Sensitivity analysis and probabilistic performance assessment of transmission tower-line systems subjected to downbursts

Abstract

Transmission tower-line systems (TTLSs) featured by large span and strong flexibility are particularly sensitive to wind loads. Since the wind field characteristics of downbursts are different from atmospheric boundary layer winds, existing design methods are insufficient to study the ability of TTLSs to resist the effects of downbursts. This study performs the sensitivity analysis and probabilistic performance assessment of a TTLS under downbursts. Initially, a finite element model of the TTLS is established considering tower-line coupling effect. Fluctuating effect and spatial correlation effect are incorporated to generate downburst wind speed time histories for multiple target points. Several key parameters of the downburst wind field model subsequently are selected for sensitivity analysis of the wind-induced responses of the TTLS. Furthermore, a fragility analysis of the TTLS under downbursts is conducted. The results indicate that special attention should be given to the impact of the maximum wind speed in the vertical wind profile. When the wind speed reaches 51 m/s and 45 m/s, the probabilities of collapse and windage yaw reach 50%. This study contributes to providing support for addressing the threats posed by extreme meteorological disasters to TTLSs.

Keywords

transmission tower-line system downburst sensitivity analysis fragility analysis windage yaw

Introduction

As a critical medium for transmitting electrical power from generation plants to end users, electric transmission systems hold a pivotal position in modern society. Transmission tower-line systems (TTLSs), consisting of lattice steel towers, conductors and insulators, are characterized by large spans, high flexibility and strong nonlinearities. These systems exhibit significant geometric nonlinearity and are highly sensitive to wind loads. Existing standards typically consider wind forces as the governing loads for the structural design of TTLSs (DL/T 5254-2010, 2010; IEC 60826, 2017). The collapse of transmission tower structures under extreme wind loads is a recurring issue, significantly affecting economic development and social stability (Meng et al., 2024a). Statistical analyses have indicated that in countries such as the United States, Australia and South Africa, more than 80% of weather-related TTLSs’ failures are attributed to strong wind events, including downbursts (Dempsey and White, 1996). For example, in March 2019, an extreme downburst event in eastern China caused the failure of nine transmission towers, widespread wind-induced displacement and tripping of insulators, as well as damage to hardware components, resulting in over 1600 distribution circuit outages (Han et al., 2024). As a special type of strong wind hazard, downbursts feature a highly non-stationary stochastic process in the wind speed time course, and their mean wind speed varies with time (Chen et al., 2024; Le and Caracoglia, 2021). Downbursts exhibit characteristics distinctly different from conventional atmospheric boundary layer winds, leading to differences in the response behavior and failure mechanisms of transmission towers under these two wind conditions. However, current building codes and standards provide limited guidance on extreme wind events such as downbursts. Therefore, investigating the performance of TTLSs under downburst conditions is of critical importance for enhancing the downburst resistance of transmission towers and ensuring the safety and reliability of the power grid.

In recent years, research on the resistance of transmission towers to downburst events has gained increasing attention both domestically and internationally. Zheng and Fan (2022) simulated the progressive collapse patterns of a TTLS subjected to downbursts with varying translation paths. The results indicated that downbursts of the same intensity but with different paths could lead to the collapse of either one or three towers in the system. Fang et al. (2022) conducted a nonlinear dynamic analysis of a tower-line system considering the effects of three wind field parameters that closely related to the average wind profile. The findings revealed that under downburst conditions, the tower-line coupling somewhat mitigates the dynamic responses. Zhu et al. (2023) investigated the uncertain collapse of a transmission tower under downburst conditions, and determined the locations of the initial buckling members and the corresponding probabilities. The results indicated that the fragility curves of the tower under downburst conditions pose a greater risk compared to those under atmospheric boundary layer winds. Ahmed and El Damatty (2024) examined the effect of conductor’s response to tower failure under downburst loads using nonlinear dynamic analysis. They found that the conductor’s response to the dynamic excitation caused by tower failure is influenced by the velocity of the tower movement, the magnitude of the transverse load on the conductors, and the height of the tower failure. Zhang et al. (2024) proposed an analytical approach to evaluate the extreme non-stationary dynamic response of transmission towers subjected to downbursts in the frequency domain. The results demonstrated that the proposed theoretical framework can accurately assess the extreme response values of transmission towers subjected to non-stationary moving downbursts. Alawode et al. (2023) found that self-supported towers can experience greater wind-induced vibrations under downburst winds, even when the peak wind speeds are similar to those of synoptic winds. However, the downburst wind field model involves numerous key parameters that may influence the generated wind speed time histories, leading to significant uncertainties in the wind-induced responses of TTLSs. It is therefore essential to conduct studies to identify the critical downburst parameters significantly affecting the wind-induced responses of TTLSs. Additionally, quantifying the downburst-induced damage probabilities of TTLSs is warranted.

