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CONTENTS
Volume 33, Number 4, October 2021
 


Abstract
Strong wind disasters, especially tornadoes with high damage scales, constantly cause huge damage to electric power grids (EPGs). In this paper, a concept is presented to quantify the connectivity reliability of EPGs under tornadoes. First, a tornado wind field is established using a modified Rankine vortex model, which is a representative 2D tornado wind field model. Second, fragility models of grid components, including transmission substations, transmission support structures, distribution poles, distribution conductors, and local circuits, are introduced. Third, a Monte Carlo simulation is presented to evaluate the connectivity reliability of EPGs under tornadoes. Finally, the connectivity reliability is verified under different scales and propagation angles of tornadoes by taking an actual EPG in China as a case study. Results show that the connectivity reliability directly correlates with the maximum wind speed and the propagation angle of the tornado, and the EPG experiences severe damage when the tornado exceeds the Enhanced Fujita 3 scale.

Key Words
connectivity reliability; electric power grid; failure progress; fragility model; Monte Carlo simulation; tornado

Address
Wei Liu:1)Department of Stuctural Engineering, Tongji University, Shanghai, 200091, China
2)State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200091, China

Binbin Zhou:Department of Stuctural Engineering, Tongji University, Shanghai, 200091, China

Qianxiang Wu:Department of Stuctural Engineering, Tongji University, Shanghai, 200091, China

Huiquan Miao:Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

Abstract
Generally, the fluctuating wind is simplified as several independent one-dimensional multivariate stationary Gaussian processes in simulating a natural wind field. The correlation in the lateral, longitudinal and vertical directions should all be considered in the simulation of longitudinal wind field for the large-span spatial structures. In fact, this type of structure has lots of simulation points. The calculation amount of wind field simulation by the harmonic superposition method depends on the scale of cross-spectral density matrix, which is directly related to the number of simulated points, leading to a low efficiency when generating the time-varying wind speed. This paper innovatively proposes a high-efficiency simulation method for the longitudinal wind field based on Taylor's hypothesis. Subsequently, the effectiveness of the proposed wind field method was verified by the numerical simulation. Finally, the dynamic responses of a transmission tower-line system under the wind loadings generated with the new method and traditional method are calculated and compared. The percentages difference of the mean and maximum axial force at the main tower members are less than 0.02% and 1%, respectively, indicating the effectiveness of the proposed time delay method. The results also show that the proposed simulation method of wind field can not only ensure the simulation accuracy, but also significantly improve the efficiency of wind speed generation, which is suitable for the wind load simulation of large-span spatial structures.

Key Words
coherence function; Taylor's hypothesis; time delay; transmission line; wind field simulation

Address
Xing Fu:1)State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China 2)Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education,
Chongqing University, Chongqing 400045, China

Xing-Heng Zhang: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China

Hong-Nan Li:State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China

Gang Li:State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China

Hui-Juan Liu:State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China

Abstract
The spatiotemporal impact of typhoons moving across transmission networks is increasingly evident, which may result in the failure of the overhead transmission tower-line (TL) system. The structural design and safety assessment to transmission TL systems that subjected to extreme winds are necessary. This paper aims to provide fundamental insights on the wind field caused by typhoons as well as the typhoon-induced dynamic loads and responses of the transmission TL system, by means of the numerical simulation. This paper offers a numerical scheme to simulate the typhoon-induced wind field on a TL system, in which the movement of the typhoon center and the nonstationary fluctuation of the wind are concerned. In the scheme, the near-surface mean wind speed is calculated based on the radial profile and translation of storms; the nonstationary fluctuation component is generated by a time-varying modulation function. By applying the simulated wind field to the finite element model of TL system, we yield the dynamic responses of the TL system as well as the dynamic loads resulting from the interaction between the structure and wind. Utilizing the evolutionary power spectral density (EPSD) function, the fluctuating wind loads and structural responses are addressed both in the time and frequency domains. Further discussion is done on the typhoon-induced loads by constructing the dynamic equivalent factors. The time-varying equivalent factors show the stationary process, which demonstrates the fading out of the non-stationarity for simulated wind loads. The comparison result indicates that the gust response factor of tower recommended by design codes may not be safe enough when the typhoon impact is concerned.

