Search

Galloping of an iced transmission line subjected to a moderating airflow has been analysed in this study, and a new form of galloping is discovered both theoretically and experimentally. The partial differential equations of the iced transmission line are established based on the Hamilton theory. The Galerkin method is then applied on the continuous model, and a discrete model is derived along with its first two in-plane and torsional modes. A trapezoidal wind field model is built through the superposition of simple harmonic waves. The vibrational amplitude is generally observed to be more violent when the wind velocity decreases, except in the 2nd in-plane mode. Furthermore, the influence of the declining wind velocity rates on galloping is analysed using different postdecline wind velocities and the duration of the decline in wind velocities. Subsequently, an experiment has been carried out on a continuous model of an iced conductor in the wind tunnel dedicated for galloping. The first two in-plane modal profiles are observed, along with their response to the moderating airflow. Different declining rates of the wind velocity are also verified in the wind tunnel, which show good agreement with the results simulated by the mathematical model. The sudden increase in the galloping amplitude poses a significant threat to the transmission system, which also improves the damage mechanism associated with the galloping of a slender, a long structure with a noncircular cross-section.

This study aims to conduct galloping experiments using a full aeroelastic model to investigate the galloping controlling effects of interphase spacers with different kinds of arrangements on three-phase iced eight-bundled transmission lines. A low-speed wind tunnel was designed and built to assess the compact transmission lines on a single span. The similarity conditions between the aeroelastic model and the prototype were determined by the similarity theory and the proposed modification method. Four common arrangements of interphase spacers were considered. Compared with the situation without interphase spacers, the composite amplitude reduction rate of the first two modes and amplitude reduction rate varying with wind speed were evaluated. Then, the anti-galloping effects of interphase spacers were investigated and the controlling effects of interphase spacers on the interphase distance were analyzed. Besides, the corresponding arrangements under different conditions were determined. In addition, the galloping phenomena varying with wind speed were explored. The results suggested that their galloping phenomena were changed because of the effects of interphase spacers, and coupling effects of interphase spacers with different arrangements were different. This research could be used to estimate the positions of interphase spacers and offered a theoretical foundation for the anti-galloping design of transmission lines.

To study the anti-galloping effect of interphase spacers with different kinds of arrangements on an iced transmission line, wind tunnel experiments using a full aeroelastic model are carried out in this work. Using similarity theory, the similarity criteria between the aeroelastic model and the prototype have been deduced. A triangular arrangement of three phases is considered, and the arrangements of iced eight-bundled conductors with and without the spacers are divided into six cases. In the experiments, laser sensors at different positions along the span of each phase are used to measure the variation of dynamic displacements with wind speed. Furthermore, galloping characteristics, such as the responses, frequencies, vibration modes, amplitudes and distance between two phases, are obtained for different wind speeds and arrangements. The obtained results show that interphase spacers have a certain inhibitory effect on the first symmetric mode and the first anti-symmetric mode galloping, but not all of the arrangements have a positive effect. The regularity of the variation with wind speed of the anti-galloping effect with interphase spacers is summarized. The galloping amplitude curves indicate that the amplitude is likely to be larger when a modal transformation occurs, in contrast to the results obtained without interphase spacers. The motion of the phase C located close to the diffusion section is different from those of the other two phases. Moreover, due to interphase spacers, the distance between the two phases is increased. The obtained conclusions can be used to predict the positions of interphase spacers and provide a fundamental tool for anti-galloping of eight-bundled conductors.

The mooring cable system in plane motion can be modeled as two coupled partial differential equations, which can be numerical solved by finite difference method directly. The difference scheme is analyzed, and parameters selection for time-marching of displacement and velocity are deduced. The stability condition of the scheme is analyzed through Fourier series method, and parameters range which match stable scheme is given. Then, the parameters range is verified by a numerical example.

A dynamic model of a galloping transmission line able to describe for the coupling of its longitudinal, in-plane, out-of-plane and torsional vibrations is established. It also considers the effects of geometrical nonlinearity and aerodynamic nonlinearity. By the static configuration, the reduced model is obtained. Then, the equations of motion are obtained through the Galerkin method. It contains two in-plane, two out-of-plane and two torsional components. By numerical calculation, the maximum amplitudes at wind speeds are drawn and the galloping behavior of transmission line with thin ice accretions is analyzed. The obtained results show that the second galloping mode is more triggered. The double-mode galloping occurs in all motions, in which the maximum amplitude is bigger than in single-mode galloping. And the double-mode galloping presents the track of inclined ‘8’ in longitudinal direction.

