H. Verma

On the Solution of Transcendental Eigenvalue Problem in Transmission Line Bundled Conductors

Overhead electrical transmission lines are always susceptible to aeolian vibrations, caused by light to moderate winds. Spacer dampers are used in bundled transmission lines to keep the conductors at required minimum spacing and to suppress the wind induced vibrations. Mathematical models are necessary for the computation of the conductor vibrations for studying the efficiency of damping measures. The so called energy balance method gives good results for estimating the vortex excited vibrations of overhead electrical transmission lines. In its standard form it requires the knowledge of the eigenfunctions, which are routinely calculated for the single conductor lines. However, the problem becomes more involved in the case of bundled conductors with spacer dampers due to very dense spectrum of the natural frequencies. In the present paper some approaches towards solving the transcendental eigenvalue problem (EVP) for the bundled conductors with spacer dampers are discussed. It is formulated as an algebraic transcendental EVP, which however presents several numerical difficulties. Reasons for these numerical difficulties are discussed in some detail. A new approach, named as “continuous spectrum approach,” provides better engineering solution for the transmission line bundled conductors. The solution of the EVP gives the necessary input data for applying the energy balance.© 2004 ASME