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.

The torsional behavior of twin bundle conductor lines is investigated by means of experiments. Based on similarity principle, the reduced-scale modelling method for simulating the torsional behavior of bundle conductor lines is presented and validated by the test results of full-scale transmission lines. Parameter study on torsional behavior of twin bundle conductor lines under different parameters, including loading and unloading rates of applying torque, initial tension in sub-conductors, layout of sub-conductors, number of spacers, clamps between spacers and sub-conductors and arrangement of spacers, is carried out by means of reduced-scale modelling tests. The effects of these parameters on the torsional stiffness, collapse moment, collapse angle, self-restoring moment of twin bundle conductor lines are obtained. It is observed that a collapsed bundle conductor line may not be able to return to its initial position after releasing load, which reflects the phenomenon observed in real transmission lines, and optimal arrangement of spacers in a bundle conductor line may exist to prevent or mitigate the torsional instability in the case without considering other factors such as sub-span oscillation. The presented reduced-scale modelling method and test results provide a foundation for further understanding of torsional instability and control of bundle conductors rolling.

A new calculation method of critical wind speed based on three degrees of freedom (3-DOF) is proposed for galloping problem of iced transmission line. Based on the quasistatic theory, the aerodynamic load of iced transmission line is obtained, which considers the influence of transverse and torsional motion on the relative wind angle of attack. Finally, the equivalent galloping model of 3-DOF iced transmission line is established. At the initial angle of attack, the aerodynamic load is expanded by Taylor, and the unsymmetrical linear aerodynamic coefficient matrix is obtained. The Routh–Hurwitz criterion is used to judge the stability of iced transmission line system, and then the critical wind speed is calculated. The in-plane and out-plane frequencies corresponding to the first-order mode of the transmission line are solved by the analytical method and numerical simulation method. The results obtained by the two methods are compared and verified. The influence of dimensionless transmission line parameterλon the in-plane and out-of-plane frequencies is discussed. The aerodynamic coefficients of the iced transmission line are measured by wind tunnel test and the aerodynamic characteristics are analyzed. According to the theoretical formula, the critical wind speed is calculated by MATLAB. The critical wind speed determined in this paper is compared with the critical wind speed determined by Den Hartog and Nigol theory. The influences of torsional vibration frequency, ice thickness, and ice shape on critical wind speed are analyzed. The research results of this paper have important theoretical significance for the stability judgment of iced transmission lines.

Finite element model of a typical ultra-high voltage direct current transmission line section, in which buckling collapse of the tension plate took place during operation, is established. In the finite element model, the tension plate and the connected hardware fittings are discretized with 3D solid elements and the sub-conductors, spacers, clamps and insulator strings with spatial beam elements. Dynamic responses of the line after ice shedding are numerically simulated and the maximum loads on the tension plate in the cases with different ice thicknesses and ice-shedding are obtained. Buckling behaviors of the tension plate are analyzed and the conditions leading to buckling collapse are discussed. Finally, the topology optimization of the tension plate is performed and two optimized schemes of the tension plate are proposed based on the optimization result and manufacture cost. Efficiency analysis demonstrates that the buckling loads of the optimized tension plates increase more than 20% nearly without increasing weight.

Perturbation method is a commonly used method to solve galloping equation of iced transmission lines, but few scholars have studied the influences of perturbation method on the accuracy of approximate solutions of the galloping equation. In order to analyze the accuracy of approximate solutions obtained by perturbation method for galloping equation of iced transmission lines, the partial differential galloping equation of iced transmission lines with quadratic and cubic nonlinear terms is obtained firstly. Then, the partial differential galloping equation is transformed into ordinary differential galloping equation by Galerkin method. Finally, the approximate solutions of the partial differential galloping equation are obtained by averaging method and first-order, second-order, third-order, and fourth-order multiple scales methods, and the results obtained by these methods are compared systematically. By comparing the numerical solutions and the approximate solutions obtained by averaging method, it can be found that, with the increasing in wind velocity and Young’s modulus of iced transmission lines, the nonlinearity of the system would strengthen and the drift of the vibration center of the system would also increase. The larger the drift is, the greater the error between the approximate solutions obtained by averaging method and the numerical solutions will be. And when the wind velocity reaches 32 m/s, the error would arrive at 17.321%. By comparing the numerical solutions and the approximate solutions obtained by the first-order, the second-order, the third-order, and the fourth-order multiple scales methods, it can be concluded that the first-order multiple scales method is less complex computationally. The accuracy of approximate solutions obtained by the fourth-order multiple scales method is better than that obtained by the first-order, the second-order, and the third-order multiple scales methods, and the error between the approximate solutions obtained by the fourth-order multiple scales method and the numerical solutions is less than 0.639%. The conclusions obtained in this paper would be helpful to the solutions of galloping equation of iced transmission lines and could also give some references to practical engineering.