Probabilistic assessment and fragility analysis refer to the likelihood of a system being damaged, harmed, or impaired by a hazard, that is, the failure probability of a structure under varying levels of hazard intensity (Liu et al., 2024a, 2025a; Meng et al., 2025a). Due to their clear conceptual framework and the ability to quantify results, many researchers have applied probabilistic assessment and fragility analysis to the quantification of the wind resistance performance of TTLSs. Li et al. (2022) proposed a comprehensive probabilistic analysis framework for conducting lifetime multi-hazard fragility evaluation, incorporating wind-induced fatigue. Wang et al. (2022) introduced a wind fragility framework that accounts for the uncertainties in each line component, wind environment, and aerodynamic parameters. The results indicated that wind fragility is especially sensitive to the uncertainties in the wind profile exponent, the outer diameter, and the aerodynamic parameters of the conductors. Fu et al. (2020a) conducted a fragility evaluation for an actual TTLS to calculate its failure probabilities. Zhu et al. (2024) performed a wind-induced fragility analysis and failure probability evaluation of a transmission tower considering wind directionality. The results revealed the most unfavorable wind attack angle. Tian et al. (2020) performed a fragility analysis to assess the anti-collapse performance of a TTLS, accounting for the uncertainty in wind loads. Meng et al. (2024b, 2024c) evaluated the failure probabilities of a TTLS under varying temperatures, using a copula-based joint probability distribution of temperature and wind speed. Their findings indicated that when considering the actual distribution of wind-temperature hazards, lower temperatures do not necessarily result in the highest wind-induced damage probabilities. However, current fragility analyses and dynamic performances for TTLSs predominantly focus on atmospheric boundary layer winds, with limited attention given to the impact of downbursts. Given the significant threats posed by downbursts to TTLSs, it is essential to investigate the effect of downbursts on the wind resistance performance of TTLSs from a probabilistic assessment perspective.

In light of this, this study conducts the wind-induced response analysis and probabilistic assessment for a TTLS under downburst conditions, focusing on the safety and stability of the TTLS. The structure of this paper is as follows: Sections 2 and 3 establish the finite element model of the TTLS and randomly generate the wind speed time histories of downbursts, respectively; Section 4 selects several key parameters from the downburst wind field model and performs a sensitivity analysis of the wind-induced responses of the TTLS. Section 5 investigates the fragility analysis of the TTLS under downburst conditions; and finally, Section 6 summarizes the main conclusions.

Finite element model

This study focuses on a 1000 kV ultra-high-voltage TTLS, for which a three-dimensional finite element model is established using the numerical software ABAQUS. The total height of the transmission tower is 108.6 m, and it is primarily constructed using Q345 and Q420 steel pipes. The detailed configuration of the transmission tower is presented in Figure 1. The steel tube members exhibit a range of section sizes from Φ610 × 11 mm to Φ219 × 6 mm, while the brace members include section sizes from Φ203 × 5 mm to Φ89 × 4 mm. The transmission tower is equipped with crossarms at heights of 66 m, 85.5 m, and 108.6 m, which are designated as the lower, middle, and upper crossarms, respectively. These crossarms are used for suspending the conductors and ground wires, with a span distance of 650 m between transmission line supports. The conductors and ground wires are JLK/G1A-725 (900)/40 and OPGW-185, respectively, with detailed specifications provided in Figure 1(b).

Figure 1.

Geometric information of the TTLS.

