sustainability Article
Some Results on the Vulnerability Assessment of HAWTs Subjected to Wind and Seismic Actions Alberto Maria Avossa 1 , Cristoforo Demartino 2 , Pasquale Contestabile 1 , Francesco Ricciardelli 1 and Diego Vicinanza 1, * ID 1
2
*
Department of Civil Engineering, Design, Building and Environment, DICDEA, University of Campania “Luigi Vanvitelli”, Aversa 81031, Italy;
[email protected] (A.M.A.);
[email protected] (P.C.);
[email protected] (F.R.) College of Civil Engineering, Nanjing Technology University, Nanjing 211816, China;
[email protected] Correspondence:
[email protected]; Tel.: +39-081-501-0245
Received: 21 July 2017; Accepted: 22 August 2017; Published: 27 August 2017
Abstract: The spread of the wind energy industry has caused the construction of wind farms in areas prone to high seismic activity. Accordingly, the analysis of wind turbine loading associated with earthquakes is of crucial importance for an accurate assessment of their structural safety. Within this topic, this paper presents some preliminary results of a probabilistic framework intended to be used for the estimation of the probability of failure of Horizontal Axis Wind Turbine-supporting structures when subjected to the wind and seismic actions. In particular, the multi-hazard fragility curves of the wind turbine-supporting structure were calculated using Monte Carlo simulations. A decoupling approach consisting of aerodynamic analysis of the rigid rotor blade model and subsequent linear dynamic Finite Element analyses of the supporting structure, including aerodynamic damping, was used. The failure condition of the tower structure was estimated according to the stress design procedure proposed by EC3 for the buckling limit state assessment. Finally, the vulnerability assessment of HAWTs to wind and seismic actions was evaluated in terms of fragility curves describing the probability of failure of the supporting tower structure as a function of the Peak Ground Acceleration (PGA) for each parked and operational wind condition. In particular, the results highlight a probability of failure larger than 50% for high levels of seismic action (PGA greater than 0.7 g) combined with the rotor in parked condition (wind speed of 3 m/s) or in operational rated condition (wind speed of 11.4 m/s). Keywords: land-based wind turbine; wind action; seismic action; uncoupled analysis; aerodynamic damping; seismic response; fragility
1. Introduction The seismic response of Horizontal Axis Wind Turbines (HAWTs) has recently attracted growing interest, as the wind energy industry has increased its size, globally. As is well known, the power produced from wind is proportional to the third power of wind speed and to the second power of the rotor radius. Accordingly, to produce more electricity, one has to increase the rotor diameter and hub height. In these cases, the nacelle and rotor mass increase, therefore increasing the tower base moment due to the combined effect of wind thrust and seismic loads. Experience shows that, for high-rise buildings, a good design for wind action generally results in a reliable seismic retrofit [1]. In this case, the lateral loads are rather distributed along the height, and the effects of the wind are generally dominant with respect to those of the earthquake. On the other hand, for HAWTs, wind and seismic loads are mainly concentrated at the top of the tower support structure.
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Consequently, the Consequently, effects of seismic dominant when the turbinewhen increases in size, support structure. theloads effectscan of become seismic loads can become dominant the turbine as in the case of multi-megawatt HAWTs. increases in size, as in the case of multi-megawatt HAWTs. In this this context, context, itit is is important importantto toconsider considerthat thatmany manyareas areaswith withhigh highwind windresources resourcesalso alsohave have In a a high level of seismic hazard. These include the west coast of the US, the coasts of Japan and China, high level of seismic hazard. These include the west coast of the US, the coasts of Japan and China, and some some countries countries of of Europe. Europe. In In particular, particular, Figure Figure 11 shows shows the the European European maps maps of of the the peak peak ground ground and acceleration for 10% exceedance exceedance probability the mean mean wind wind speed speed and and mean mean wind wind acceleration for 10% probability in in 50 50 years years (a), (a), and and the power density at 50 m above ground level for 5 different topographical conditions (i.e., sheltered power density at 50 m above ground level for 5 different topographical conditions (i.e., sheltered terrain, open seasea coast, openopen sea and ridges) It can(b). be seen thatbe regions terrain, openplain, plain, coast, seahills andand hills and (b). ridges) It can seen characterized that regions by high wind resources are often seismic areas. In particular, this can be observed in the southern characterized by high wind resources are often seismic areas. In particular, this can be observed in European countries. The interested reader is referred to the COST action RELY for information on the the southern European countries. The interested reader is referred to the COST action RELY for distribution of turbines throughout European territory. European territory. information onwind the distribution of wind turbines throughout
(a)
(b)
Figure 1. (a) European Seismic Hazard Map showing the 10% exceedance probability in 50 years for Figure 1. (a) European Seismic Hazard Map showing the 10% exceedance probability in 50 years for Peak Ground Acceleration [2]; (b) European Wind Atlas [3]. Peak Ground Acceleration [2]; (b) European Wind Atlas [3].
