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Edited by: Acir Mércio Loredo-Souza, Universidade Federal do Rio Grande do Sul, Brazil

Reviewed by: Franklin Lombardo, Rensselaer Polytechnic Institute, USA; Ioannis Zisis, Florida International University, USA

Specialty section: This article was submitted to Wind Engineering and Science, a section of the journal Frontiers in Built Environment

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Serving as one key component of the most important lifeline infrastructure system, transmission towers are vulnerable to multiple nature hazards including strong wind and could pose severe threats to the power system security with possible blackouts under extreme weather conditions, such as hurricanes, derechoes, or winter storms. For the security and resiliency of the power system, it is important to ensure the structural safety with enough capacity for all possible failure modes, such as structural stability. The study is to develop a probabilistic capacity assessment approach for transmission towers under strong wind loads. Due to the complicated structural details of lattice transmission towers, wind tunnel experiments are carried out to understand the complex interactions of wind and the lattice sections of transmission tower and drag coefficients and the dynamic amplification factor for different panels of the transmission tower are obtained. The wind profile is generated and the wind time histories are simulated as a summation of time-varying mean and fluctuating components. The capacity curve for the transmission towers is obtained from the incremental dynamic analysis (IDA) method. To consider the stochastic nature of wind field, probabilistic capacity curves are generated by implementing IDA analysis for different wind yaw angles and different randomly generated wind speed time histories. After building the limit-state functions based on the maximum allowable drift to height ratio, the probabilities of failure are obtained based on the meteorological data at a given site. As the transmission tower serves as the key nodes for the power network, the probabilistic capacity curves can be incorporated into the performance-based design of the power transmission network.

Serving as one key component of the lifeline infrastructure system, electrical transmission networks, and distribution systems including transmission towers and lines are under a complex set of multiple threats from natural and manmade hazards. Possible failures from transmission towers and lines and associated large area blackouts could pose severe threats to the power system security, which has been a great challenge for the stakeholders, decision makers, and the whole society. In the Americas, Australia, and South Africa, about 80% of the transmission tower failures are due to the strong wind loadings from tornados, hurricanes, or isolated thunderstorms and such failures could lead to large area power outages (Dempsey and White,

To avoid future transmission tower failure and achieve a quick recovery of regional areas from future extreme nature hazards, understanding the structural capacity and the characteristics of interactions between the transmission tower and strong wind are essential for the power system’s safety and reliability. Therefore, many codes, specifications, or manuals are available for the transmission tower design, such as the ANSI National Electric Safety Code (NESC) (ANSI 2006), the International Electrotechnical Commission (IEC) Standard 60826:2003 (IEC 2003), and the ASCE Manual 74 (American Society of Civil Engineers (ASCE),

In addition, due to the localized and unpredictable characteristic of local wind environments, wind profiles, and time histories could be different for different sites with different meteorological data. During an extreme storm event, the wind could be non-stationary based on the anemometry data and transient flow from such non-stationary gusts could have significant effects on structural responses (Schroeder and Smith,

The present study focuses on building effective capacity assessment approach for transmission towers subjected to strong winds. A new probabilistic capacity assessment approach for transmission towers under strong wind loads is proposed and implemented for a 3-D lattice tower. At first, the wind loading for the transmission tower are modeled based on the randomly generated wind time history as a summation of time-varying mean and fluctuating components. The varied drag coefficients for different panels and wind yaw angles are obtained from wind tunnel experiments. To assess the structural capacity in different yaw angles of wind loadings, incremental dynamic analysis (IDA) is carried out and sets of IDA curves are created to predict the probabilistic capacity curves. Based on the meteorological data for a given site, the probability of failure for all wind yaw angles is evaluated with defined limit states and the risk analysis for transmission tower can be carried out. The paper is organized as the following four main sections. In the first section, the wind-structure dynamic system is modeled. The finite element model of the transmission tower is built and stochastic wind field is generated. In the second section, the wind tunnel experiments for the transmission tower are introduced and the wind loading coefficients are obtained. In the third section, the IDA analysis for capacity assessment is introduced and the capacity curves for different wind directions are obtained. In the fourth section, the set of IDA curves are obtained for probabilistic capacity assessment and the approach is summarized, as well. After defining limit states, the probabilities of failure for the transmission tower are obtained for wind speeds in different return periods using the meteorological data at a given site.

The lattice transmission towers are built with L-shape steel members and truss, beam elements or their combinations are usually used to model the structure. The material non-linearity and the geometric non-linearity are included by using bilinear elastoplastic material properties and by implementing large deformation analysis, respectively.

