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Major disasters and losses would be caused by the galloping of transmission lines. The basis for studying the galloping mechanism of transmission lines is to analyze the aerodynamic characteristics of iced conductors. The wind tunnel test is a traditional way to obtain the aerodynamic coefficients of an iced transmission line under wind load. Due to the high cost and long duration of wind tunnel tests, an experimental method based on machine learning to predict aerodynamic coefficients is proposed. Here, the steady and unsteady aerodynamic coefficients of an iced conductor under different parameters were obtained by wind tunnel test, and then the aerodynamic coefficients of the iced conductor under different parameters were predicted by machine learning. The aerodynamic coefficients of each iced conductor varied with the angle of wind attack by the wind tunnel test. The Den Hartog and Nigol coefficients determined based on the aerodynamic coefficients obtained by machine learning and wind tunnel test are in agreement. The results show the feasibility of the machine learning prediction method. [ABSTRACT FROM AUTHOR]

Aiming at the problem of nonlinear vibration of current-carrying iced conductors, the aerodynamic forces are introduced into the previous vibration equation of current-carrying conductors that only considered Ampere's forces. At the same time, on this basis, a forced excitation load is further introduced to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors, and a new current-carrying iced conductors system under the combined action of Ampere's forces, forced excitation, and aerodynamic forces has been established, and the improved theoretical modeling of current-carrying iced transmission lines made the model more in line with practical engineering. Firstly, the model of current-carrying iced conductors was established, and then the vibration equation of the model was derived. And the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method. The amplitude-frequency response functions of the nonlinear forced primary resonances and super-harmonic and subharmonic resonances of the system are derived by using the multiscale method. Through numerical calculation, the influence of current-carrying, spacing, wind velocity, tension, and excitation amplitude on the response amplitude when the primary resonance of the system appears is analyzed, and the difference between the two working conditions (considering the aerodynamic forces and without considering aerodynamic forces) is compared. The influence of the variation of current-carrying i on the response amplitude of super-harmonic and subharmonic resonances and the stability of the steady-state solution of forced primary resonance was analyzed. The results show that the response amplitude and the nonlinearilty of system under the action of aerodynamic forces are smaller and weaker than without the action of aerodynamic forces; the variation of line parameters has a certain influence on the response amplitude of conductor and the nonlinearity of system; the response amplitudes of the primary resonance, super-harmonic resonance, and subharmonic resonance increase with the increase in the excitation amplitudes, and the resonance peak is offset towards the negative value of the tuning parameter σ, showing the characteristics of soft spring, and the response amplitudes are accompanied by complex nonlinear dynamic behaviors such as the multivalue and jump phenomenon. The change of current-carrying i has an obvious effect on the nonlinearity of the system. The nonlinear and response amplitudes of the system are also enhanced with the increase in wind velocity. The stability of the system is judged when the primary resonance occurs, and it is found that the response amplitude shows synchronization and the out-of-step phenomenon with the change of tuning parameters. The research results obtained in this paper would help to further improve the theoretical modeling about current-carrying iced lines, and the research of line parameters can give a certain reference value to practical engineering, and it will have a positive effect on the safe operation of high-voltage transmission lines. [ABSTRACT FROM AUTHOR]

Perturbation method is a commonly used method to solve galloping equation of iced transmission lines, but few scholars have studied the influences of perturbation method on the accuracy of approximate solutions of the galloping equation. In order to analyze the accuracy of approximate solutions obtained by perturbation method for galloping equation of iced transmission lines, the partial differential galloping equation of iced transmission lines with quadratic and cubic nonlinear terms is obtained firstly. Then, the partial differential galloping equation is transformed into ordinary differential galloping equation by Galerkin method. Finally, the approximate solutions of the partial differential galloping equation are obtained by averaging method and first-order, second-order, third-order, and fourth-order multiple scales methods, and the results obtained by these methods are compared systematically. By comparing the numerical solutions and the approximate solutions obtained by averaging method, it can be found that, with the increasing in wind velocity and Young's modulus of iced transmission lines, the nonlinearity of the system would strengthen and the drift of the vibration center of the system would also increase. The larger the drift is, the greater the error between the approximate solutions obtained by averaging method and the numerical solutions will be. And when the wind velocity reaches 32 m/s, the error would arrive at 17.321%. By comparing the numerical solutions and the approximate solutions obtained by the first-order, the second-order, the third-order, and the fourth-order multiple scales methods, it can be concluded that the first-order multiple scales method is less complex computationally. The accuracy of approximate solutions obtained by the fourth-order multiple scales method is better than that obtained by the first-order, the second-order, and the third-order multiple scales methods, and the error between the approximate solutions obtained by the fourth-order multiple scales method and the numerical solutions is less than 0.639%. The conclusions obtained in this paper would be helpful to the solutions of galloping equation of iced transmission lines and could also give some references to practical engineering. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines. [ABSTRACT FROM AUTHOR]