In the past few years, researchers have tried to incorporate seismic loads into the structural In the past few years, researchers have tried to incorporate seismic loads into the structural assessment of wind turbines, and yet the work is limited. Early publications by Bazeos et al. and assessment of wind turbines, and yet the work is limited. Early publications by Bazeos et al. and Lavassas et al. [4,5] speculate that seismic design could become critical in regions with higher seismic Lavassas et al. [4,5] speculate that seismic design could become critical in regions with higher seismic hazard and less favorable soil conditions. Witcher [6] calculated the seismic response of a 2 MW hazard and less favorable soil conditions. Witcher [6] calculated the seismic response of a 2 MW upwind turbine with an 80 m diameter rotor and 60 m tower height in different loading scenarios upwind turbine with an 80 m diameter rotor and 60 m tower height in different loading scenarios (parked, operational and induced emergency shutdown), emphasizing the significance of time (parked, operational and induced emergency shutdown), emphasizing the significance of time domain domain analysis and the effects of aerodynamic damping. The author stated that operational wind analysis and the effects of aerodynamic damping. The author stated that operational wind turbines can turbines can experience total damping (aerodynamic plus structural) of close to 5%, and noted that, experience total damping (aerodynamic plus structural) of close to 5%, and noted that, conveniently, conveniently, this is the same value commonly prescribed by the seismic design spectra within many this is the same value commonly prescribed by the seismic design spectra within many building codes. building codes. However, this is clearly a mere coincidence as, though similar in value, the two However, this is clearly a mere coincidence as, though similar in value, the two damping mechanisms damping mechanisms are quite different. Subsequently, Prowell and Veers [7] performed a comprehensive study on the assessment of wind turbine seismic risk. Results showed that wind-
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are quite different. Subsequently, Prowell and Veers [7] performed a comprehensive study on the assessment of wind turbine seismic risk. Results showed that wind-driven loads could grow faster than seismic-driven loads in the absence of control systems. However, for modern turbines with a blade pitch control system, the dominant loads would be the seismic ones, as the turbine increased in size. Then, Prowell et al. [8] conducted experimental work on a 65 kW Nordtank wind turbine, applying earthquake motions in two horizontal directions, and concluding that the importance of considering seismic demand increases as the turbine grows in capacity. Again, Prowell et al. [9,10] showed that earthquakes can produce, in the NREL 5 MW HAWT, a bending-moment demand at the tower base well above the one from extreme wind events in operational, emergency shutdown and parked simulations. Moreover, an extensive investigation into the seismic response of a 1.65 MW Vestas turbine was conducted using ANSYS by Nuta [11]. The author developed fragility curves by performing incremental dynamic analyses and considering different intensity measures, damage measures, and damage states. However, aerodynamic loading was not considered in the analyses. In order to study the earthquake response under operational wind loads, full models, including the rotor-nacelle assembly (RNA) component, have generally been preferred over simplified models. Recently, full system models have been used in conjunction with fully-coupled, nonlinear time-domain simulations capable of accounting for inherent coupling between aerodynamic and seismic response [12]. Based on this approach, a complete Finite Element model that accounts for flexibility of the blades in the flapping direction, the bending and twisting flexibility of the tower, and the gyroscopic effects of the rotor has been proposed by Diaz and Suarez [13]. They investigated the seismic response of a 76 m high, 1.65 MW HAWT, and showed that stresses at some tower sections may exceed those from extreme winds. Moreover, a Finite Element model of the NREL 5 MW HAWT involving shell elements with nonlinear material behavior for the tower, beam elements for the blades, and a coupling joint between rotor and rigid nacelle has been developed by Asareh [14] for fragility analyses under operational loads. Although fully-coupled, nonlinear time-domain simulations are certainly most suitable to carry out a numerical solution for seismic assessment, the main disadvantage is that computational costs may be significant. As an alternative, an uncoupled approach, where the response to simultaneous wind and earthquake loads is obtained by combining two uncoupled analyses, one under wind and another under earthquake only, can be applied [15]. In this manner, the response to a given wind state, once computed, could be combined with the response to different potential earthquake events, with a significant reduction of computational costs with respect to fully-coupled time-domain simulations. International Standards such as IEC 61400-1 [16] and Guidelines such as ASCE-AWEA RP2011 [17] allow the combination of uncoupled analyses, instead of performing fully-coupled, nonlinear time-domain simulations. To address these issues, uncoupled analyses, where separate wind and earthquake responses are both computed in the time domain would be desirable, as they would allow nonlinearities, such as those deriving from foundation or structural modelling, to be considered directly in the structural model. It is apparent that the implementation of the uncoupled approach requires an appropriate level of aerodynamic damping, for which there is only little data available in the literature. Recently, Valamanesh et al. [18] presented a closed-form solution for the longitudinal and transversal aerodynamic damping of HAWTs. The formulation was intended as a convenient method to include the effect of aerodynamic damping in the seismic analysis of HAWTs through multibody dynamic analysis. While there is extensive analytical and empirical information on the seismic response and vulnerability of buildings and other common structures, similar data are not available for wind turbines. In fact, wind turbine installations have not yet experienced severe ground shaking, given their recent installation in highly seismic regions; the analytical tools for the design also seem to be sparse, with more focus on operational aspects than their seismic performance.
