Two-Parameter Bifurcation and Stability Analysis for Nonlinear Galloping of Iced Transmission Lines

Abstract

This paper presents an analytical approach in the study of bifurcation and stability behavior for nonlinear galloping of iced transmission lines. Equations of motion are established to describe three-dimensional galloping behavior observed on iced transmission lines. Stability analysis of iced conductor galloping is carried out. The center manifold theory, together with the normal form theory, is used to derive the governing bifurcation equations. A new formula is also proposed to calculate the maximum dynamic tension of iced conductors. The technique developed in this paper is implemented using a symbolic analysis module for practical usage. A real transmission line with a span of 244 m, which was damaged by the galloping accidents, is presented to demonstrate the effectiveness and accuracy of the developed two-parameter bifurcation analysis technique for nonlinear galloping of iced conductors. The galloping amplitudes in three orthogonal directions are analytically obtained for a broad range of galloping wind speeds and attack angles. The analytical solutions of galloping amplitudes are also verified by the numerical time-stepping method.