A new calculation method of critical wind speed based on three degrees of freedom (3-DOF) is proposed for galloping problem of iced transmission line. Based on the quasistatic theory, the aerodynamic load of iced transmission line is obtained, which considers the influence of transverse and torsional motion on the relative wind angle of attack. Finally, the equivalent galloping model of 3-DOF iced transmission line is established. At the initial angle of attack, the aerodynamic load is expanded by Taylor, and the unsymmetrical linear aerodynamic coefficient matrix is obtained. The Routh–Hurwitz criterion is used to judge the stability of iced transmission line system, and then the critical wind speed is calculated. The in-plane and out-plane frequencies corresponding to the first-order mode of the transmission line are solved by the analytical method and numerical simulation method. The results obtained by the two methods are compared and verified. The influence of dimensionless transmission line parameter λ on the in-plane and out-of-plane frequencies is discussed. The aerodynamic coefficients of the iced transmission line are measured by wind tunnel test and the aerodynamic characteristics are analyzed. According to the theoretical formula, the critical wind speed is calculated by MATLAB. The critical wind speed determined in this paper is compared with the critical wind speed determined by Den Hartog and Nigol theory. The influences of torsional vibration frequency, ice thickness, and ice shape on critical wind speed are analyzed. The research results of this paper have important theoretical significance for the stability judgment of iced transmission lines. [ABSTRACT FROM AUTHOR]

Two-dimensional air flows around a quad bundle conductor covered with crescent-shaped ice of different thickness are numerically simulated, based on which the aerodynamic coefficients of each iced subconductor vary with the angle of wind attack are determined. The numerically obtained aerodynamic coefficients are compared with those by the wind tunnel test carried out previously. It is seen that the laws of the aerodynamic coefficients against the angle of attack determined by the two methods are similar, and the corresponding Den Hartog coefficients and Nigol coefficients agree well. Moreover, the galloping frequencies, vibration modes, and galloping traces of a typical iced-quad bundle conductor line obtained by the finite-element method based on the aerodynamic coefficients, respectively, determined by the two methods are similar even though their vibration amplitudes are somewhat different. It is demonstrated that the aerodynamic coefficients determined by numerical simulation can be used to investigate galloping behavior and anti-galloping techniques of overhead transmission lines. [ABSTRACT FROM AUTHOR]

Highlights • A new model for free vibration of multi-span transmission lines. • The effect of the motion along the axial direction of a transmission line and insulator string swing is considered. • Asymmetrical hybrid mode of multi-span is obtained. • The natural frequency is dependent on span number, insulator string length, and other parameters. • The formula of frequencies and modes is simple and the most efficient. Abstract A theoretical dynamic model of two-span and three-span transmission lines with multiple insulator strings is presented. Unlike existing single-span models, the model has a considerable potential that the effect of the motion along the axial direction of transmission lines and insulator string swing on adjacent spans is considered. The equations of in-plane and out-plane motion of multi-span are set up by using a combination of moment equilibrium of insulator string swing and free vibration equation of each span, in which the longitudinal component of inertia is considered due to a motion of the support. Accurate and approximate solutions for the equations governing multi-span vibrations under self-weight are achieved with the continuity conditions of the displacement and force. Based on the theoretical formulas, a rich variety of symmetrical and asymmetrical modal features of adjacent spans interaction occurring in various parameters of transmission lines are discussed. The results show that the natural frequencies of corresponding in-plane and out-plane modes are heavily dependent on span number, the ratio of span lengths, Irvine's parameter λ and insulator string length. Furthermore, the finite element results based on the ABAQUS are reported, which establish the validity of the theory. [ABSTRACT FROM AUTHOR]