Objective:The galloping of transmission conductors critically affects the safety of transmission lines and often leads to accidents that jeopardize operations of the power grid. This phenomenon is attributed to the asymmetry ice covering on the conductor, resulting in low-frequency and large-scale self-excited vibrations under the action of wind. Clearly, this galloping that is involved with three-dimensional (3D) continuum systems coupled with in-plan, out-plane, and torsion deserves the research attention.
Methods: In this study, a nonlinear dynamic model of in-plane, out-plane, and torsion multi-order modal coupling of iced-conductors is proposed. The stability criterion of iced-conductor is determined by Lyapunov stability theory. The random wind field simulation method based on Hermite interpolation to improve Cholesky decomposition is used to further analyze galloping characteristics of the iced-conductor in each order mode in a random wind field. Then it is compared with the method used in a uniform wind field.
Results: A numerical example is analyzed in detail and second-order modes are expanded in each direction. In the uniform wind field, according to the system stability characteristic curve, when the wind speed (V) is less than the first critical wind speed (V_c1), the iced-conductor does not gallop in each mode. For V_c1V_c2, the in-plane second-order mode of the system begins to gallop. As coupling effects among the in-plane, out-plane, and torsion modes increases, out-plane and torsional modes also begin to gallop. The galloping of torsion mode is dominated by the first-order mode. In the random wind field, compared with the uniform wind field when V> V_c2, the two-order modes of the in-plane, out-plane and torsion direction of the iced-conductor both gallop, and the amplitude of the gallop increases. The amplitude of the out-plane first-order mode increases approximately 10 times, indicating that galloping characteristics of each mode of the iced-conductor have changed due to the influence of the fluctuating wind. According to the displacement response spectrum in the in-plane, out-plane and torsional direction, the modal vibration in the uniform wind field is dominated by the first-order mode, and its frequency approaches the in-plane first-order natural frequency. In addition, the first-order modal galloping amplitude in the plane becomes the largest, and modal-vibration frequencies of the iced-conductors in the random wind field change, prompting the first order frequency out-plane to increase. Furthermore, and the torsional first-order frequency component also appears in the torsion direction. In comparison with response amplitudes of each order mode, amplitudes of first order modes in uniform wind fields increase, and the galloping mode changes with the stronger modal coupling.
Conclusions: In this paper, based on the nonlinear dynamic model of multi-modal coupling of in-plane, out-plane and torsion directions of iced-conductor, two-order modes of each direction are respectively developed. In a stable wind field, the Lyapunov theory is applied to determining the stability criteria of the iced-conductor, and two critical wind speeds are obtained. Combined with the fourth-order varying step Runge-Kutta method, vibration responses of the iced-conductor in each mode under different wind speeds are calculated. It can be found that, as the wind speed increases, the stability property of some mode changes, inducing the galloping of the iced-conductors. Galloping characteristics of each mode under multi-mode coupling are analyzed in detail. The random wind field simulation method of Cholesky decomposition is improved by using Hermite interpolation. The computational efficiency is improved, and the random wind speed time history is obtained by simulations. The vibration response of the iced-conductor in the random wind field is further calculated, and compared with the vibration in the uniform wind field. The fluctuation is analyzed by the displacement-time history response and the displacement spectrum. Results show that the fluctuating wind exhibits a wide excitation frequency range and can excite low-order out-plane and torsional modes.