power Delivery, 26(4), (2011), 2111-2117. [12] LI, L., KONG, D., LONG, X., LIANG, Z., “Analysis of Aeolian Transmission Conductor with Dampers by the Finite Element Method”, High Voltage Engineering, 02(12), (2008) [13] Dhotard, M. S., Ganesan, N., Rao, B. V., “Transmission line Vibrations”, Journal of Sound and Vibration, No. 60 (2), (1978), 217- 237. [14] Hagedorn, P., “Ein einfaches Rechenmodell zur Berechnung winderregter Schwingungen an Hochspannungsletitungen mit Dampfern”, Ingenieur Archiv, No. 49, (1980), 161- 177. [15] Hagedorn, P., “On the Computation of Damped Wind Excited Vibrations of Overhead Transmission Lines”, Journal of Sound and Vibration, No. 83 (2), (1982), 253-271. [16] Wolf, H., Adum, B., “Using the Energy Balance Method in Estimation of Overhead Transmission Lines Aeolian Vibrations”, Strojarstvo, No. 50 (5), (2008), 269-276. [17] Kasap, H., “Investigation of Stockbridge Dampers for Vibration Control of Overhead Transmission Lines”, Master of Science Thesis in Mechanical Engineering Faculty of Middle East Technical University, (2012). [18] Sadeghi, M., Rezaei, A., “Extending Energy Balance Method for Calculating Cable Vibration with Arbitrary Number of Dampers and their Optimal Placement”, Modares Mechanical Engineering, No. 15(8), (2015), 438-448. [19] Vecchiarelli, J., “Aeolian Vibration of a Conductor with a Stockbridge Type Damper”, Ph. D. Thesis in mechanical Engineering Department of Toronto University, (1997) [20] Vecchiarelli, J., Currie, I. G., Havard, D.G., “Computational Analysis of Aeolian Conductor Vibration with a Stockbridge type Damper”, Journal of Fluid and Structures, No. 14, (2000), 489-509 [21] Rezaei, A., Sadeghi, M., “Aeolian Vibrations of Transmission Line Conductors with More than One Damper”. IJE TRANSACTIONS B: Applications, Vol. 28, No. 10, (2015), 1515-1524. [22] Langlois, S.; Legeron, F.; Levesque, F., “Time History Modeling of Vibrations on Overhead Conductors With Variable Bending Stiffness”, IEEE Transactions on Power Delivery, 29(2), (2014), 607-614. [23] Levesque, F.; Goudreau, S.; Langlois, S.; Legeron, F., “Experimental Study of Dynamic Bending Stiffness of ACSR Overhead Conductors”, IEEE Transactions on Power Delivery, 99, (2015). [24] Braga, G. E., Nakamura, R., Furtado, T. A., “Aeolian Vibration of Overhead Transmission Line Cable: Endurance Limits”, IEEE/PES Transmission Land Distribution Conference and Exposition, Latin America, (2004). [25] LI, L., KONG, D., LONG, X., LIANG, Z., “Analysis of Aeolian Transmission Conductor with Dampers by the Finite Element Method”, High Voltage Engineering, 02(12), (2008) [26] LI, L., KONG, D., LONG, X, LIANG, Z., “NUMERICAL SIMULATION OF AEOLIAN VIBRATIONS TRANSMISSION LINES BY CFD”, Engineering Mechanics, 02, (2009) [27] Kraus, M., Hagedorn, P., “Aeolian Vibration: Wind Energy Input Evaluated From Measurements on an Energized Transmission Line, IEEE Transmissions on Power Delivery, 6(3), (1991). [28] Hagedorn, P., “Wind-Excited Vibrations of Transmission Lines: a Comparison of Different Mathematical Models”, Mathematical Modeling, Vol. 8, (1987), 352-358. [29] Diana, G., Falco, M., “On the Forces Transmitted to a Vibrating Cylinder by a Blowing Fluid”, Meccanica, (1971), 9-22. [30] IEEE Standards, “IEEE Std. 563- IEEE Guide on Conductor Self Damping Measurements”, IEEE Power & Energy Society, New York, U. S. A., (1978). [31] Guerard, S., “Power Line Conductors, a Contribution to the Analysis of their Dynamic Behavior”, Ph. D. Thesis in Applied Science Faculty of University of Liege, (2011). [32] Noiseux, D. U., “Similarity Laws of the Internal Damping of Stranded Cables in Transverse Vibrations”, Transmission and Distribution Conference, IEEE power Engineering Society, (1991), 1574-1581. [33] IEC Standards- “IEC Std 61897- Requirements and tests for Stockbridge type Aeolian vibration dampers”, International Electro technical Commission, Switzerland, (1998). [34] Dimargonas, A. D., Vibration for Engineers, Prentice Hall, 1992

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