Investigation On Galloping Characteristics Of Iced Transmission Lines And Influencing Factors Of Galloping Characteristics

With the rapid development of extra-high voltage(EHV)and ultra-high voltage(UHV)transmission lines,China’s power grid has become the most complex and largest power grid in the world.Coupled with the frequent occurrence of bad-weather caused by changeful climate in recent years,the harm of galloping to the safe operation of transmission lines is becoming more and more serious.Large-scale galloping of iced transmission lines would cause frequent tripping,worn hardware,power failure,broken insulator string and damaged tower arm.Therefore,it is a subject with theoretical significance and engineering value to establish galloping model of iced transmission lines and analyze its galloping characteristics.(1)The aerodynamic coefficients of iced quad bundle conductor and single conductor were obtained under four different conditions though wind tunnel test.The equivalent aerodynamic coefficients of the central axis of quad bundle conductor were obtained by equivalent method.And the equivalent coefficients were compared with those of single conductor under the same conditions.Based on Den Hartog’s galloping mechanism and Nigol’s torsional mechanism,the stable and unstable regions of equivalent aerodynamic coefficients and aerodynamic coefficients of single conductor are analyzed,and the stability of iced quad bundle conductor and single conductor is also analyzed.(2)The galloping of iced transmission lines belongs to self-excitation vibration,and it is also a typical geometric nonlinear vibration.Aiming at the galloping of iced transmission lines,the effects of bending stiffness and two discrete methods on the galloping characteristics of iced transmission lines were investigated.Based on variational principle for Hamiltonian,the partial differential equations(PDEs)of iced transmission lines considering the influences of bending stiffness are deduced,and the PDEs are transformed into ordinary differential equations(ODEs)by Galerkin method.Two different discrete methods are used to convert PDEs into ODEs.One is to average the dynamic tension over the span length,then Galerkin method is used.The other is that Galerkin method is used to convert the PDEs into ODEs directly.The results show that for the iced transmission lines with 300 m span length,the influences of bending stiffness on phase and amplitude of iced transmission lines are only 0.1%,but the influences would increase with the increasing of the diameter of iced transmission lines.It is conclusion that when studying the galloping characteristics of large-diameter iced transmission lines,the influences of bending stiffness on the galloping characteristics of iced transmission lines should be considered.The results of the numerical method show that the two discrete methods have certain influences on the galloping frequency,phase and amplitude of iced transmission lines.(3)The multiscale method is used to study the galloping characteristics of iced transmission lines,and then an average method with two degree of freedom(DOFs)is proposed.The results of these two methods are compared to prove the rationality of the average method with two DOFs.The parameter analysis shows that for the iced transmission lines with 300 m span length,the two discrete methods have significant influences on the nonlinear coefficients and coupling coefficients of the two DOFs ODEs of iced transmission lines.The results of multiscale method and average method show that the multiscale method has high accuracy but complex calculation;the average method is simple,but it can only get the first-order approximate solution,and the out-of-plane vibration displacement history curve can’t be obtained for solving the in-plane and out-of-plane coupling galloping of the iced transmission lines.The results of the average method and the multiscale method both show that the two discrete methods have certain influences on the galloping frequency,phase and amplitude of iced transmission lines,especially on the frequency.The rationality of the conclusions obtained by numerical method is verified.(4)The galloping of iced transmission lines is the eccentric coupling vibration of conductor after iced.Based on variational principle for Hamiltonian,the galloping equations with three DOFs of iced transmission lines under eccentric coupling effect are derived.The influences of two discrete methods proposed in this paper on galloping characteristics of iced quad bundle conductor under eccentric coupling effect are studied.An equivalent method is proposed and used to fit the equivalent aerodynamic coefficients obtained from wind tunnel tests.The angle of attack of 55° is selected to analyze the galloping characteristics of iced quad bundle conductor.Based on the numerical method,the displacement response curves of the two discrete methods are obtained.By comparing the differences between the two displacement response curves,it is found that different discrete methods have certain effects on the phase,frequency and amplitude of the system.(5)Aiming to neglect the influences of temperature effect on galloping characteristics of iced transmission lines,the galloping equations considering temperature effect are derived.Based on catenary method and thermal stress theory,the partial differential galloping equations of iced transmission lines are derived,then the PDEs are transformed into ODEs by Galerkin method.The aerodynamic loads model was established and the aerodynamic loads was introduced into the galloping equations.Then the displacement response of iced transmission lines is obtained by the multiscale method.Finally,parameter analysis and numerical example analysis are carried out.The results show that the temperature effect has a significant effect on the in-plane and out-of-plane frequency of iced transmission lines,and also has certain influences on the galloping amplitude of iced transmission lines.It can be seen that the influences of temperature effect on galloping characteristics of iced transmission lines must be considered when studying the influences of galloping characteristics of iced transmission lines.The research results of this paper are conducive to the improvement of theoretical modeling,and can also provide certain reference for practical engineering.(6)Based on the variational principle for Hamiltonian and Galerkin method,the galloping equations of single span iced transmission lines are obtained.The galloping equations of multi-span iced transmission lines are established by taking the balance equation of insulator string as the bridge.Finally,the fourth-order Runge Kutta is used to solve the galloping equations.The numerical example shows that the displacement response of any span conductor is different due to the interaction between the multi-span iced transmission lines and the insulator string,and the displacement response of any span conductor is also can be different due to the different direction of rotation of the insulator string.Compared with the traditional single span iced transmission lines model,the multi-span iced transmission lines model established in this paper is more in line with the actual conditions,and can provide an important reference value for the actual project.(7)The model of iced transmission lines with axial linear speed feedback control are established,and the corresponding galloping equations of the model are derived.The galloping equations are dimensionless,and the dimensionless galloping equations are obtained and solved analytically.The amplitude-frequency response equation and the first-order analytical solution are obtained.Finally,the influences of key parameters such as time-delay value and control coefficient on the main resonance are analyzed.The results show that the galloping of transmission lines can be effectively restrained by selecting appropriate control coefficient and time-delay value,and the suppression effect is more obvious when the aerodynamic load is not considered.When the aerodynamic load is considered,the amplitude-frequency response curve may change from single value curve to multi value curve under different time-delay values.When the aerodynamic load is not considered,the time-delay value mainly affects the galloping amplitude.Wind tunnel tests of iced transmission lines under various conditions are carried out in this paper,which can provide complete test data for the analysis of the galloping characteristics of iced transmission lines.The influences of two discrete methods,bending stiffness,temperature effect,time-delay effect and the effect between adjacent transmission lines on the galloping characteristics of iced transmission lines were investigated systematically.It also improves the galloping model and the galloping equation of ice transmission lines,and has great practical significance for the practical engineering.