Two Simplified Methods for Galloping of Iced Transmission Lines

For the galloping of iced transmission lines, the influences of two simplified methods of dynamic tension on the galloping characteristics of transmission lines are investigated. Based on the variational principle for Hamiltonian, the partial differential equation of galloping of iced transmission lines is derived, then it is transformed into ordinary differential equation by Galerkin method. Two different simplified methods are used to convert the partial differential equation into ordinary differential equation. One is to average the dynamic tension over the span length, then Galerkin method is used. The other is that Galerkin method is used to convert the partial differential equation into ordinary differential equation directly. Firstly, the influences of two simplified methods on coefficients of ordinary differential galloping equation are studied. Second, the influences of the bending stiffness on the first-order frequency have been researched. In addition, the average method of two degrees of freedom (DOFs) is proposed and the galloping characteristics of iced transmission lines are studied by using multiscale method and average method, then the results are compared with that obtained by using numerical method. The parameters analysis shows that the two simplified methods of dynamic tension have significant influences on the coefficients of the two DOFs ordinary differential equation. By comparing the coefficients of galloping equation obtained by the two simplified methods of dynamic tension, it can find that with the increasing of tension and span length, the influences of bending stiffness on in-plane and out-of-plane natural frequency becomes smaller and smaller. The results of multiscale method and average method both show that the two simplified methods of dynamic tension have certain influences on the frequency, phase and amplitude of galloping of iced transmission lines. The conclusions obtained by this paper would promote the perfection of theoretical modeling about iced transmission lines, and could also give some references to practical engineering.