Key Words
dynamic response; transmission tower-line system; typhoon; wind field; wind load

Address
Yunzhu Cai:College of Civil Engineering, Nanjing Tech University, NO. 30 South Puzhu Road, Jiangbei New District,
Nanjing, Jiangsu Province, China, 211816

Jiawei Wan:State Environmental Protection Key Laboratory of Atmospheric Physical Modeling and Pollution Control, State Power Environmental Protection Research Institute, No. 10 Pudong Road, Pukou District, Nanjing, Jiangsu Province, China, 210031

Qiang Xie:College of Civil Engineering, Tongji University, No. 1239 Siping Road, Yangpu District, Shanghai, China, 200092

Songtao Xue:College of Civil Engineering, Tongji University, No. 1239 Siping Road, Yangpu District, Shanghai, China, 200092

Abstract
The current study investigates the aerodynamic characteristics of four-bundled conductors designed by distorted approach with a series of wind tunnel tests. The distorted aeroelastic model is designed at a geometry scale of 1:25 with two different span correction coefficients of 0.8 and 0.5. Two sag ratios of 5% and 10% are considered in the test, and the sag ratio of 5% is the major focus. A continuous PVC hose is adopted to simulate the aerodynamic shape of the conductor. The aeroelastic tests are performed on three kinds of uniform turbulent flow and for four different wind directions. The test results show that the mean drag of the distorted model with four-bundled conductors is smaller than that of the normal model, although the consistency of the drag force for each conductor has been satisfied according to the distortion theory. The mean tension for the distorted models is also lower than that of the normal model. However, there is an increasing trend in the fluctuating component of drag force and tension for the distorted model, except for a decrease in the fluctuating tension when the span correction coefficient is 0.5. The increase of turbulence intensity can enlarge the mean and fluctuating values of the aerodynamic forces for the four-bundled conductors, but no significant effects are found in the relative error between the mean values of the distorted and normal models. A substantial imbalance in mean drag and tension on the upstream and downstream conductors is observed under oblique wind. And the differences between the distorted and normal model gradually decrease with the increase of wind yaw angles. The increase of sag ratio can further enhance the unbalanced effect in tension under oblique wind, and has obvious influence on the variance of the drag force and tension. For the four-bundled conductors using distorted modeling, a ratio of around 0.8 rather than a smaller ratio around 0.5 is recommended.

Key Words
aeroelastic model; distortion theory; drag force; four-bundled conductors; sag ratio; tension; turbulence; wind tunnel

Address
Muguang Liu:School of Civil Engineering & Transportation, State Key Laboratory of Subtropical Building Science,
South China University of Technology, 381 Wushan Road, Guangzhou, China

Cheng Liu:School of Civil Engineering & Transportation, State Key Laboratory of Subtropical Building Science,
South China University of Technology, 381 Wushan Road, Guangzhou, China

Zhuangning Xie:School of Civil Engineering & Transportation, State Key Laboratory of Subtropical Building Science,
South China University of Technology, 381 Wushan Road, Guangzhou, China

Abstract
The wind-induced collapse of transmission towers has raised many concerns. Progressive collapse analysis is recognized as a promising method for the assessment of the collapse-resistant capacity of the transmission tower. The finite element model of an actual transmission tower is firstly built for the analysis, in which the dynamic behavior of the member in failure is taken into account to be in accord with the actual tower collapse. The analysis considering the main design load cases is conducted in advance to determine the case under which the tower has the potential to collapse. The incremental dynamic analysis in association with the explicit time integration algorithm is employed to perform a progressive collapse analysis, where the wind loads are simulated by using the linear filtering method, and the developed failure criterion with axial force and bending moment involved is based on the stability bearing capacity of the members. It is found the tower collapse begins with the horizontal bracing member near the waist. Then, the adjacent members, including the leg members, fail sequentially, and the tower collapses eventually with a shear-type failure. The demand to capacity ratio (DCR) in terms of bearing capacity of the member is defined to quantify the structural behavior, the location of the member that has the potential to fail, and when the initial failure occurs are thereby identified. It is concluded that compared to the member capacity-based analysis, the ultimate strain-based analysis, which is most likely to be an inelastic dynamic analysis permitting a large deformation, may overestimate the bearing capacity of the structure in wind-induced collapse.