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Within this topic, this paper presents some results on the multi-risk structural response assessment of a 5-MW land-based HAWT subjected to wind and seismic actions, to be used in a probabilistic Sustainability 2017, 9, 1525 4 of 16 framework. First, the specifications of the HAWT considered are presented. Then, the numerical tools used to generate random wind and seismic loadings are introduced. Subsequently, a decoupled decoupled tocoupled solvingequations the coupled motionmodel of an ofaeroelastic model of approach toapproach solving the of theequations motion ofof anthe aeroelastic HAWTs under wind HAWTs under windisand seismic and loading is presented Toofthis aim, the concept of and seismic loading presented discussed. To thisand aim,discussed. the concept aerodynamic damping aerodynamic damping is used. Again, numerical Monte Carlo simulations are performed to estimate is used. Again, numerical Monte Carlo simulations are performed to estimate the distribution of the the distribution of the maximum bending moment atinthe HAWTloadings tower base in different random maximum bending moment generated at the HAWTgenerated tower base random and in loadings in different modes. Finally, a failure statefragility is determined fragility operationand modes. Finally,operation a failure state is determined allowing curves allowing to be plotted and curves to be plotted and vulnerability assessment to be carried out. vulnerability assessment to be carried out.
2. 2. Case Case Study Study of of 55 MW MW NREL NREL Land-Based Land-Based HAWT HAWT The impact of ofthe thecombined combinedwind wind and seismic action effects onstructural the structural response of a The impact and seismic action effects on the response of a HAWT HAWT is evaluated on a dynamic of 5land-based MW land-based developed by NREL, is evaluated on a dynamic model model of 5 MW turbineturbine developed by NREL, whosewhose main main specifications are provided Table 1. This windisgenerator is three-bladed, an upwind, variable-speed three-bladed, specifications are provided in Table in 1. This wind generator an upwind, variable-speed andmachine. variable-pitch machine. Each blade of the land-based turbine composed of eight and variable-pitch Each blade of the land-based turbine is composed of is eight segments, each segments, each with a different airfoil designation (17 sections with three cylinders—see Table 1); the with a different airfoil designation (17 sections with three cylinders—see Table 1); the maximum chord ◦ maximum chord is 4.652 m, and the maximum twist angle θ is 13.08°. The turbine has a rotor diameter is 4.652 m, and the maximum twist angle θ is 13.08 . The turbine has a rotor diameter of 126 m and a of 126 m and aoftower 87.60 m withand cut-in, rated, and speeds cut-outof wind speeds 3 m/s, m/s tower height 87.60height m withofcut-in, rated, cut-out wind 3 m/s, 11.4of m/s and11.4 25 m/s, and 25 m/s, respectively. The pitch and rotor speed are controlled to optimize power output for any respectively. The pitch and rotor speed are controlled to optimize power output for any wind speed. wind speed is associated with nearon zero on the generator, with no of Cut-inspeed. speedCut-in is associated with near zero torque thetorque generator, with no generation of generation power. Rated power. Rated speed is thethe point where thesystem pitch control system is the activated, and the blades start wind speed is wind the point where pitch control is activated, and blades start to be rotated so to be rotated so that the torque and generated power remain at a constant at higher wind speeds. that the torque and generated power remain at a constant at higher wind speeds. Cut-out wind speed Cut-out speed shuts is when the in turbine shutsspeeds down in high wind to prevent the damaged. structure is when wind the turbine down high wind to prevent thespeeds structure from being from being damaged. For steady-state conditions, the dependence of rotor speed and blade on For steady-state conditions, the dependence of rotor speed and blade pitch on wind speeds pitch between wind speeds between