To effectively present the proposed probabilistic capacity assessment methodology, the finite element model for a 550-kV single circuit lattice transmission tower is built first for the structural capacity analysis. The tower is 68.6 m high and the side length of the square base for the tower is 14.094 m. The prototype transmission tower is shown in Figure

Mode number | Frequency (Hz) | Mode shape description |
---|---|---|

1 | 1.631 | First lateral bending |

2 | 1.706 | First longitudinal bending |

3 | 2.737 | First torsion |

4 | 4.696 | Second lateral bending |

5 | 4.860 | Second longitudinal bending |

6 | 6.776 | Second torsion |

As shown in Figure _{d} is the drag coefficient, and _{p} is the projected area of the test subsection in the plane that is perpendicular to the incoming wind. In many wind design codes for transmission towers, the drag coefficient is defined as a function of solidity ratio. In the present paper, the drag coefficients are obtained through wind tunnel experiments, which will be detailed in the following sections.

Wind fluctuations can be treated as stationary Gaussian process and could be simulated using a superposition of trigonometric functions with random phase angles or the spectral representation method (Shinozuka and Deodatis,

In the present study, the historical wind data from one meteorological observatory (Xiaoyangshan Meteorological Observatory) are adopted in the probabilistic capacity assessment approach for a demonstration purpose (Ge et al.,

In the present study, the wind-structure interactions are simplified as wind loading on structures using Eq. _{d} can be obtained through wind tunnel experiments. The wind tunnel experiments for the transmission tower were carried out in HD-2 wind tunnel at Hunan University, China. A rigid model for measuring drag coefficient _{d} and an aeroelastic model for gust response factor (GSF)

To obtain the drag coefficient _{d} at different heights, the rigid transmission tower is divided into six sections, as shown in Figure _{X}_{Y}

Since the transmission tower has a square base, the drag coefficients for subsections D–F only have limited differences for the yaw angle of 0° and 90°. With the increase of the height, the tower shape change gradually. The drag coefficients have 11% difference for subsection C in 0° and 90°, 20% difference for subsection B, and 110% difference for subsection A. For all subsections, the maximum drag coefficients are at the yaw angle of 30°. In the present paper, for a demonstration purpose, only four yaw wind yaw angles of 0°, 30°, 60°, and 90° will be used to evaluate wind–tower interactions.

Gust response factor is used to consider the dynamic effect of turbulent flow. A series of wind tunnel experiments were carried out for the aeroelastic tower model and the buffeting responses at different yaw angles of the model were measured. Based on a sensitivity study, the stiffness for the transmission tower is found to be provided mainly by the four major vertical columns and the contributions from lateral bending of each L-shape steel member are relatively small (Hua et al., _{d} and _{s} are dynamic load and static load, respectively; _{D}(_{z}_{p}(_{a} is the peak factor of the acceleration; and σ_{a}(

As shown in the figure, the gust loading factors increase with the height of the subsection. When the height ratio (_{i}_{i}

Based on the wind loading defined in Eq. _{d} obtained from wind tunnel experiments, the dynamic analysis of the wind–transmission tower system can be simulated in the time domain and the time histories could be obtained. Figures

Meanwhile, the dynamic effects of wind loading are usually considered in the design codes as a dynamic amplification factor, such as GSF in ASCE74. The wind loading for each panel in a given wind angle is calculated using the following equation (American Society of Civil Engineers (ASCE), _{w} is the load factor to adjust the wind load for the desired return period; _{50} is the 3-s gust basic wind speed with a 50-year return period; _{z}_{zt}_{d} is the drag force coefficient values and

Based on the dynamic analysis, the maximum base shear force and top tip displacement at all wind directions can be obtained as shown in Figures

To assess the global behavior of a structure from its elastic response to global dynamic instability through yielding and non-linear response, the IDA has been widely used for structure performance under earthquake loading. By analogy with passing from a single static analysis to the incremental static push over (SPO), the seismic loading is scaled to extend the single time history analysis into an incremental one (Vamvatsikos and Cornell,

To define a limit state for the structural model, damage measure (DM) is defined as a non-negative scalar that characterizes the additional response of the structural model to a prescribed loading, which could be obtained through a corresponding non-linear dynamic analysis, such as a seismic analysis (Vamvatsikos and Cornell,

The capacity curves are obtained for the relation between the total base shear force versus the top tip displacement based on the maximum base shear force and corresponding top tip displacement (Curve A), the maximum top tip displacement and corresponding base shear force (Curve B), and the maximum base shear force and the maximum top tip displacement (Curve C). The capacity curves for the transmission tower in longitudinal direction, where β = 0°, are shown in Figure

The analysis can be repeated for other wind directions to obtain the relationship between the maximum base shear force and the maximum top tip displacement for all wind directions. Figure

As the IDA study for seismic loadings is accelerogram and structural model specific, different ground motions could lead to different IDA curves (Vamvatsikos and Cornell,