Key Words
demand to capacity ratio; failure mode; member capacity-based failure criterion; progressive collapse analysis; transmission tower

Address
Yongquan Li:College of Civil Engineering and Architecture, Zhejiang University, 886 Yuhangtang Road, Xihu District, Hangzhou, China

Yong Chen:College of Civil Engineering and Architecture, Zhejiang University, 886 Yuhangtang Road, Xihu District, Hangzhou, China

Guohui Shen:1)College of Civil Engineering and Architecture, Zhejiang University, 886 Yuhangtang Road, Xihu District, Hangzhou, China 2)School of Civil Engineering, Southeast University, 2 Southeast University Road, Jiangning District, Nanjing, China

Wenjuan Lou:College of Civil Engineering and Architecture, Zhejiang University, 886 Yuhangtang Road, Xihu District, Hangzhou, China

Weijian Zhao:College of Civil Engineering and Architecture, Zhejiang University, 886 Yuhangtang Road, Xihu District, Hangzhou, China

Hao Wang:School of Civil Engineering, Southeast University, 2 Southeast University Road, Jiangning District, Nanjing, China


Abstract
This study aims to investigate the performance of wind-excited 1000 kV substation gantry via the aero-elastic model wind tunnel test. An aero-elastic model that can simulate the first four frequencies was designed and manufactured by the method of combining semi-rigid segments by V-shape springs. Making use of the aero-elastic model wind tunnel test, the structural displacement and acceleration responses of the model were investigated for different wind speed and wind direction cases. Results show that the method of combining semi-rigid segments by V-shape springs can simulate the key parameters such as geometric shape, mass, frequency and damping ratio well. Wind direction plays an important role in the mean displacement responses, and the worst wind direction is 15° deviating from the corresponding axis. The root mean square of acceleration responses is remarkable in both the along-wind and cross-wind directions. In the direction perpendicular to the span, the wind-induced vibration of the middle tower mainly depends on the resonance component of the first mode. By contrast, the contributions of the first and higher modes are all important for the side towers' wind-induced responses. Gust response factors (GRFs) were estimated by the inertial wind loading method and the gust loading factor method, respectively. The range of the GRFs determined by the two methods is close to each other, which can provide guidance for assessing the performance of similar substation gantries subjected to wind.

Key Words
aero elastic model; gust response factor; substation gantry; wind-induced response; wind tunnel test

Address
Feng Li:School of Civil Engineering, Wuhan University, Wuhan 430072, China

Yin Chen:Central Southern China Electric Power Design Institute Co., LTD of China Power Engineering Consulting Group, Wuhan 430071, China

Liang-Hao Zou:School of Civil Engineering, Wuhan University, Wuhan 430072, China

Jie Song:School of Civil Engineering, Wuhan University, Wuhan 430072, China

Shu-Guo Liang:School of Civil Engineering, Wuhan University, Wuhan 430072, China

Abstract
Overhead power transmission line systems consisting of long-span conductors and high-rise towers are wind-sensitive structures featured with significant structural nonlinearity and fragility under wind hazards. To assess wind-induced structural fragility of a transmission tower, a novel efficient quasi-static approach, which is based on the analytical probability distribution of extreme wind effect in frequency domain and the probabilistic wind-resistant capacity, is developed in the present study. The 90-degree wind direction (perpendicular to conductors), which is always the worst scenario, is considered in this paper. The structural nonlinearity and failure modes are captured using a nonlinear static push-over analysis method, which simulates the failure process of the tower structure with random initial geometric defects. Wind-resistance performance of the tower is quantified based on the principle of energy equivalence. Damage of the tower is classified into three levels including slight damage, severe damage, and collapse. The tower fragility curve, which predicts damage of the tower as a function of wind speed, is presented and discussed.

Key Words
fragility analysis; nonlinear structural analysis; probability of failure; quasi-static wind load; transmission tower

Address
Dahai Wang:Department of Building Engineering, Wuhan University of technology, Wuhan, 430070, China

Sen Li:Department of Building Engineering, Wuhan University of technology, Wuhan, 430070, China

Chao Sun:Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, 70803, U.S.A.

Guoqing Huang:School of Civil Engineering, Chongqing University, Chongqing 400044, China

Qingshan Yang:School of Civil Engineering, Chongqing University, Chongqing 400044, China


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