cut-in and cut-out is shown in Figure 2, where the trend of the angular velocity cut-in and cut-out is shown in Figure 2, where the trend of the angular velocity of the rotor Ω and of Ω and of the Tip Speed Ratio TSR (ratiotip between the blade velocity wind of the the rotor Tip Speed Ratio TSR (ratio between the blade velocity and the tip wind speed)and as athe function speed) as a function of the wind speed are depicted. All the results shown for the operational of the wind speed are depicted. All the results shown for the operational conditions are based on conditions areofbased combinations of and wind speed, rotor speed, and blade 2, pitch as specified in combinations windon speed, rotor speed, blade pitch as specified in Figure whereas the results Figure 2, whereas theconditions results presented foronparked conditions on a blades. stationary rotor with presented for parked are based a stationary rotor are withbased feathered feathered blades. 25.0 Angular Velocity (rpm) Pitch Angle (deg) Tip Speed Ratio - TSR
20.0
Rated Wind Speed
15.0
10.0
Cut out Wind Speed
5.0
Cut in Wind Speed
0.0
0.0
5.0
10.0
15.0
20.0
25.0
Vw (m/s) Figure Figure 2. 2. Values Values of of rotor rotor speed speed Ω, Ω, blade blade pitch, pitch, and and tip tip speed speed ratio ratio (TSR) (TSR) versus versus wind wind speed speed for for operational m/s) and operational conditions conditions between between cut-in cut-in (3 (3 m/s) andcut-out cut-out (25 (25 m/s) m/s)for forthe the5-MW 5-MWland-based land-basedturbine. turbine.
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Table 1. Specifications and blade sections of 5 MW HAWT. Characteristic
Value
Section
r (m)
Airfoil Type
Twist Angle (◦ )
Chord (m)
Power Output Rotor diameter Hub height Cut in wind speed Rated wind speed Cut out wind speed Rated Tip Speed Cut-in rotor speed Rated rotor speed Overhang—Shaft Tilt—Precone Number of blades Nacelle Mass Hub Mass Rotor Mass Tower Mass Tower top diameter—wall thickness Tower base diameter—wall thickness
5 MW 126 m 87.60 m 3 m/s 11.4 m/s 25 m/s 80 m/s 6.9 rpm 12.1 rpm 5 m—5◦ —2.5◦ 3 240,000 kg 56780 kg 53220 kg 347460 kg 3.87 m—0.019 m 6.00 m—0.027 m
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
2.86 5.60 8.33 11.75 15.85 19.95 24.05 28.15 32.25 36.35 40.45 44.55 48.65 52.75 56.16 58.90 61.63
Cylnder 1 Cylnder 1 Cylnder 2 DU40_A17 DU35_A17 DU35_A17 DU30_A17 DU25_A17 DU25_A17 DU21_A17 DU21_A17 NACA64_A17 NACA64_A17 NACA64_A17 NACA64_A17 NACA64_A17 NACA64_A17
13.080 13.080 13.080 13.080 11.480 10.162 9.011 7.795 6.544 5.361 4.188 3.125 2.319 1.526 0.863 0.370 0.106
3.542 3.854 4.167 4.557 4.652 4.458 4.249 4.007 3.748 3.502 3.256 3.010 2.764 2.518 2.313 2.086 1.419
The tower is the main structural component of a HAWT structure; it is composed of a steel tubular cantilever beam with a hollow circular cross-section. Specifically, the tower structure has a total height of 87.60 m, with an external diameter of 6.00 m at the base and 3.87 m at the top. Shell thicknesses vary from 27 mm at the base to 19 mm at the top. Steel density was taken to be 8500 kg/m3 to account for paint, bolts, welds, and flanges that are not included in the tower thickness data. Further specifications of this HAWT are given in Jonkman et al. [19]. 3. Wind and Seismic Actions The assessment of the structural response of a HAWT requires the definition of wind loads and seismic loads. To calculate the wind loads on the blade, random wind field velocity time histories must be defined. Generally, wind velocity can be decomposed into mean and fluctuating parts. Given that the wind can be treated as a random process, its mean velocity can be obtained by probabilistic wind climate studies, and the fluctuating wind can be defined by a power spectral density and a coherence function. Different values of the mean wind velocity are here considered; these are the cut-in (3 m/s), the rated (11.4 m/s) and the cut-out (25 m/s) velocities, evaluated at the hub height (equal to 87.60 m). The vertical wind profile, U(z), is assumed to be a logarithmic profile in atmospherically neutral conditions: U (z) = U (zr ) ln(z/z0 )/ln(zr /z0 ) (1) where z0 is the roughness