In the finite element model of the TTLS developed in this study, B31 beam elements are used to model the transmission tower, while T3D2 truss elements are employed to model the transmission lines. The mass of the tower’s flanges, bolts, and node plates is compiled and applied as lumped mass points at selected nodes of the transmission tower. It is assumed that the transmission tower is rigidly fixed to the ground, with the soil-structure-effect being neglected. One end of the transmission line is suspended by insulator strings to the cross-arms of the transmission tower, and the other end is set up with articulation constraints. To facilitate analysis, the tower is segmented into 10 parts along its height, which are labeled as Segments 1–10. X, Y, and Z coordinates are utilized to designate the longitudinal, transverse, and vertical directions of the tower, respectively.

Downburst simulation

This study employs the deterministic-stochastic hybrid model proposed by Chen and Letchford (2004) to simulate the multi-point wind speed time series of downbursts. Specifically, the Wood vertical wind profile model and the Holmes empirical model are used to simulate the mean wind component of the downburst, while an autoregressive model is applied to generate a fluctuating stochastic process with spatial correlation, thereby obtaining the wind speed time series for the downburst. Since the vertical wind speed of a downburst is confined to a small area around the center of the thunderstorm and rapidly decreases with distance from the center, it is not considered in this study. The downburst wind speed at different spatial locations can be expressed as the sum of the mean wind speed and the fluctuating wind speed, as given by:

U (z, t) = \bar{U} (z, t) + u (z, t)

(1)

where

U (z, t)

represents the total wind speed of the downburst;

\bar{U} (z, t)

and

u (z, t)

represent the mean wind speed and the fluctuating wind speed of the downburst, respectively.

The mean wind speed of a downburst can be considered a non-stationary stochastic process, with temporal variability throughout the duration of the storm (Meng et al., 2025b). Assuming that the mean wind speed of the downburst reaches its maximum value at different heights at the same time, the mean wind speed at different heights and times can be expressed as the product of the maximum mean wind speed at that height and a time function, as given by:

\bar{U} (z, t) = U (z) \times d (t)

(2)

where

U (z)

represents the maximum horizontal wind speed at height z;

d (t)

is the time function.

The vertical wind profile of the maximum mean wind speed is modeled using the Wood model, and its expression is given by:

U (z) = 1.55 {(\frac{z}{δ})}^{1 / 6} \times [1 - \erf (0.7 \frac{z}{δ})] \times V_{v, \max}

(3)

where

δ

represents the height above ground at which the wind speed reaches half of the maximum value in the vertical wind profile; erf denotes error function,

\erf (x) = 2 / \sqrt{π} \int_{0}^{x} e^{- y^{2}} d y

;

V_{v, \max}

is the maximum speed in the profile.

The time function $d (t)$ describes how the mean speed changes with time (Sun et al., 2020), which can be expressed as:

f (t) = \frac{| V_{c} (t) |}{\max | V_{c} (t) |}

(4)

where

V_{c} (t)

represents the vector sum of the radial wind speed

V_{r} (t)

and the thunderstorm’s translational velocity

V_{t}

V_{c} (t) = V_{r} (t) + V_{t}

(5)

V_{r} (t)

is modeled using the downburst radial wind speed profile model proposed by Holmes and Oliver (2000), which can be expressed by:

V_{r} (t) = {\begin{cases} V_{r . \max} \cdot (r / r_{\max}) 0 < r < r_{\max} \\ V_{r . \max} \cdot e^{- {[(r / r_{\max}) / R_{r}]}^{2}} r \geq r_{\max} \end{cases}

(6)

where

r

is the radial distance from thunderstorm center;

V_{r, \max}

is the maximum speed in the profile;

r_{\max}

represents the radial distance from the center of the thunderstorm at which the maximum radial wind speed is achieved;

R_{r}

is the radial length scale.

Figure 2 illustrates the synthesized diagram of the mean wind speed of the downburst. As the downburst moves, the relative position with respect to the observation point changes, causing the direction of the radial wind speed at the observation point to continuously vary. Consequently, the direction of the synthesized wind speed also changes over time (Ahmed et al., 2022). For example, at the initial moment, the center of the downburst is at the coordinate origin, and the coordinates of the observation point are $P (x_{0}, y_{0})$ . When the direction of thunderstorm motion is along the positive X-axis, the position of the observation point is $P^{'} (x_{0} - V_{t} t, y_{0})$ at time t. The angle between the radial wind speed direction and the motion direction is given by:

θ (t) = \arccos [\frac{d_{0} - V_{t} t}{\sqrt{{(d_{0} - V_{t} t)}^{2} + e_{0}^{2}}}]

(7)

α (t) = \arccos [\frac{V_{r} (t) \cos θ (t) + V_{t}}{\sqrt{{(V_{r} (t) \cos θ (t) + V_{t})}^{2} + {(V_{r} (t) \sin θ (t))}^{2}}}]

(8)

Figure 2.

