Study On Nonlinear Galloping Theory For Long Conductors Of Power Transmission Lines

Galloping of power transmission lines can lead to severe disruptions in the electrical power supply. But because of the complexity of the galloping, its mechanism hasn't been understood clearly. So it's difficult to prevent and cure the galloping in practice. In order to guarantee the safety and reliability of electrical network, the galloping phenomenon of power transmission lines must be studied seriously.In this dissertation, the studies on nonlinear galloping theory for long conductors of power transmission lines are described. With the objective to develop a complete set of methods for galloping research, this project consists of a few tasks: static analysis of power transmission lines, galloping finite element modeling, development of galloping oscillator model and studies on global behaviors of nonlinear galloping.The static analysis includes tow aspect: form-finding analysis and static response analysis. In this dissertation, the method for form-finding of cables is applied to compute the initial equilibrium state of power transmission lines. The exact element method is developed and expanded, so it can be used for analyzing more complex loading cases and for the form-finding analysis of multi-span power transmission lines. After determining the initial equilibrium state and tension of power transmission lines, a nonlinear finite element method is applied to compute the static response of power transmission lines under aerodynamic forces. The general expression of Lagrange nonlinear cable element is established firstly by using virtual work principle. And then occording to the properties of the iced cable, a 5-node cable element having rotational degree of freedom is derived. The difference between the exact element method and the nonlinear finite element method is also discussed in this thesis. The correctness and reliability of the element and the arithmetic proposed in this chapter are approved by several examples.The displacement relationship of a three-degree-of-freedom model for galloping is derived and the general method for establishing galloping finite element model is provided. For the nonlinear galloping equations, the limitations of the traditional time integral scheme are given first. An improved time integral scheme is then introduced with fine details. The stability of the improved scheme is also studied and the stability condition is given. Except for the improved scheme, the Runge-Kutta method is also introduced to solve the galloping equations, and the detailed steps are given. The mode superposition method is used to overcome the difficulty brought by geometric nonlinear. The finite element model of an actual power transmission line is established. Using this model, the free oscillation analysis and galloping analysis of the power transmission line are performed. The results match well with the experimental findings.Single-degree-of-freedom and two-degree-of-freedom oscillator models are studied. In this study, dimensionless form is used to express each oscillator model. The single-degree-of-freedom oscillator model is studied by using the exact expression of relative wind velocity. The analytical expressions of the critical wind velocity and the galloping amplitude are given and the stability of the periodic solution is also studied. By comparison the model proposed in this dissertation with other tow simplified models, conclusions can be drawn that the system damp can't be ignored, but the relative wind velocity can be expressed by approximate formula. A new two-degree-of-freedom oscillator model that couples with the lateral and plunge vibrations is established. By analyzing this model, conclusions can be drawn that lateral vibration plays an important role in galloping and the constant items of aerodynamic coefficients not only affect the initial equilibrium of power transmission lines but also affect galloping. The non-eccentricity and eccentricity two-degree-of-freedom oscillator models are studied respectively and their analytical solutions are given. The local behaviors of nonlinear galloping equations are also studied. Moreover, a numerical solution is used for verifying the analytical solution.By comparing the galloping finite element model and the galloping oscillator model, the advantages, the disadvantages and the scope of application for each model are found.This study on the nonlinear global behavior of galloping equations is carried out for the first time. The single-degree-of-freedom and non-eccentricity two-degree-of-freedom oscillator models are studied respectively by using cell mapping method and the Poincare cell mapping method. The global stability of the periodic solution of single-degree-of-freedom oscillator model is verified. The stable periodic solutions of non-eccentricity oscillator model are recognized and their domains of attraction in a determined state space are presented. Moreover, a strange attractor of this model is given clearly. The results do not only deepen the understanding of galloping mechanism, but also provide a theoretical basis for preventing and curing power transmission line galloping.