On the Euler-Lagrange formalism to compute power line bundle conductors subject to aeolian vibrations

Abstract

Analytical models of aeolian vibrations for both twin and quad bundle conductors are summarized in this paper. These analytical models are defined by equations of motion and developed using the Euler-Lagrange formalism. They describe the behavior of bundle conductors under combined effects. The generated swinging, and flexural and torsional motion are addressed. To simplify the complexity of the calculus during the development of the analytical models, several assumptions are made: (i) aeolian vibrations remain in the range of small oscillations; (ii) acceleration is constant at each frequency; and (iii) the Kelvin-Voight rheological model is considered for the vertical and horizontal stiffness in the spacer-damper. These analytical models are compared and validated by means of numerical simulations using the results from indoor experiments on an overhead transmission line-span with quad-bundle conductors. This has only one spacer-damper attached at its mid-span. The comparisons show good agreement between experiments and numerical simulations in the rigid mode, and an insignificant discrepancy in the damping mode. Finally, the performance of twin spacer-dampers in terms of dissipating wind-induced power in transmission line twin-bundled conductors is assessed and compared with quad bundles through developed analytical models, and the physical significance are highlighted.