Modelling And Multi-Scale Method Of Galloping Of Iced Transmission Line Considering Boundary Condition

After ice coated on the transmission lines, the lines would do self-excited, low frequency and large amplitude vibration under the nonlinear aerodynamics generated by the natural wind power, a phenomenon known as Conductor Galloping. Due to the long duration and up to several meters or even ten meters amplitude, galloping will cause great damage to the transmission lines, in severe cases can lead to power supply system paralyzed in large areas.This paper briefly illustrates the galloping mechanism of the transmission lines, and then established the three degrees of freedom galloping model based on the curved beam theory and considering complete boundary condition and eccentricity of cross-section. Our model is developed on the work of Zhimiao Yan about the three degrees of freedom galloping model, further considering the influence of the adjacent spans and insulator string and adding horizontal stiffness coefficient and quality coefficient to the model. In order to verify the superiority of the model in this thesis, four different models have been established based on the theory of cable structure: single degree of freedom galloping model which considering the vertical component only; two degrees of freedom galloping model which taking account of vertical and horizontal component at the same time; three degrees of freedom galloping model which taking into account the boundary conditions; and three degrees of freedom galloping model based on curved beam theory. Using Mathematica to programme on the above models and using the test data of classic TYPE-D iced cross-section to do the time-domain analysis, then compare the obtained results with the time-distance graph produced by the model in this study. The results showed that the three degrees of freedom galloping model which is based on curved beam theory in this paper can achieve a high accuracy, the errors of amplitude in vertical direction and torsional displacement were only 1.3% and 1.9%, respectively. That means this model can be used for practical engineering analysis. Subsequently, in order to understand the occurrence rule of transmission lines’ galloping, using a set of test data which was obtained from China Aerodynamics and Developing Center to further analyze the model established in this paper. Compared with both ends fixed model, the vertical and lateral displacement amplitude have reduced and the torsional displacement amplitude has increased after considering the impacts of adjacent straddle stiffness and insulator string boundary conditions. The galloping amplitude in vertical, horizontal and torsional directions increased from 0 to the biggest then deceased to 0 along with wind speed. The results indicated that with the spring stiffness increases, the vertical and lateral galloping amplitude and critical wind speed increase, the torsional amplitude decreases; with the increase of insulator’s quality, the vertical amplitude and critical wind speed also increase, but the lateral and torsional galloping amplitude decrease. Finally, this study further analyzed icing transmission line galloping model in a multi-scale method after considering the boundary conditions based on curved beam theory, which only considered vertical and horizontal directions and simplified the model into a two degrees of freedom galloping model. Then established a 1:1 and a 2:1 internal resonance amplitude equation and followed by a simplified version in the same multi-scale method. And using crescent-shaped cross-section ratio to analyze galloping performance under the situation of considering section eccentricity and not considering that, respectively. It turned out that when didn’t consider the section eccentricity, the galloping amplitude increases together with wind speed and the eigenvalues of Jacobian array all were negative in the galloping range under 1:1 and 2:1 internal resonance, and the galloping was in a steady state. However, when considered section eccentricity, the galloping decreased along with increasing wind speed, and there were some positive eigenvalues in Jacobian array and the galloping was not always in a steady state under 1:1 internal resonance, the galloping was still in a steady state under 2:1 internal resonance because of all negative eigenvalues in the Jacobian array. Next, in order to verify the correctness of the galloping rule obtained by numerical analysis method, further analysis has been conducted on the impacts of elastic boundary on the galloping rule under 1:1 and 2:1 internal resonance. The results indicated that no matter considered section eccentricity or not, after considering boundary stiffness, the vertical and horizontal galloping amplitude have decreased compared to fixed boundary condition, so did the up critical wind speed. After considering the impact of border insulator quality, the former items all increased compared to under the fixed boundary conditions. These conclusions were coincide with the previous results using numerical analysis method. Finally, this study calculated the vertical and horizontal galloping amplitude according to time integral of the simplified amplitude equations under 1:1 and 2:1 internal resonance and two degrees of freedom equation, then verified the accuracy of the multi-scale method.