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In order to study the influence of dynamic wind on the nonlinear galloping characteristics of iced transmission lines, an external excitation load is added to the governing equation of iced transmission lines under the condition of stable wind, and a new forced self-excited system has been established. The frequency-amplitude relationship of the forced self-excited system under weak excitation and strong excitation is obtained by using the multiple-scale method. The principal resonances and superharmonic and subharmonic resonances of the forced self-excited system have also been analyzed. The results show that, in the forced self-excited system under strong excitation, when the excitation frequency is close to the integral and fractional times of the natural frequency, it is easier to produce 1/2-order subharmonic resonance, 2-order superharmonic resonance, and 3-order superharmonic resonance. In addition, numerical techniques provide bifurcation diagrams of different control parameters, which are able to highlight the effects of the simultaneous presence of the sources of excitation. When the control parameters (wind velocity, excitation amplitude, tuning parameter, tension, and Young’s modulus) change, the response amplitudes of the principal resonance and harmonic resonance will have multivalues, jump phenomenon, and hardening behavior. The control parameters can be used as a reference for engineering design. More importantly, as a combination of the Duffing equation and the Rayleigh equation, the forced self-excited system also has high theoretical research value.

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A numerical method to simulate air flow around a bundle conductor line by means of the FLUENT software is presented and verified by a wind tunnel test for aerodynamic characteristics of a twin bundle conductor line. The lift and drag coefficients of the leeward sub-conductor of a twin bundle conductor varying with its relative position in the wake zone to the windward one under different wind velocities are numerically determined by the presented method. A user-defined subroutine of ABAQUS software is developed to apply the aerodynamic loads on each sub-conductor and the electromagnetic force between sub-conductors. The numerical simulation method for wake-induced oscillation of a bundle conductor line is proposed. By means of the numerical method, wake-induced oscillation processes of twin bundle conductor transmission lines under different parameters, including current intensity, spacer layout, span length and wind velocity, are numerically simulated. Moreover, the effects of those parameters on the oscillation characteristics of the lines, such as vibration mode, frequency, amplitude and motion trace, are discussed. The results obtained provide a fundamental basis for the understanding of wake-induced oscillation behaviour of twin bundle conductor transmission lines and the development of control technique for wake-induced oscillation.

The partial differential galloping equation of iced quad conductors can be transformed into an ordinary differential galloping equation by two discrete methods: one is a direct discrete method and the other is an indirect discrete method. The two discrete methods are reasonable and effective and have their own advantages and disadvantages, but whether the two different discrete methods would cause the differences in galloping characteristics of the iced quad conductor has not been studied. Based on this concept, this paper studies this problem systematically. Firstly, based on the variational principle for Hamiltonian, the partial differential galloping equation with 3DOFs of the iced quad bundle conductor is derived and then two discrete methods are used to transform the partial differential galloping equation into an ordinary differential galloping equation. One is to use a direct method to transform partial differential galloping equation into an ordinary differential galloping equation, while the other is to use an indirect method to transform partial differential galloping equation into an ordinary differential galloping equation. Secondly, based on the wind tunnel test, the three-component aerodynamic coefficients of each subconductor of the iced quad conductor are obtained, and the equivalent aerodynamic coefficients at the central axis of the quad bundle conductor are obtained by using a reasonable method. Then, the aerodynamic coefficients are fitted by Taylor rules and the aerodynamic coefficients of wind angle of attack which is 55° are used in the analysis of galloping characteristics of the iced quad conductor. Finally, based on the numerical method, the displacement response of the two discrete methods is obtained. By comparing the differences of the displacement response obtained by the two discrete methods, it is found that the two discrete methods have certain influences on the phase, frequency, and amplitude of the iced quad bundle conductor. By comparing the calculation process of these two discrete methods, it can be obtained that the calculation process of the direct discrete method is more complex and the calculation process of the indirect discrete method is simpler. By comparing the calculation results of these two discrete methods, the amplitude obtained by the indirect discrete method is bigger than that obtained by the direct discrete method, especially the amplitude in the torsional direction. The research conclusion of this paper can offer some guidance to civil and electric engineering.