length, U(zr ) is the mean velocity at the reference height, corresponding to the hub height zr . A value for z0 equal to 0.05 m for all the scenarios is assumed, characterizing farmland with boundary edges and occasional buildings. For each value of the mean wind speed, fifteen turbulent wind fields (grid 20 × 20 with a step of 6.68 m) were generated using the Sandia Method [20] implemented in Q-Blade [21], setting the minimum value of 10% for the turbulence intensity. The mean wind speed profile for the three conditions considered and a sample of the instantaneous turbulent wind field for the rated wind speed condition are represented in Figure 3. On the other hand, the seismic input action is represented by fifteen artificial accelerograms. Specifically, the input signals were generated using the SeismoSignal software [22] with a total duration of 40 s, and a strong motion duration of 20 s, according to EC8 [23]. The accelerograms were selected such that their mean spectrum was never lower than 90% of the corresponding EC8 elastic spectrum for type C soil with a 5% damping ratio. In Figure 4, the acceleration spectra of the generated artificial input and the EC8 target spectrum are reported. These input signals were scaled to a peak ground
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duration s, and a strong motion duration s, according to EC8 accelerograms duration of 40ofs,40 and a strong motion duration of 20ofs,20 according to EC8 [23].[23]. The The accelerograms werewere selected such that their mean spectrum was never lower than 90% of the corresponding EC8 elastic selected such that their mean spectrum was never lower than 90% of the corresponding EC8 elastic Sustainability 2017, 9, 1525 6 of 16 the spectrum for type C soil with a 5% damping ratio. In Figure 4, the acceleration spectra of spectrum for type C soil with a 5% damping ratio. In Figure 4, the acceleration spectra of the generated artificial input the EC8 target spectrum are reported. These input signals scaled generated artificial input and and the EC8 target spectrum are reported. These input signals werewere scaled to a peak ground acceleration ranging from 0 to 1 g, with a step of 0.05 g. The scaling of the signals to a peak ground acceleration ranging from 0 to 1 g, with a step of 0.05 g. The scaling of the signals acceleration ranging from 0 to 1 g, with a step of 0.05 g. The scaling of the signals was done varying only varying the amplitude, leaving the same frequency content the same shape was was donedone varying onlyonly the amplitude, and and leaving the same frequency content (i.e.,(i.e., the same shape the amplitude, and leaving the same frequency content (i.e., the same shape of the response spectrum). of response the response spectrum). of the spectrum).
120 120 100 100
Height (m)
Height (m)
160 160 140 140
80
80
60
60
40
40
20
20
0
0 0
Cut-in Cut-in Rated Rated Cut-outCut-out
0
5
5 10 10 15 15 20 20 25 WindWind SpeedSpeed (m/s)(m/s)
25 30
30
(a) (a)
(b) (b)
3.0
3.0
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0 0.0 0.0 0.5
1.0 1.0
Artificial Artificial Input Input EC8-CEC8-C Type 1Type 1
0.5 0.5
Sa / PGA
3.5
Sa / PGA
3.5
Sa (g)
Sa (g)
Figure (a) Vertical speed profiles; (b) Example the instantaneous turbulent 3. (a) meanmean windwind speed profiles; (b) Example of theofinstantaneous turbulent windwind fieldfield Figure (a)3.Vertical Vertical for rated speed condition and centered on hub axis. for rated windwind speed condition and centered centered on hub axis. on hub axis.
0.0 0.0 0.0 0.0
10.0 10.0 20.0 20.0 30.0 30.0 40.0 40.0
-0.5 -0.5 0.5 1.0
1.0 1.5
1.5 2.0
2.0 2.5
2.5 3.0
Period Period (s) (s)
(a) (a)
3.0 3.5
3.5 4.0
4.0
-1.0 -1.0 t (s) t (s)
(b) (b)
Figure (a) Acceleration response spectra diagram and comparison elastic target spectrum; Figure 4. (a)4.Acceleration response spectra diagram and comparison withwith EC8 EC8 elastic target spectrum; Figure 4. (a) Acceleration response spectra diagram and comparison with EC8 elastic target spectrum; (b) Sample an artificial earthquake signal. (b) Sample of anofartificial earthquake inputinput signal. (b) Sample of an artificial earthquake input signal.