Synthesized diagram of the mean wind speed.

The fluctuating wind speed of the downburst is a non-stationary stochastic process. Assuming that the frequency-domain characteristics of the downburst’s fluctuating wind speed do not change over time, the fluctuating wind speed $u (z, t)$ can be expressed as the product of a time−varying modulation function $φ (z, t)$ based on the mean wind speed and a Gaussian stochastic process $k (z, t)$ with a given power spectral density (Solari and De Gaetano, 2018), which is given by:

u (z, t) = φ (z, t) \times k (z, t)

(9)

where

φ (z, t)

the modulation function and can be approximately calculated as

φ (z, t) = (0.08 \sim 0.11) \bar{U} (z, t)

;

k (z, t)

is a stationary Gaussian stochastic process, which can be simulated and generated using a linear filtering method. The power spectral density function of

k (z, t)

is adopted as the normalized Kaimal spectrum (Chen and Letchford, 2004).

When simulating the wind speed, the correlation between different simulation points should be considered (Fu et al., 2020b). The coherence function used is expressed as follows:

{c o h}_{i j} = \exp [\frac{- 2 n \sqrt{C_{y}^{2} {(y_{i} - y_{j})}^{2} + C_{z}^{2} {(z_{i} - z_{j})}^{2}}}{U (z_{i}) + U (z_{j})}]

(10)

where

| y_{i} - y_{j} |

and

| z_{i} - z_{j} |

represent the lateral and vertical distances between two points in space, respectively;

C_{y}

and

C_{z}

can be adopted as 16 and 10, respectively. Based on the above method, the downburst wind speed time histories are simulated, as shown in Figure 3.

Figure 3.

Wind speed time histories of Downburst.

According to the Guidelines for electrical transmission line structural loading (ASCE NO. 74 2009), the wind load on transmission towers under downburst conditions is expressed as:

{\begin{cases} F_{t o w e r, x} = 0.5 ρ U^{2} \cos^{2} α D_{x} S_{x} \\ F_{t o w e r, y} = 0.5 ρ U^{2} \sin^{2} α D_{y} S_{y} \end{cases}

(11)

where

F_{t o w e r, x}

and

F_{t o w e r, y}

represent the downburst-induced wind loads applied to the transmission tower along the X and Y directions, respectively;

ρ

is the air density, taken as

1.226 kg / m^{3}

;

D_{x}

and

D_{y}

are the drag coefficients in the X and Y directions, respectively;

S_{x}

and

S_{y}

are the projected areas of the tower in the X and Y directions, respectively.

The wind load applied to the conductor and ground wire can be calculated as:

F_{l i n e} = 0.5 ρ U^{2} \cos^{2} α C_{f} S_{A}

(12)

where

F_{l i n e}

is the wind load on the conductor or ground wire;

C_{f}

is the drag coefficient; and

S_{A}

is the windward area of the transmission line.

Assuming that the relative position between the TTLS and the downburst is as illustrated in Figure 4, where the origin of the coordinate system is located at the center of the thunderstorm. The movement direction of the downburst is perpendicular to the transmission line. For the convenience of applying wind loads, the transmission tower is divided into 10 segments (see Figure 1), and each span of the transmission line is divided into four segments. The wind loads are applied to the finite element model of the TTLS in the form of concentrated forces.

Figure 4.

Transmission tower-line system under downbursts.

Sensitivity analysis

There are many critical parameters in the theoretical model of downburst wind fields that significantly affect the simulation of wind speed time histories, thereby introducing considerable uncertainty into the wind-induced vibration response of transmission lines. Therefore, this study adopts the controlled variable method to investigate the influence of different parameters, with the selected key parameters including the maximum wind speed of the vertical wind profile ( $V_{v, \max}$ ),the maximum wind speed of the radial wind profile ( $V_{r . \max}$ ), translation speed of downburst ( $V_{t}$ ),the distance between tower and downburst center (d_o) and (e).

