Galloping Computation And Analysis For Long Multi-span Bundle Conductors Of Power Transmission Lines

Galloping of an overhead, iced transmission line is characterized by high amplitude, low frequency, self-excited oscillations produced by a steady side wind. The inability to control galloping can lead to severe disruptions in the electrical power supply. Further, galloping can cause wear and fatigue damage to conductors, insulator strings, support hardware and tower components. Galloping has been documented since the 1930s and, despite extensive analytical and experimental investigations has not been resolved satisfactorily. One reason for this shortcoming is that a comprehensive but computationally efficient method is not available. The basic approach to the galloping analysis is to compute the static configuration, linear free vibration modes of the conductor structure, transfer the problem to one in a lower dimensional mode space, add the nonlinear aerodynamic force in, and then analyze and compute the galloping as the last step. Nonlinear geometric constrains and nonlinear gravitational moments are present as a result of the spacers and galloping control devices. In this paper, basic dynamic equations for bundle transmission lines in a global coordinate system are developed on the basis of direct equilibrium method and virtual work principle, respectively. The nonlinear dynamics of the spacers and galloping control devices are investigated. A galloping model for dynamic configurations of bundle transmission lines is obtained. The present results lay down the foundation for further study of the problem. The static profile and tension distribution analysis of conductor of overhead transmission lines are important for the line design, dynamic behavior determination and galloping prediction. It is difficult to compute the static configuration and tension for a long multi-span transmission line with galloping control devices, because the tension distributions are not continuous and transferred between the spans in this case. There are no effective static analysis methods for such conductor structures. In consideration of the suspended weights, a set of governing differential equations for the conductor static analysis is developed with the bending stiffness effects to be neglected. The analytical solutions of the equations are obtained and the corresponding computational schemes are suggested. The catenary configuration and tension of the conductor can be calculated by using these formuals and schemes. A new type of element which is suitable for solving the static response and modes of the galloping long multi-span bundle conductor structures is presented. The element is composed of all sub-conductor segments between two spacers. Based on the linearized governing differential equations of the conductors, the mass matrix and stiffness matrix of the element in consideration of the constrained relations imposed on the conductors by spacers are derived. The dynamic characteristics of the galloping control devices can be directly added to the element. The modes for a realistic power line structure are computed by using the element formula and FEM procedures, where seven cases of different galloping control device allocations are considered. The analysis of galloping is complicated greatly by the non-linear, geometry dependent, time varying aerodynamic loads and the resulting high amplitudes of vibration which may cause interactions between vibration modes and also between adjacent spans and their support hardware. Aerodynamic forces and moments depend non-linearly upon the geometry of the iced conductor as well as the relative angle of the wind's attack to the conductor. One kind of piecewise polynomial interpolation method is adopted, instead of the curve fitting method for improving precision. Efficient perturbation schemes are presented to compute the galloping vibrations of a multi-span, overhead transmission line. Systematic procedures are formulated to assess the stability of conductor's wind and ice loaded static profile by employing a multiple-degree-of-freedom finite element model. The averaging method of Krylov-Bogoliubov is employed. The methods are applied successfully to simulate field galloping records and their usefulness and advantages are demonstrated through illustrative examples.