For a demonstration purpose, three wind speed time histories are simulated for the IDA analysis in the present study, which lead to three sets of capacity curves. Based on the three sets of capacity curves, the mean, 16%, and 84% IDA curves could be obtained to take into account the inherent randomness with respect to the wind loadings. As shown in Figure

For a performance-based design framework, structural performance is associated with reaching criteria that a limit-state rule is satisfied. In the present study, as the DMs are defined as damage indicators, the limit states can, therefore, be defined when DMs increase beyond a certain value that the structural model is assumed to be in the limit state. For example, in FEMA guidelines, the maximum drift to height ratio θ_{max} = 2 or 8.5% is defined as the limit state for steel moment-resisting frames (SMRFs) with type-1 connections for the immediate occupancy structural performance level or collapse prevention level (FEMA, _{max} = 2% is used as the limit state for the transmission towers in the present study for a demonstration purpose. Therefore, in the present study, failure is defined as the maximum drift to height ratio being over θ_{max}, which does not mean a catastrophic collapse. Since the set of IDA curves are dependent on the yaw wind angles, the probability of failure of the structure for the defined limit state could be obtained as
_{i}_{f}_{i}_{i}_{max} = 2% is the limit state defined for structural capacity, and

The probabilistic capacity assessment approach based on IDA analysis is summarized in Figure

In the present study, for a 50-year return period wind, as the tower is still in the elastic range for most of the twelve wind yaw angles (except for β = 120°, 150°, and 240°), the probability of failure is 0 by using evaluating Eq. _{max}_{f} = 4.2%. Similarly, probability of failures for 100 and 300-year return period wind speed can be obtained as 4.8 and 39.5%, respectively. Since the structure is still in an elastic range at the 50 and 100-year return period wind speed, the differences of the probability of failures for the two wind speeds are small. However, as yielding begins to develop in many wind yaw angles, the probability of failure increases drastically as the wind speed increases to a 300-year return period wind speed. It is noteworthy that only a single transmission tower is considered in the present study and the possible failure modes due to the cascading effects from adjacent towers and lines are not included in the limit states. However, the proposed probabilistic capacity assessment approaches can be implemented for the other high-intensity winds such as tornados, downbursts, and microbursts and any other scenarios with different hazards or their combinations, such as ice loads and cable vibrations.

With continuous climate change and associated severe natural hazards, such as hurricanes and winter storms, accurate predictions of structural capacity and failure modes of the transmission towers and power systems have been critical to ensure community resiliency and avoid large area blackout. This paper presents a probabilistic approach for capacity assessment for transmission towers under strong wind loadings. After modeling the transmission towers with beam elements and simulating stochastic wind field, the IDA for a transmission tower is carried out. Multiple wind time histories in four different wind directions were used for the dynamic analysis of the wind and transmission tower dynamic system. Wind tunnel experiments were carried out to obtain the drag coefficient and dynamic response factor for different wind yaw angles and different subsections of the tower. In the present study, the maximum base shear forces and top tip displacements are chosen as the DMs and the capacity curves for different wind yaw angles are obtained. To take into account the inherent randomness with respect to the wind loadings, different wind time histories are used in the wind-structure dynamic system to obtain the mean, 16%, and 84% IDA curves. After building the limit states according to the maximum drift to height ratio, the probabilities of failure are obtained for a given site meteorological data with different return periods. From the present study, the following conclusions are drawn: (1) the failure modes for different wind yaw angles could be different and the structural capacity for the transmission tower varies for different wind yaw angles; (2) in the elastic range of the transmission tower, the random wind effects are very small. The random wind effects begin to develop after yielding of different structural members over the elastic range; and (3) probability of failure for different yaw angles could be different.

The present study has demonstrated an effective probabilistic capacity assessment approach framework for transmission towers considering stochastic wind loadings. However, for performance-based design of transmission towers and power systems, other failure modes, such as fatigue damages or cracks and large amplitudes of vibrations, should be included. In addition, the randomness of structural members and progressive deterioration of structural members in structure’s life cycles are not considered in the present study. For a better understanding the resilience of the power transmission and delivery network, more research efforts are needed under the performance-based design framework using the probabilistic approach to assess all possible failure modes for all possible extreme weather scenarios. This will enable the stake holders and decision makers to better understand the system performance of the power transmission system under extreme events and help propose possible effective mitigation plans and strategies to avoid possible system failures and large area blackouts.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work is partially supported by University of Connecticut under the first author’s startup funding and the National Science Foundation of Guangxi (Grant No: 2014GXNSFBA118264) and Key Laboratory of Engineering Disaster Prevention and Structural Safety of the China Ministry of Education in Guangxi University (Grant No: 2014ZDX06) for the third author. The support is greatly appreciated. The contents of the paper reflect only the views of the authors.