4. Aeroelastic Model Decoupled Approach 4. Aeroelastic Model and and Decoupled Approach 4. Aeroelastic Model and Decoupled Approach Wind turbines are highly dynamic tightly coupled systems characterize a multiphysics Wind turbines are highly dynamic and and tightly coupled systems that that characterize a multiphysics Wind turbines are highly dynamic and tightly coupled systems thatchallenges characterize a multiphysics problem, and their structural design and assessment pose specific [24,25]. problem, and their structural design and assessment pose specific challenges [24,25]. The The rotorrotor of a of a problem, and their structural design and assessment pose specific challenges [24,25]. The rotor of a wind turbine is subject to aeroelastic effects result in feedback of rotor the rotor motion on forces the forces wind turbine is subject to aeroelastic effects that that result in feedback of the motion on the windacting turbine is to aeroelastic effects that result in feedback of the rotor motion on the forces on supporting thesubject supporting structure. acting on the structure. acting onThe the supporting structure. aerodynamic forces strongly depend on wind the wind speed experienced by blades, the blades, The aerodynamic forces strongly depend on the speed fieldfield experienced by the The aerodynamic forces strongly depend on the wind speed field experienced by the blades, the which is irregular an irregular environmental condition characterized turbulence. Moreover, which is an environmental condition characterized by by turbulence. Moreover, the which is an irregular environmental condition characterized by turbulence. Moreover, the aerodynamic aerodynamic forces also depend on the dynamic response of the HAWT support structure when aerodynamic forces also depend on the dynamic response of the HAWT support structure when forces also depend on the dynamic response of In thefact, HAWT support structure whendue subjected to wind subjected to wind and seismic excitation. the tower top oscillations to ground motion subjected to wind and seismic excitation. In fact, the tower top oscillations due to ground motion and affect seismic In fact, the tower top oscillations duewind to ground motion affectdepending the rotor theexcitation. rotor aerodynamics, in particular the relative speed at the blades, affect the rotor aerodynamics, and and in particular the relative wind speed at the blades, depending on on aerodynamics, and in particular the relative wind speed at the blades, depending on which the which the aerodynamic loads, lift and forces on blades, the blades, are calculated. An essential which the aerodynamic loads, i.e., i.e., lift and dragdrag forces on the are calculated. An essential aerodynamic loads, i.e., lift and drag forces on the blades, are calculated. An essential outline of an is outline of aeroelastic an aeroelastic model for study the study of dynamic the dynamic response of HAWT the HAWT structure outline of an model for the of the response of the structure is aeroelastic model for the of the and dynamic response the HAWT structure is depicted in Figure 5a depicted in Figure 5astudy (black while the of general equation of motion canexpressed be expressed depicted in Figure 5a (black lineslines and text),text), while the general equation of motion can be as: as: (black lines and text), while the general equation of motion can be expressed as: MHAWT x¨ + CHAWT x˙ + KHAWT x = Faerodyn (U, x¨ , x˙ , x) - MHAWT I x¨ g (t)
(2)
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where MHAWT , CHAWT and KHAWT are the structural mass, damping and stiffness matrices, respectively; x¨ , x˙ and x are the time-dependent acceleration, velocity, and displacement vectors, respectively; Faerodyn (U, x¨ , x˙ , x) is the load vector due to the aerodynamic forces on the rotor blades, MHAWT I x¨ g (t) is the seismic force vector, wherein I is the influence coefficient vector and x¨ g (t) is the input 2017, 9, 1525 7 of 16 groundSustainability acceleration. Therefore, in general, the aerodynamic force vector Faerodyn is dependent on the wind action and on the dynamic response of the overall system. According to this equation of (2) MHAWThave ẍ + CHAWT + KHAWT x = Faerodyn (U,with ẍ, ẋ, fully-coupled, x) - MHAWT I ẍg(t)nonlinear time-domain motion, full system models to beẋused in conjunction wherecapable MHAWT, CHAWT and KHAWT arefor the structural mass, coupling damping and stiffness matrices, respectively; simulation of accounting the inherent between aerodynamic and seismic ẍ , ẋ and x are the time-dependent acceleration, velocity, and displacement vectors, respectively; responses. Although fully-coupled time-domain simulations are the most suitable choice to carry out a Faerodyn (U, ẍ, ẋ, x) is the load vector due to the aerodynamic forces on the rotor blades, MHAWT I ẍg(t) is numerical solution for seismic assessment, their disadvantage is their high computational cost, which the seismic force vector, wherein I is the influence coefficient vector and ẍg(t) is the input ground is quiteacceleration. prohibitiveTherefore, when several analyses have to be implemented for different environmental states in general, the aerodynamic force vector Faerodyn is