Wind loads can induce nonlinear vibrations in transmission towers and transient windage yaw displacement in the insulators. At higher wind speeds, the resulting tower collapse and wind-induced deflection can disrupt the normal operation of the power system (Bi et al., 2023). Therefore, this study selects the displacement at the tower top and the windage yaw displacement of the insulator for quantification, aiming to comprehensively investigate the impact of key downburst parameters on the wind-induced vibration responses of the TTLS. The tower top displacement and windage yaw displacement can be calculated as follows:

U_{t o p} = \max {\max | U_{1} (t) |, \max | U_{2} (t) |}

(13)

D_{c o n, i} = \max [D_{t o p, i} (t) - D_{b o t t o m, i} (t)]

(14)

where

U_{t o p}

is extreme top displacement;

U_{1} (t)

and

U_{2} (t)

represent the time histories of the top displacement of the transmission tower in the X- and Y-directions, respectively;

D_{c o n, i}

denotes the windage yaw displacement of the i-th insulator, where i = 1, 2, and 3 correspond to the lower, middle, and upper crossarms, respectively;

D_{t o p, i} (t)

and

D_{b o t t o m, i} (t)

represent the displacements of the top and bottom ends of the i-th insulator, respectively.

To capture the impact of the uncertainty of key parameters on the wind-induced vibration responses of the TTLS, this study defines an influence index $λ$ , which can be calculated as:

λ = \frac{μ - μ_{d}}{μ_{d}}

(15)

where

μ_{d}

represents the response of a baseline model, while

μ

denotes the response of the model when a key parameter undergoes a change.

Impact of V_v,max

The range of the maximum wind speed in the vertical wind profile ( $V_{v, \max}$ ) is selected from 32 m/s to 50 m/s, with an interval of 2 m/s. The influences of different $V_{v, \max}$ on the top displacement of transmission tower and the windage yaw displacement of insulators are investigated. Figure 5 illustrates the time history curves of top displacement and windage yaw displacement under varying $V_{v, \max}$ , while Figure 6 presents the variation trend of peak responses. It is evident that $V_{v, \max}$ has a significant impact on top displacement and windage yaw displacement. With the increase of $V_{v, \max}$ , both the displacement at the top of the transmission tower and the windage yaw displacement of the insulator gradually increase. As the wind speed increases from 32 m/s to 50 m/s, the top displacement rises from 0.33 m to 0.87 m. The windage yaw displacement of insulators at the lower, middle, and upper cross-arms increases from 7.47 m to 9.63 m, 7.73 m to 9.71 m, and 7.47 m to 9.59 m, respectively.

Figure 5.

Time history responses under varying $V_{v, \max}$ .

Figure 6.

Peak responses for varying $V_{v, \max}$ .

Impact of V_r,max

To investigate the influence of varying $V_{r, \max}$ on the top displacement of transmission towers and the windage yaw displacement of insulators, a range of $V_{r, \max}$ from 20 m/s to 38 m/s is selected, with an increment of 2 m/s. Figure 7 presents the time history curves of top displacement and windage yaw displacement under different $V_{r, \max}$ , while Figure 8 illustrates the variation trends of the peak responses. It can be observed that $V_{r, \max}$ has little effect on the top displacement and windage yaw displacement. This is because the radial wind profile mainly influences the shape and local magnitude of the normalized time function, while having a limited effect on the peak values of the downburst wind speed time history.

Figure 7.

Time history responses under varying $V_{r, \max}$ .

Figure 8.

Peak responses for varying $V_{r, \max}$ .

Impact of V_t

The downburst moves along a path perpendicular to the transmission line at a translation speed $V_{t}$ . To investigate the effect of the translation speed, this study selects 10 different values of $V_{t}$ , namely 4 m/s, 6 m/s, 8 m/s, 10 m/s, 12 m/s, 14 m/s, 16 m/s, 18 m/s, 20 m/s, and 22 m/s. Figure 9 presents the time history curves of the top displacement and windage yaw displacement of the transmission tower under downbursts with different $V_{t}$ , while Figure 10 illustrates the variation patterns of the peak responses. It can be observed that as $V_{t}$ increases, the peak values of both the top displacement of the transmission tower and the windage yaw displacement of the insulators gradually shift to the left. However, the peak values of both responses are relatively insensitive to the translation speed.

