Extreme Wind Speed Estimation for Wind-Resistance Design of a Transmission Line Situated in a Typhoon-Prone and Hilly Area

The southeastern coast of China is annually threatened by typhoons originating from the northwestern Pacific Ocean, posing a risk of severe damage to coastal transmission lines. This study employs the random forest-based typhoon full-track simulation method and YM wind field to assess the wind-resistance reliability of transmission lines. The obtained extreme wind speeds of a transmission line site in Wenzhou are 33.7m/s and 35.8m/s under the 50-year and 100-year return periods, respectively. The effects of micro-topography on the extreme typhoon wind speed are further analyzed, and the extreme wind speed distribution maps of Wenzhou City and Yueqing City are plotted, respectively. The results indicate a decreasing trend in typhoon wind speed within inland regions, while micro-topography displays a substantial effect on enhancing the typhoon wind speed.


Introduction
The southeastern region of China borders the Northwest Pacific Ocean and experiences frequent typhoon occurrences throughout the year.Due to their highly-destructive nature, typhoons pose a great threat to the safety and security of people [1] .High-voltage overhead transmission lines are highly flexible structure with great sensitivity to wind field changes [2,3] .Due to climate change, the intensity of typhoons has been on the rise, resulting in frequent occurrences of transmission line disasters [4][5][6] .In view of this, the effect of typhoons should be given more consideration in the structural wind resistance reliability design of transmission lines.
In recent years, scholars have conducted stochastic simulations of typhoons via parametric typhoon numerical simulation methods [7,8] , and performed extreme value statistical analysis on a large number of simulation results to achieve typhoon hazard assessment.Additionally, it is worth noting that transmission lines are primarily situated in mountainous locales, and certain sections may traverse micro-topographic areas.Transmission towers located in valleys should take into account the wind speed increase caused by funnelling, while towers situated on mountains should also consider the effect of wind speed increase near the peaks [9] .Li et al. [10] found that China's wind load code is conservative in terms of micro topographic corrections when compared to models of terrain influence on wind field in load codes of developed countries.Gao and Yang [9] conducted simulations and analysis of wind field characteristics on three typical microtopographies and derived the micro topographic correction coefficients for tower wind speed.
In this paper, the full track model based on random forest is used for typhoon numerical simulation to demonstrate the process of evaluating extreme wind speeds and to generate a distribution map of extreme wind speeds with varying accuracies of transmission lines in Wenzhou.Using an actual site in Yueqing as an illustration, computational fluid dynamics (CFD) is utilized to conduct a numerical simulation of the terrain area, and the results of the acceleration ratio under different wind directions are obtained to adjust the extreme wind speed for design references.

Stochastic Simulation of Typhoons
The first step of typhoon numerical simulation is to randomly generate a substantial amount of typhoon samples.The full-track simulation method proposed by Vickery [11] in 2000 can model the entire process of the typhoon, which has been frequently employed to obtain a large number of virtual typhoon samples.

Random Forest-Based Typhoon Full-Track Simulation Method
To address the limitations of the conventional linear regression approach in the Vickery full-track model, Huang et al. [12] proposed a random forest-based typhoon full track simulation method (RFFT).Due to the significant variation in tropical cyclone tracks in the Northwest Pacific Ocean, Huang et al. [12] categorized typhoon paths into four categories to improve simulation accuracy.The number of decision trees is determined according to the computational efficiency of the Random Forest (RF) model, then established the RF travel model, intensity model, and termination model required for the iteration of data points during typhoon movement.

Result Verification
The starting point information of simulated typhoon generated by Monte Carlo sampling is input into the random forest model, with previous historical data used as the starting item.The model then simulates the track and intensity of the tropical cyclone step-by-step, creating a virtual typhoon with key parameter information on the entire path.The simulation runs for 10,000 years, after which the above steps are repeated until all numerical typhoons are generated.
To verify the effect of typhoon full-track simulation, we selected 25 equidistant coastal stations in China as displayed in Fig. 1 to perform a statistical analysis on key parameters such as annual occurrence rate, orientation, movement speed and central pressure difference.The orientation refers to the angle measuring from the north direction to the typhoon forward direction, with positive angles indicating a clockwise direction.Based on the CMA-STI best track dataset, the mean and standard deviation of the key parameters of the historical typhoons within the simulation circle centered on each coastline station with a radius of 250 km were counted and compared with the numerical typhoons.The results are shown in Fig. 2. Overall, the results of the RF-based typhoon simulation are in general agreement with the historical data, suggesting that the full-track model has a great capability of reproducing typhoons in the southeastern coastal region of China.