dependent on the wind and system parameters. action and on the dynamic response of the overall system. According to this equation of motion, full Insystem this study, aerodynamic and seismic loads acting on the structural model of the HAWT modelsthe have to be used in conjunction with fully-coupled, nonlinear time-domain simulation capable of accounting for the inherent coupling between aerodynamic and seismic responses. were evaluated by decoupling the aerodynamic behavior of the rotor from the dynamic response of Although fully-coupled simulations are the mostforce suitable choice to as: carry out a the support structure. Using time-domain this assumption, the aerodynamic is expressed numerical solution for seismic assessment, their disadvantage is their high computational cost, which is quite prohibitive when several analyses have to be implemented for different environmental states F (U, x¨ , x˙ , x) = Faerodyn (U) - Ca (U) · x˙ (3) and system parameters. aerodyn In this study, the aerodynamic and seismic loads acting on the structural model of the HAWT where the vector to the aerodynamic onofthe only onofthe wind wereload evaluated bydue decoupling the aerodynamicforces behavior therotor rotor blades from thedepends dynamic response speed U, Ca is the aerodynamic damping the matrix. theand support structure. Using this assumption, aerodynamic force is expressed as:
First, the response of the rotor with rigid blades neglecting the dynamic behavior of the tower (3) Faerodyn (U, ẍ, ẋ, x) = Faerodyn (U) – Ca (U) ·ẋ structures is evaluated. Then, the loads derived from the first step are applied to the structural dynamic where the load vector due to the aerodynamic forces on the rotor blades depends only on the wind model of the tower considering the aerodynamic damping. The structural approximate response of the speed U, and Ca is the aerodynamic damping matrix. HAWT was calculated by applying the wind thrust of the rotor and the seismic excitation to a structural First, the response of the rotor with rigid blades neglecting the dynamic behavior of the tower dynamic model of the towerThen, neglecting anyderived feedback (see 6).are In particular, thestructural HAWT support structures is evaluated. the loads from theFigure first step applied to the structure is modelled using the SAP2000 Finite Element software, and two different time-history dynamic model of the tower considering the aerodynamic damping. The structural approximate response of the HAWT was calculated by applying the wind thrust of the rotor and the seismic analyses are carried out, applying the wind action as a time-dependent rotor thrust to the tower top, to a structural dynamic of the respectively. tower neglecting any feedback (see Figure 6). In and theexcitation seismic action as a tower basemodel excitation, particular, the HAWT support structure is modelled using the SAP2000 Finite Element software, and Within this decoupled approach, the aeroelastic interaction was taken into account through two different time-history analyses are carried out, applying the wind action as a time-dependent a proper definition of aerodynamic damping [26]. When the wind turbine moves into the wind (tower rotor thrust to the tower top, and the seismic action as a tower base excitation, respectively. motion in the along-wind direction), thethe relative wind velocitywas experienced by thethrough blades achanges, Within this decoupled approach, aeroelastic interaction taken into account and theproper aerodynamic force in the opposite In contrast, moving out of the wind definition of aerodynamic dampingdirection [26]. Whenincreases. the wind turbine moves into the wind (tower in the along-wind direction), the relativeThis windresults velocityinexperienced by additional the blades changes, results motion in a decrease of the force in that direction. an apparent damping force and thethe aerodynamic force in the of opposite direction increases. contrast, moving outsignals of the wind that reduces horizontal motion the wind turbine. The In aerodynamic force are thereby results in a decrease of the force in that direction. This results in an apparent additional damping explicitly dependent on the motions of the turbine, and this means an accurate structural analysis of force that reduces the horizontal motion of the wind turbine. The aerodynamic force signals are a wind thereby turbineexplicitly has to bedependent coupled with aerodynamic rotor simulation, in order to take tower motions on thean motions of the turbine, and this means an accurate structural into account. This decoupled pattern divided in rotor aerodynamic model and structural analysis of a wind turbine has to be coupled with an aerodynamic rotor simulation, in order to takedynamic tower aerodynamic motions into account. This decoupled pattern divided5b. in rotor aerodynamic model and model with damping is also depicted in Figure structural dynamic model with aerodynamic damping is also depicted in Figure 5b.
(a)
(b)
Figure 5. (a) Aeroelastic model and its decoupling into (b) aerodynamic model, structural model, and
Figure 5. (a) Aeroelastic model and its decoupling into (b) aerodynamic model, structural model, aerodynamic damping. and aerodynamic damping.
