Recently, a number of wind power structures in tropical cyclone zones are damaged by typhoon. In order to study the failure mechanics and failure modes of wind power structure subjected to typhoon, the typhoon wind field in Dongtai wind farm is simulated based on the classical autoregressive (AR) model and a regional power-spectrum-density (PSD) model, and the simulated spectrum is verified to be in good agreement with the target spectrum. An integrated finite element (FE) model of wind power structure, composed of rotor, nacelle, tower, pile cap, and PHC piles, is established. Modal analysis reveals that pile stiffness decreases the structure’s natural frequencies, especially for high order frequencies. Structural responses under the simulated typhoon are calculated by dynamic analysis. Results show that tower buckling is the most prone failure mode of the structure. The horizontal displacement of the hub and the axial force of the most unfavorable piles are both under the limit. This study provides a way to the antityphoon design of large-scale wind power structures.
With the increase of investment of clean energy from governments, wind energy has grown enormously all over the world in the past decade and will stand to benefit from its role as both a source of energy security and a key to solving the problem of climate change in the future. Compared with the year 2011, wind power market grew by more than 10% in 2012, and the new global total installed wind power capacity at the end of 2012 was 282.5 GW, representing cumulative market growth of more than 19% [
It should be noted that more and more wind farms are established in tropical cyclone zones, making the wind turbine and its support structure have to face the threat of typhoon. For instance, typhoon Maemi struck the Miyakojima Island with an average speed of 38.4 m/s and a maximum gust of 74.1 m/s on September 11, 2003. All of the wind turbines on the island were extensively damaged. Three of six turbines collapsed and the others suffered from destructive damage, whose blade were broken or the nacelle cover drooped. Based on FEM simulation and wind response analysis, Ishihara et al. [
Although massive losses in coastal wind farms have been caused by typhoon, the failure mechanism and failure modes of wind power structures are not clear yet. Generally, modern wind turbines are designed mainly according to the international standard (IEC 61400-1) [
In offshore wind turbines, the structural responses are driven not only by wind but also by water wave. Consequently, the dynamic analysis of offshore wind turbines is more complex than that of land-based ones. Karimirad and Moan [
This paper aims at analyzing the potential failure modes of wind power structure subjected to typhoon and is organized as follows. The location and wind condition of Dongtai wind farm is introduced in Section
Dongtai wind farm is located in Dongtai City, Jiangsu Province, southeastern China, at 120°54′ east latitude and 32°47′ north longitude, as shown in Figure
Location of Dongtai wind farm.
Although Dongtai is not a typhoon landing site in general, it still has to face the threat of typhoon. For example, in 2009, typhoon Morakot passed through Dongtai with an average wind speed of 33 m/s and moved into East China Sea, as shown in Figure
The track map of typhoon Morakot.
The track map of typhoon Damrey.
According to [
Tropical cyclone classification.
Classification | Average wind speed (m/s) | Wind scale |
---|---|---|
Tropical depression (TD) | 10.8–17.1 | 6-7 |
Tropical storm (TS) | 17.2–24.4 | 8-9 |
Severe tropical storm (STS) | 24.5–32.6 | 10-11 |
Typhoon (TY) | 32.7–41.4 | 12-13 |
Severe typhoon (STY) | 41.5–50.9 | 14-15 |
Super typhoon (SuperTY) | ≥51.0 | ≥16 |
Natural wind consists of two components, that is, mean wind and fluctuating wind, and the latter represents turbulence and randomness. Consequently, the instantaneous velocity of wind can be described as
According to the random vibration theory, the fluctuating wind velocity can be regarded as a zero-mean Gaussian process and described by the power-spectrum-density (PSD) model in the frequency domain [
Discrete models of wind speed based on Box-Jenkins methods are used commonly in time-series analysis. These models, including autoregressive (AR) [
The covariance between
Considering that
Postmultiplying (
The cospectrum and the covariance function satisfy the Wiener-Khintchine equation; that is,
Considering that wind power structure is a typical slender structure, a simplified expression of
Postmultiplying (
The vector
Substituting
Based on the AR model, the fluctuating wind speeds at the height of 5 m, 15 m, 25 m, 35 m, 45 m, 55 m, and 65 m in the wind farm are simulated. For simplicity, the wind speed histories at the height of 5 m, 35 m, and 65 m are shown in Figures
Fluctuating wind speed histories at different heights.
At the height of 5 m
At the height of 35 m
At the height of 65 m
In order to verify the simulated wind speed history, the PSD of the simulated wind is compared with that of the target spectrum (see (
Comparison between the target spectrum and the simulated spectrum.
The wind rotor is a complex aerodynamic system that converts wind energy into mechanical power. The blade element theory is commonly used to calculate the wind load acting on the rotating rotor. Considering that the wind turbine should be shut down before the coming typhoon, the aerodynamic force acting on the rotor can be estimated by
The relationship between wind speed and wind pressure under ambient conditions is described by the Bernoulli equation:
Assuming that the wind speed is parallel to the normal direction of the rotor, which is the most unfavorable condition for the support structure, the wind load acting on each element of tower can be calculated by the following expression:
In order to study the dynamic responses of the wind power structure subjected to typhoon load varying in time, a transient dynamic analysis should be conducted. Based on the D’Alemberts principle and due to the discretization process of a continuous structure with FEs, the following equation of motion can be derived:
The Newmark integration method, which is an implicit time integration algorithm, is employed to solve (
It should be pointed out that damping plays an important role in the dynamic response of the wind power structure. Ambient vibration tests are always employed to estimate the damping ratio because of its strong advantage of being practical and economical, using the freely available ambient wind wave excitation. Shirzadeh et al. [
A modal analysis is performed to calculate the natural frequencies of the wind power structure. Omitting the damping matrix and force vector in (
Assume the general form of the solution is
The block Lanczos method is a very efficient and robust algorithm to perform a modal analysis for large models; thus it is employed on the platform of ANSYS [
As mentioned before, 1.5 MW wind turbines are installed in Dongtai wind farm. The tower is 62.75 m in height (the hub height is 65 m) and is fixed on the pile cap by an anchor ring. The tower consists of 3 segments of cylinder with dimensions shown in Table
Dimensions of the tower.