Figure 9.

Time history responses under varying $V_{t}$ .

Figure 10.

Peak responses for varying $V_{t}$ .

Impact of the distance from downburst center to the tower ( $d_{o}$ )

The movement of the downburst results in a change in the distance between the storm center and the transmission tower. Specifically, as the downburst travels along a path perpendicular to the transmission line, the distance from the storm center to the tower $d_{o}$ varies. To examine the effect of the distance from the storm center to the tower ( $d_{o}$ ), a range of 1500 m–6000 m is selected for the response analysis of the TTLS under downburst conditions. Figure 11 shows the time history curves of top displacement and windage yaw displacement for different values of $d_{o}$ , while Figure 12 illustrates the changes of the peak responses. It can be observed that as $d_{o}$ increases, the impact of the downburst on the transmission line occurs later, and both the top displacement and windage yaw displacement gradually shift to the right. Following the change in $d_{o}$ , the range of variation in the top displacement is from 0.50 m to 0.56 m, while the windage yaw displacements at the lower, middle, and upper cross-arms vary from 9.33 m to 9.00 m, 9.36 m to 8.91 m, and 9.13 m to 8.85 m, respectively.

Figure 11.

Time history responses under varying $d_{o}$ .

Figure 12.

Peak responses for varying $d_{o}$ .

Impact of the offset distance of the storm center from the tower ( $e$ )

On the other hand, the offset distance between the storm center and the tower ( $e$ ) is also a key parameter influencing the wind-induced response of the TTLS. To quantify its effect, a range of 0–900 m is selected to analyze the top displacement of the tower and windage yaw displacement of the insulators under downburst conditions. Figures 13 and 14 show the time history curves and peak responses, respectively. It can be observed that as $e$ increases, the impact of the downburst on the top displacement of the transmission tower and the windage yaw displacement of the insulators gradually decreases; when e increases from 0 to 900 m, the top displacement of the transmission tower decreases from 0.53 m to 0.38 m. The windage yaw displacement at the lower, middle, and upper crossarms decreases from 8.94 m to 7.51 m, 8.96 m to 7.79 m, and 8.79 m to 7.76 m, respectively.

Figure 13.

Time history responses under varying $e$ .

Figure 14.

Peak responses for varying $e$ .

Discussions of sensitivity analysis

Figure 15 presents a bar chart illustrating the impact of various key parameters on the wind-induced response of the TTLS. The length of each bar reflects the sensitivity of the transmission tower structure to the corresponding parameter, with longer bars indicating higher sensitivity. It can be observed that the impact of different key parameters associated with the downburst wind field model on the wind-induced response of the TTLS varies significantly. Among these, the maximum vertical wind speed ( $V_{v, \max})$ has the most substantial effect, followed by the distance from the storm center to the tower $d_{o}$ and $e$ ; In contrast, the impact of the maximum radial wind speed ( $V_{r, \max}$ ) and translation speed ( $V_{t}$ ) is relatively small. Therefore, when performing risk analysis of the TTLS under downburst conditions, particular attention should be given to the impact of the maximum vertical wind speed ( $V_{v, \max}$ ).

Figure 15.

The impact of key downburst parameters on the TTLS.

Fragility analysis under downburst

The wind disaster fragility of TTLSs is typically described using a fragility curve, which represents the probability of exceeding a target performance threshold under varying wind speed intensities (Liu et al., 2023, 2024b). In general, the wind-induced vibration demand and structural capacity of TTLSs under a specific wind load intensity are assumed to follow a lognormal distribution. The fragility conditional probability can then be expressed as:

P_{f} = P (D \geq C | I M) = Φ (\frac{\ln (S_{D | I M}) - \ln (S_{C})}{\sqrt{β_{D | I M}^{2} + β_{C}^{2}}})

(16)

where

D

and

C

represent the wind-induced vibration demand and structural capacity, respectively;

I M

is the wind load intensity indicator;

S_{D | I M}

is the mean wind-induced response of the TTLS under a given wind load intensity;

S_{C}

is the target structural capacity value;

β_{D | I M}

and

β_{C}

are the log-standard deviations of the wind-induced vibration demand and structural capacity, respectively. By plotting the conditional probability of the TTLS’s wind-induced vibration demand exceeding the given structural capacity at various

I M

levels, the fragility curve can be derived. In this study, the incremental dynamic analysis (IDA) method is employed to calculate the performances of the TTLS from a fully intact state to failure. To assess the statistical characteristics of the wind-induced vibration response obtained through the IDA method, a probabilistic demand model is employed using linear regression to approximate the mean value of the wind-induced vibration response (Liu et al., 2025b).