Extreme Wind Speed Estimation
Typhoon Lekima made landfall in Wenling, Zhejiang on August 10th, 2019 at 1:45.The storm caused a severe wind deviation accident at the 31# tower of the 500kV Duling 5862 line in Yueqing.Due to the lack of first-hand meteorological data at the accident site, we can use the RFFT method to conduct the typhoon full-track simulation and invert to obtain the wind speed data at the accident site.
For a specific site, typhoons that enter the simulated point within 250 km radius are statistically selected as typhoon samples affecting the site.Subsequently, average wind speed series and extreme wind speed are obtained for different return periods at the target site.In cases where there exist sufficient typhoon data samples, the empirical distribution can be utilized to avoid tailing error under higher return periods [13] .The cumulative probability density function of empirical distribution of the annual extreme wind speed with a sample size of m can be expressed as: where vi (i=1,2,…, m) represents the sequence of typhoon wind speeds sorted in ascending order, and the extreme wind speed VT during T-year return period corresponds to the quantile value with a cumulative probability of (1-1/T) on the curve.The simulation result for 31# tower accident site (121.14°E,28.44°N) is displayed in Fig. 3.The extreme wind speed V50 during 50-year return period is 33.

Typhoon Design Wind Speed Distribution in Wenzhou
Wenzhou City is susceptible to high typhoon risk situated in a transmission line corridor area.Every simulation point is taken with the interval of 0.1° to plot the distribution map of extreme wind speed in Wenzhou, as shown in Fig. 4(a).The result indicates that the extreme wind speed on land in Wenzhou ranges from 28.4m/s to 34m/s, gradually decreasing as it moves inland.This trend is directly related to the increase in ground roughness, which leads to greater kinetic energy loss and thus a lower near-ground wind speed.

Wind Speed Correction Considering Micro-topographic Accelerations
The 31# tower wind deviation accident site is situated in Yueqing City, flanked by rolling hills to the west and the sea to the east so that the micro-topography acceleration effect cannot be overlooked.In order to enhance the accuracy of design wind speed derived from the RFFT method, we conducted CFD numerical simulation using the actual terrain.The micro-topography acceleration ratio in Yueqing City was calculated to correct the typhoon full-track simulation result.The acceleration ratio is defined as the ratio of the horizontal mean wind speed on the terrain surface to the wind speed at the corresponding height of the incoming flow.

Initial Typhoon Design Wind Speed Distribution in Yueqing
The study encompasses the entirety of Yueqing City, with a surface roughness length z0 of 0.05m and a calculation accuracy of 0.03°.Based on the previous calculations, the 50-year-design wind speed at the 31# tower determined by the RFFT method is 33.7 m/s, which is higher than the design wind speed of Wenzhou provided by the code (30.98 m/s).The difference between the simulation result and the code recommended result mainly come from the following aspects: 1) Our study primarily examines the empirical distribution of extreme wind speed under typhoon climate, which may slightly differ from Gumbel distribution of wind speed under normal state climate utilized by the code.2) For wind field simulations, the surface roughness length is idealized and uniformly taken as 0.05m, which may introduce some errors.

Design Wind Speed Correction for Yueqing
To ensure the accuracy of the wind field simulation in Yueqing, the terrain has been properly extended to prevent significant height differences.The calculation range depicted in Fig. 5 as a red closed line area, spans 74km x 37km and has a maximum elevation of 1079m.The wind direction of the deviation accident is determined to be 296° and the average wind field of Yueqing under the two dominant wind directions of 135° and 45° are also considered taken into consideration.

