Galloping Equation and Primary Resonance Investigation of Overhead Transmission Lines

Abstract

The galloping of overhead transmission lines is one of the main causes for line damages. How to accurately describe the galloping of transmission lines is a worthy topic. Firstly, a partial differential equation of a transmission line is derived with Hamiltonian variational principle. And then the equation is nondimensionalized, and the modal function and linear frequencies of the transmission line are calculated under in-plane symmetrical mode and anti-symmetric mode. The partial differential equation is transformed into ordinary differential equation with Galerkin method. Finally, the influence of Irvine parameters on amplitude-frequency response is analyzed with the method of multiple scales. From the curves of the amplitude-frequency response, it is found that the larger the Irvine parameters are, the stronger the nonlinear effects are and the more remarkable the jump phenomenon is. When the primary resonance occurs, the amplitude of galloping is mainly determined by the first-order modal function, and the amplitude caused by the higher-order modal function is much smaller than that caused by the first-order modal function.

Keywords

• transmission line
• primary resonance
• tensile force
• amplitude-frequency response
• method of multiple scales