S_{D | I M}

can be expressed by:

S_{D | I M} = \ln (a) + b \cdot \ln (I M)

(17)

where

D

and

C

are the regression coefficients. It is assumed that the log-standard deviation term

β_{D | I M}

is constant across the entire IM range, which can be calculated as:

β_{D | I M} = \sqrt{\frac{\sum_{i = 1}^{N} {[\ln (d_{i}) - S_{D | I M}]}^{2}}{N - 2}}

(18)

where

d_{i}

is the wind-induced vibration demand from the i-th simulation;

N

represents the total number of simulations.

Definition of damage level

The collapse of the transmission tower and the windage yaw displacement of the insulator are the two main failures caused by wind loads on TTLSs (Bi et al., 2023), each involving structural safety and normal operational conditions, respectively. In this study, the maximum top displacement of the tower and the windage yaw displacement of the insulator are selected as the quantitative indicators for two typical failures. For the transmission tower structure, three damage states are defined: slight damage ( ${D S}_{1}$ ), moderate damage ( ${D S}_{2}$ ) and collapse ( ${D S}_{3}$ ), These states can be determined through nonlinear static pushover analysis, and the resulting structural capacity curve of the transmission tower is shown in Figure 16. It can be observed that there is a buckling point on the capacity curve. Before this buckling point, the tower top displacement increases gradually and linearly with the lateral force. After surpassing the buckling point, even a small lateral force can cause a rapid increase in the tower top displacement. Therefore, the tower top displacement at this buckling point can be considered as the threshold for ${D S}_{3}$ , recorded as 1.10 m. The thresholds for ${D S}_{1}$ and ${D S}_{2}$ are 50% and 75% of ${D S}_{3}$ , respectively, corresponding to displacements of 0.55 m and 0.825 m, as shown in Table 1.

Figure 16.

Pushover analysis.

Table 1.

The designated risk levels (m).

Threshold	Level 1	Level 2	Level 3
Tower top displacement	0.550	0.825	1.100
Windage yaw displacement of insulator at lower crossarm	8.768	9.200	9.875
Windage yaw displacement of insulator at middle crossarm	8.799	9.474	10.110
Windage yaw displacement of insulator at upper crossarm	8.525	9.443	10.110

Under wind loads, insulator displacement reduces the clearance between the transmission line and the tower. When the clearance falls below the allowable value, wind-induced flashover can occur, thereby affecting the normal operation of the power system. According to the Chinese code (GB 50665-2011, 2011), the minimum permissible clearance ( $D_{i n s}$ ) between the charged component of the double circuit and the tower structure is specified as 2.7 m at power-frequency voltage. Based on the geometric relationship between the tower and the insulators shown in Figure 17, the displacement at the lower, middle, and upper crossarms are calculated to be 9.875 m, 10.110 m, and 10.110 m, respectively. In the figure, $x_{1}$ and $x_{2}$ represent the distances between the transmission line and the crossarm and tower body, respectively. Both distances must meet the minimum clearance requirements. Table 1 lists three risk levels reflecting the wind-induced displacement of insulators, corresponding to $1.5 {0 D}_{i n s}$ , $1.25 D_{i n s}$ and $D_{i n s}$ .

Figure 17.

Windage yaw displacement threshold.

Fragility curves

Figure 18 presents the verification model for transmission tower collapse and windage yaw displacement failures. As shown in Figure 18(a), the tower top displacement gradually increases with wind speed. When the wind speed reaches 52 m/s, the tower top displacement increases rapidly, indicating the collapse of the transmission tower. As shown in Figure 18(b), when the wind speed gradually increases from 10 m/s to 32 m/s, the windage yaw displacement of the insulators at the three crossarms increases approximately linearly. When the wind speed reaches 46 m/s, the insulator displacement exceeds risk level 3.

