Investigation on Influences of  Two Discrete Methods on Galloping Characteristics of Iced Quad Bundle Conductors

Abstract

The partial differential galloping equation of iced quad conductors can be transformed into an ordinary differential galloping equation by two discrete methods: one is a direct discrete method and the other is an indirect discrete method. The two discrete methods are reasonable and effective and have their own advantages and disadvantages, but whether the two different discrete methods would cause the differences in galloping characteristics of the iced quad conductor has not been studied. Based on this concept, this paper studies this problem systematically. Firstly, based on the variational principle for Hamiltonian, the partial differential galloping equation with 3DOFs of the iced quad bundle conductor is derived and then two discrete methods are used to transform the partial differential galloping equation into an ordinary differential galloping equation. One is to use a direct method to transform partial differential galloping equation into an ordinary differential galloping equation, while the other is to use an indirect method to transform partial differential galloping equation into an ordinary differential galloping equation. Secondly, based on the wind tunnel test, the three-component aerodynamic coefficients of each subconductor of the iced quad conductor are obtained, and the equivalent aerodynamic coefficients at the central axis of the quad bundle conductor are obtained by using a reasonable method. Then, the aerodynamic coefficients are fitted by Taylor rules and the aerodynamic coefficients of wind angle of attack which is 55° are used in the analysis of galloping characteristics of the iced quad conductor. Finally, based on the numerical method, the displacement response of the two discrete methods is obtained. By comparing the differences of the displacement response obtained by the two discrete methods, it is found that the two discrete methods have certain influences on the phase, frequency, and amplitude of the iced quad bundle conductor. By comparing the calculation process of these two discrete methods, it can be obtained that the calculation process of the direct discrete method is more complex and the calculation process of the indirect discrete method is simpler. By comparing the calculation results of these two discrete methods, the amplitude obtained by the indirect discrete method is bigger than that obtained by the direct discrete method, especially the amplitude in the torsional direction. The research conclusion of this paper can offer some guidance to civil and electric engineering.

Investigation on the Accuracy of Approximate Solutions Obtained by Perturbation Method for Galloping Equation of Iced Transmission Lines

“…Method. In order to analyze the accuracy of approximate solutions obtained by multiple scales method of the solution form of first-order small parameter, quoting the solution form of small parameter in [16,[37][38][39][40], (11) can be written as…”

“…Under the condition of different wind velocity, the accuracy of q (ε 0 ), q (ε 1 ), q (ε 2 ), and q (ε 3 ) is studied in Table 5. q (ε 0 ), q (ε 1 ), q (ε 2 ), and q (ε 3 ) represent zero-order equation (34), first-order equation (35), second-order equation (36), and third-order equation (37), and all of them are the approximate analytical solutions of multiple scales method. And the wind velocity U � 4-32 m/s is shown in Table 5.…”

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

“…According to [20], it can be obtained that the vibration of the cable would mainly occur in the y-axis direction (inplane), so this paper would only consider the vibration of the cable in the y-axis direction (in-plane). Based on the variational principle for Hamiltonian, the following results can be obtained:…”

“…According to [20], the vibration characteristics of the cable are mainly affected by the first-order mode shape. erefore, the first-order mode truncation method is used here, and the influences of higherorder mode shape on the vibration behaviors of the cable would be considered in subsequent research.…”

“…For investigating the vibration characteristics of arbitrary vibration models, such as cables [15,16], bridges [17,18], iced conductors [19,20], and plates [21][22][23][24], the partial differential vibration equation of those vibration models should be established firstly. As known for us, for the cable-bridge coupling model, the dynamic tension of cables is an important parameter to study the vibration characteristics of the model.…”