Segment | Lower diameter (m) | Upper diameter (m) | Height (m) | Shell thickness (m) | |
---|---|---|---|---|---|
Lower | Upper | ||||
Lower | 4.0 | 3.6 | 17.6 | 0.026 | 0.022 |
Middle | 3.6 | 3.0 | 22.4 | 0.022 | 0.016 |
Upper | 3.2 | 3.0 | 22.4 | 0.016 | 0.018 |
Anchor ring | 4.0 | 4.0 | 0.6 | 0.06 | 0.06 |
Material parameters.
Part | Elastic modulus (N·m−2) | Density (kg·m−3) | Poison’s ration | Yield strength (MPa) |
---|---|---|---|---|
Nacelle | 2.1 × 1011 | 563 | 0.3 | / |
Rotor | 2.1 × 1011 | 44.8 | 0.3 | / |
Tower | 2.1 × 1011 | 7850 | 0.3 | 345 |
Pile cap | 3.25 × 1010 | 2500 | 0.167 | / |
There are thirty PHC piles arranged under the pile cap. Six of them are along the inner circle with a diameter of 4.1 m, and the others are along the outer circle with a diameter of 16.8 m, as shown in Figure
Arrangement of piles.
The FE model of the wind power structure is shown in Figure
Element types of structural components.
Part | Nacelle | Rotor | Tower | Pile cap | PHC piles |
|
|||||
Element type | Solid 45 | Solid 45 | Shell 63 | Solid 45 | Combine 14 |
FE model of the wind power structure with piles.
Table
Natural frequencies of wind power structures.
Frequency order | Case 1: |
Case 2: |
|
---|---|---|---|
1 | 0.4093 | 0.4139 | 1.12% |
2 | 0.4150 | 0.4198 | 1.16% |
3 | 1.6073 | 1.6251 | 1.11% |
4 | 2.1899 | 2.2304 | 1.85% |
5 | 2.4607 | 2.5216 | 2.47% |
6 | 3.4773 | 4.7378 | 36.25% |
7 | 3.5011 | 4.9219 | 40.58% |
8 | 4.6193 | 5.8408 | 26.44% |
9 | 4.7378 | 5.8443 | 23.35% |
10 | 4.9218 | 6.1542 | 25.04% |
As a typical slender structure, wind power structure is sensitive to horizontal displacement. Consequently, the horizontal displacement of the hub (
The horizontal displacement history of the hub.
Under the wind load, the vertical stress of the tower, which is predominant, is small at the top and large at the bottom. Accordingly, the shell thickness of the tower gradually increases from the top to the bottom. However, the tower bottom is still prone to buckling. Figures
Von-Mises equivalent stress history at the bottom of tower.
The element at the windward side
The element at the leeward
Von-Mises equivalent stress at the bottom of tower while time = 111.25 sec.
At the windward side
At the leeward side
Owing to the large thickness of the anchor ring, the equivalent stress decreases rapidly and is under the steel’s yield strength at most time steps. Assuming the stress concentration is eliminated by engineering means, the yield possibility of the anchor ring can be reduced effectively (Figure
Von-Mises equivalent stress histories at the bottom of anchor ring.
The element at the windward
The element at the leeward
The maximum equivalent stress of the anchor ring also appears at time = 111.25 sec and the stress distribution is described in Figure
Von-Mises equivalent stress distribution of the anchor ring.
Each foundation pile bears different bending moment based on moment distribution method. Consequently, the piles at the windward side and the leeward side on the outer circle are the most unfavorable, and their axial force histories are shown in Figure
Axial force of the most unfavorable piles.
Pile at the windward side
Pile at the leeward side
Based on the classical AR model and a regional PSD model, the wind field of typhoon in a coastal wind farm is simulated and verified. A FE model of the wind power structure, including nacelle, rotor, tower, pile cap, and PHC piles, is established. Modal analysis shows that the natural frequencies of the wind power structure fixed on rigid foundation are higher than that of the structure with piles, which implies that piles decrease the structural stiffness and should be taken into account in the structural dynamic analysis. The primary and secondary frequencies of the structure are close to the predominant frequency of typhoon, leading to a resonance between the structure and the wind. Dynamic analysis reveals that tower buckling is the most prone failure mode of the wind power structure subjected to typhoon. The stress concentration at the junction of tower and anchor ring should be eliminated by welding seam with gradient thickness or bolts with enough strength. Although all piles are verified to be safe in this case, they still have to be checked, especially the unfavorable piles, under the conditions of typhoon.
The authors declare no possible conflict of interests.
The supports of National Natural Science Foundation of China (Grant no. 51308307), Zhejiang Provincial Natural Science Foundation of China (Grant no. LQ13E080008), Ningbo Natural Science Foundation (Grant no. 2014A610169), and Zhejiang Provincial Research Project of Technology Application for Public Welfare (Grant no. 2014C33009) are highly appreciated.