Figure 18.

Verification model for tower collapse and windage yaw displacement failure.

Figure 19 shows the fragility curves for transmission tower collapse and insulator windage yaw displacement under downburst conditions. As seen in Figure 19(a), as wind speed increases, the probability of the transmission tower top displacement exceeding each damage state gradually increases. When the exceedance probability reaches 50%, the corresponding wind speeds for transmission tower collapse at ${D S}_{1}$ , ${D S}_{2}$ and ${D S}_{3}$ are 36.3 m/s, 44.5 m/s, and 50.9 m/s, respectively. For the windage yaw displacement failure of insulators at the lower crossarm, when the exceedance probability reaches 50%, the corresponding wind speeds for the three risk levels are 39.2 m/s, 42.2 m/s, and 45.4 m/s, respectively. For the insulator windage yaw displacement failure at the middle crossarm, the corresponding wind speeds are 40.2 m/s, 42.8 m/s, and 45.2 m/s, respectively. For the insulator windage yaw displacement failure at the upper crossarm, the corresponding wind speeds are 40.7 m/s, 43.2 m/s, and 46.1 m/s, respectively.

Figure 19.

Fragility curves of tower failure and windage yaw.

Conclusions

This study performs the sensitivity analysis and probabilistic performance evaluation of a TTLS under downburst conditions. A detailed finite element model is established, and the stochastic downburst wind speed time history is generated. By selecting multiple key parameters of the downburst wind field model, a sensitivity analysis of the TTLS’s wind-induced response is conducted to identify significant sensitive parameters. Further, fragility analysis of the TTLS under downburst conditions is carried out. The main conclusions of this study are as follows:

(1) $V_{v, \max}$ has a significant impact on the tower top displacement and windage yaw displacement of insulators. When $V_{v, \max}$ increases from 32 m/s to 50 m/s, the top displacement increases from 0.33 m to 0.87 m. The insulator windage yaw displacement at the lower, middle, and upper crossarms increases from 7.47 m to 9.63 m, from 7.73 m to 9.71 m, and from 7.47 m to 9.59 m, respectively.

(2) Compared to $V_{v, \max}$ , other parameters such as the maximum radial wind profile speed $V_{r, \max}$ , translation speed $V_{t}$ and the distance between the storm center and the tower has a relatively small effect on the wind-induced vibration response of the TTLS. The impact of $V_{v, \max}$ should be prioritized in the performance analysis of TTLSs under downburst conditions.

(3) As the wind speed increases, the displacement at the tower top gradually increases. At a wind speed of 52 m/s, the transmission tower collapses. Between 10 m/s and 32 m/s, the windage yaw displacement of the insulators at the three crossarms increases approximately linearly. Once the wind speed reaches 46 m/s, the insulator windage yaw displacement exceeds risk level 3.

This paper attempts to carry out sensitivity analysis and fragility assessment of TTLSs under downbursts. The interesting findings obtained in this study need to be applied and validated on a variety of typical transmission towers with different span lengths, span orientations and elevation changes. In addition, a comprehensive post-disaster recovery process and resilience assessment of TTLSs under downbursts will be investigated to strengthen the investigation framework proposed in this paper.

Footnotes

Acknowledgments

The authors would like to thank the State Grid Corporation of China for funding this project (SGTJDK00PJJS240007).

ORCID iDs

You Dong

Juncai Liu

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Science and Technology Foundation of State Grid Corporation of China; (Grant No: SGTJDK00PJJS240007).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Sensitivity analysis and probabilistic performance assessment of transmission tower-line systems subjected to downbursts

Abstract

Keywords

Introduction

Finite element model

Downburst simulation

Sensitivity analysis

Impact of Vv,max

Impact of Vr,max

Impact of V t

Impact of the distance from downburst center to the tower ( d o )

Impact of the offset distance of the storm center from the tower ( e )

Discussions of sensitivity analysis

Fragility analysis under downburst

Definition of damage level

Fragility curves

Conclusions

Footnotes

Acknowledgments

ORCID iDs

Funding

Declaration of conflicting interests

References

Impact of V_v,max

Impact of V_r,max

Impact of V_t

Impact of the distance from downburst center to the tower ( $d_{o}$ )

Impact of the offset distance of the storm center from the tower ( $e$ )