Extending of " Energy Balance Method" for Calculating of Cable Vibration with Arbitrary Number of Dampers and their Optimal Placement

Aeolian vibration of conductors could cause extensive damages to the electric power transmission networks. The use of Stock-Bridge dampers is a very common method to control the transmission line vibration amplitude. Due to the complexity of the cable-wind interaction, the Energy Balance Method (EBM) is extensively used for calculating the steady state amplitude of the system. In the present study EBM incorporating the traveling wave method are developed for calculating the steady state amplitude of the cable with arbitrary number of dampers. The wave propagation was produced by superposition of two travelling waves. The proposed method is subsequently employed to study the effect of the number, location and impedance of dampers on dissipated energy and damper performance as well. The results show that damper installation at optimum location is more effective than the damper number increase, in which case does not necessarily leads to the dissipated energy increase. Furthermore, in this study a simple equation relating ISWR (Inverse Standing Wave Ratio) to Absorption Coefficient is introduced. The importance of this equation is due to the fact that only ISWR can be readily measured, but not the absorption coefficient itself, which is based upon the measurement of the travelling wave amplitudes. Finally, investigation on damper dynamic characteristics effects on absorption coefficient reveals that the real parts of damper impedance having complete absorption is independent of vibration frequency; and if the magnitude of damper impedance be lower than that of the cable for all the frequency range, complete absorption will never occur.