Figure 5. Calculation terrain of Yueqing
The scale ratio of CFD numerical simulation is 1:500, and the calculation domain size is 16D (length) ×11D (width) ×5H (height), where D=70km and H=1km.The horizontal encrypted area grid measures 30 meters, while the expansion rate is 1.1.The first layer vertical grid size is 1m with the expansion rate is 1.07.The total number of grids in the calculation domain is about 320 million.For the boundary conditions and other primary parameter settings, refer to the literature [14].
To intuitively display the micro-terrain acceleration effect, the maximum value of the numerical simulation results of the acceleration ratio within the 0.3° grid range is selected to correct the initial extreme wind speed in Yueqing.The results are shown in Fig. 6, and the marked point in the figure is the location of the accident tower.When wind comes from a direction of 45°, the maximum acceleration ratio in the grid is 1.3023 with the design wind speed after correction of 43.89 m/s, while the wind direction is 135°, the maximum acceleration ratio in the grid is 1.6119 with the design wind speed after correction of 54.32 m/s.The results indicate that the incoming wind direction causes significant variations in the horizontal acceleration ratio in the downwind direction.If there is no mountain shelter in the front to block the incoming wind, the micro-topographic area may result in a higher acceleration ratio, leading to a significant rise in the design wind speed.When the accident wind direction is 296°, the horizontal acceleration ratio is 1.4248 with the design wind speed after correction of 48.02 m/s, which is lower than the corrected wind speed without a front mountain obstruction at a wind direction of 135°.This finding provides further evidence that the front mountain shelter effect greatly impacts the acceleration ratio.However, the corrected wind speed at 296°wind direction is slightly larger than the corrected wind speed at 45° wind direction (significant shading by the front mountain).The discrepancy might stem from the fact that the accident site is closer to the north mountain, which has a significantly direct shading impact on the area, and farther away from the west mountain, resulting in the redevelopment of the wind field over a certain distance after crossing the mountain.
Based on the extreme wind speed correction results for three wind directions, it is evident that the acceleration effect of micro-topography increases the design wind speed beyond the code design wind speed.Therefore, the acceleration effect of micro-topography area should be further considered when adopting typhoon simulation for the extreme wind speed estimation.The wind speed for typhoon design at the engineering site should be raised adequately to enhance the wind resistance reliability of the nearby transmission line.

Summary
This paper employs a random forest-based full-track simulation method to evaluate the typhoon resistance reliability for transmission lines.Additionally, we consider the micro-topography acceleration effect to correct the design wind speed.The following conclusions are obtained: (1) A simulation of typhoons in the Northwest Pacific Ocean was conducted using stochastic methods over 10000 years.The effectiveness of the RF-based typhoon full-track simulation method was verified using key parameters from 25 stations alongside the Chinese coast.
(2) The evaluation of extreme wind speeds for 31# tower of the 500kV Duling 5862 line was conducted, and the design wind speeds under the 50-year and 100-year return periods of this site were determined to be 33.7 m/s and 35.8 m/s, respectively.
(3) The distribution map of typhoon extreme wind speed in Wenzhou City was plotted, indicating that the typhoon extreme wind speed gradually decreased as it moves further inland.The design wind speed in Yueqing City was corrected by analyzing the horizontal acceleration ratio under varying wind directions.The results suggest that the micro-topographic area has a considerable impact on wind speed acceleration.The wind resistance reliability of the transmission line in Yueqing City was evaluated effectively and intuitively, which providing a reference for the typhoon resistance design of the transmission line in hilly areas.

Figure 1 .
Figure 1. 25 equidistant stations along the coast of mainland China

Figure 2 .
Figure 2. Comparison of key parameter statistics between simulated data and historical data

Figure 3 .
Figure 3. Statistical analysis of extreme wind speed at 31# tower, Line 5862

Fig. 4 (
b) displays the distribution of extreme wind speeds during the 50-year return period without topographical considerations.The result reveals that the range of extreme wind speeds at the coastal areas of Yueqing City falls between 32m/s and 34m/s.(a) Wenzhou (b) Yueqing