Considering geometric and aerodynamic nonlinearities, in this work, a reduced dynamic model with crescent-shaped ice accretions has been established to describe the coupling effects of in-plane, out-of-plane and torsional motions on galloping with longitudinal motions limited to in-plane and out-of-plane directions for simplification. Based on natural frequencies and associated eigenfunctions obtained for each of the three directions, motion equations containing two in-plane, two out-of-plane and two torsional components are obtained by Galerkin spatial discretization. By using eigenvalue analysis and numerical methods, galloping stability is investigated at different wind speeds, sags, initial wind attack angles, in-plane damping ratios and torsional damping ratios. The effect laws of different parameters on galloping are analyzed and Hopf bifurcation points are obtained, which denote the upper and lower critical wind speeds where the upper critical wind speed is mainly related to in-plane motion. Then, multi-modal interaction mechanisms with different parameters are discussed in detail. A variety of internal resonance behaviors are observed in the system and their similarities and differences are analyzed. Meanwhile, galloping presents synchronous and limited-amplitude characteristics, the reasons of which are explained. These reveal the occurrence of different energy exchanges among various modes. This research provides a theoretical foundation for the design of transmission lines.

Sudden ice shedding from three-phase iced eight-bundled transmission lines with inverted-triangle arrangement was numerically and experimentally modeled. The staggered-arrangement groups and compact-arrangement groups (including triangular and V-shaped structures) of interphase spacers were considered to investigate the inhibition effects on ice shedding. Based on the similarity theory, a modification method was proposed to determine the natural frequency similarity between model and prototype. According to the dynamic tension, interphase distance, and jumping height, the reduction rate of dynamic tension, interphase-distance ratio, reduction rate of jumping height, and comprehensive reduction rates were determined for different arrangements of the interphase spacers. The inhibition effects of different factors on ice shedding were discussed for different lines, including the position and number of transmission lines for the ice-shedding phase and the various possible arrangements of interphase spacers. Deicing schemes for the different line configurations were proposed, and the best arrangement of interphase spacers was selected for each case. The present study provides a theoretical foundation for selecting an appropriate arrangement of interphase spacers during ice shedding.

In the present study, we investigated the changes in both anti-HAV lgG and anti-HBs lgG levels and compared the antibody seroconversion rates of different doses of combined hepatitis A and hepatitis B vaccine in children. Children who were vaccinated as infants with Hepatitis B vaccine were revaccinated at 5–15 y of age, then the antibody titers were monitored. Among 283 children, this study found that the anti-HAV seroconversion rates (defined as anti-HAV ≥ 1mIU/ml) after the first and the third dose were 79.9% and 100% respectively; these observed differences were statistically significant (P < 0.05); the corresponding geometric mean titers (GMTs) were 4.72 ± 2.63 mIU/ml and 13.46 ± 1.16 mIU/ml respectively. The anti-HBs seroconversion rates (defined as an anti-HBs ≥ 10 mIU/ml) were 82.3% and 99.0% respectively; these observed differences were statistically significant (P < 0.05); and the corresponding titers were 319.95 ± 5.16 mIU/ml and 418.59 ± 3.89 mIU/ml respectively. After the first booster dose, the difference in anti-HAV seroconversion rate was statistically significant in children aged 5–9 y and 10–15 y (P < 0.05), as was the difference of anti-HBs seroconversion, whereas after the third dose the difference was not statistically significant (P > 0.05). This study demonstrated that the immunization effects of booster vaccination with combined hepatitis A and hepatitis B vaccine is successful for children. A single booster dose is adequate for younger children, while three doses are needed for older children.

The changes in lgG antibody levels to hepatitis B surface antigen (HBsAg) and in antibody to HBsAg (anti-HBs) seroconversion rates due to different dosages of hepatitis B vaccine (HepB) were compared in 2106 children. Children who had been previously vaccinated as infants with HepB were revaccinated at 5–15 y of age, after which the antibody titers were determined. After the first booster dose, the anti-HBs seroconversion rate (defined as an anti-HBs ≥10 mIU/ml) with 10 μg of HepB (93.6%) was significantly greater than the rate with 5 µg of HepB (90.3%) (P < 0.05); the anti-HBs seroconversion rate in 10–15-y-old boys vaccinated with 10 μg of HepB (90.9%) was significantly greater than the rate with 5 µg of HepB (84.3%) (P < 0.05). The anti-HBs seroconversion rates after the third booster dose with 5 or 10 μg of HepB were greater than those after the first booster dose (99.6% and 99.7%, vs. 90.3% and 93.6%, P < 0.05); as was the corresponding GMTs (658 ± 4 mIU/ml and 2599 ± 3 mIU/ml, vs. 255 ± 11 mIU/ml and 877 ± 11 mIU/ml [P < 0.05]). The immunization effects of booster vaccination with 3 doses of HepB with 5 or 10 µg are effective; a single booster dose with 10 µg of HepB for 10–15-y-old boys and with 5 or 10 µg of HepB for 5–9 y old boys and for 5–15-y-old girls are effective in generating protective antibody against HBV; however, for anti-HBs-negative children after a single dose of booster, 3 doses are needed.