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ẍ
Figure6.6.Aerodynamic Aerodynamic model damping of land-based HAWT. Figure model and andstructural structuralmodel modelwith withaerodynamic aerodynamic damping of land-based HAWT.
The use of the uncoupled approach was validated for NREL 5MW land-based HAWTs by The use of the uncoupled approach was validated for NREL 5MW land-based HAWTs by Santangelo et al. [15]. In particular, comparative analyses in the time domain between the results Santangelo et al. [15]. In particular, comparative analyses in the time domain between the results obtained by fully-coupled simulation performed in GH BLADED [27] and those obtained by linear obtained by fully-coupled simulation performed in GH BLADED [27] and those obtained by combination of separate wind and earthquake responses, the latter computed by adding different linear combination of separate wind and earthquake responses, the latter computed by adding levels of aerodynamic damping, are carried out. The results show that errors in bending moment and different levels aerodynamic damping, are carried The results thatoferrors in bending shear forces areofwithin engineering margins, which isout. encouraging forshow the use the uncoupling moment and shear forces are within engineering margins, which is encouraging for the useASCEof the approach, and confirm that a value of 4% for the aerodynamic damping, recommended by uncoupling approach, and confirm that studies a value of 4% for thereasonably aerodynamic by AWEA RP2011 [17] and in previous [6–18], can alsodamping, be used recommended in time-domain ASCE-AWEA RP2011 [17] and in previous studies [6–18], can reasonably also be used in time-domain uncoupled analyses. uncoupled analyses. 5. Aerodynamic Model 5. Aerodynamic Model The aerodynamic analyses of the rotor subjected to wind loads is here carried out in the time The aerodynamic analyses of the rotor subjected to wind loads is here carried out in the time domain by means of the Lifting Line–Free Vortex Wake algorithm implemented in Q-Blade [28], domain byfollowing means ofthe thework Lifting Line–Free Vortex algorithm implemented in Q-Blade [28], generally of Van Garrel [29], andWake considering a rigid behavior of the rotor blades generally following the workThe of Van Garrel [29], and considering a rigidtobehavior of of thethe rotor blades and of the tower structure. lifting line simulation method belongs the family so-called and of the tower structure. The lifting line simulation method belongs to the family of the so-called “vortex methods”. Using vortex methods, the flow field is modelled as inviscid, incompressible and “vortex methods”. vortex the field of is straight modelled inviscid, and irrotational; vortexUsing elements aremethods, introduced inflow the form oras curved line incompressible segments to model irrotational; vortex elements are introduced in the form of straight or curved line segments to model both the rotor blades and the wake. The vortex lattice method models rotor blades with a lattice of both the rotor bladeswhich and the vortex lattice method The models rotor blades with the a lattice of horseshoe vortices, are wake. locatedThe on the blade mid-surface. panel method models blades horseshoe vortices, which are located the quarter blade mid-surface. panel method models the blades with a single line of vortices, located on at the chord pointsThe of the blade. Nonlinearity exists in with a single line of vortices, located at the quarter chord points of the blade. Nonlinearity the fact that the circulation, computed for the bound vortices on the lifting line, is obtained exists from innonlinear the fact that the drag circulation, for the bound vortices on the compared lifting line,toisBEM obtained from lift and polars. computed One large advantage of vortex methods, methods, nonlinear lifttoand polars. One large of flow vortex methods, to BEM methods, is that, due the drag sound modelling of theadvantage macroscopic physics, onlycompared very few empirical models isrelated that, due to the soundfluid modelling of the macroscopic physics, few empirical models to microscopic dynamics, where boundaryflow layer effects only play very an important role (such as related to microscopic dynamics, boundary layer effects an important (such dynamic stall or stall fluid delay), need to where be added. Additionally, vortexplay methods not onlyrole provide assimulation dynamic stall or stall delay), the need to beperformance added. Additionally, vortex methods not result only provide results concerning rotor and the blade loads but also in the simulation results concerning the rotor performance and the blade loads but also result in the unsteady unsteady velocity field around the rotor and wake at every time step. velocity field around the rotor and wake at every time step. 6. Structural Model of the Tower and Aerodynamic Damping 6. Structural Model of the Tower and Aerodynamic Damping The structural dynamic model of the HAWT is an Euler-Bernoulli cantilever discretized by 11 The structural model ofconnected the HAWT an Euler-Bernoulli cantilever discretized by nodes into 10-beamdynamic tapered elements, to aisrigid foundation; hence the elasticity of the pile 11and nodes into 10-beam elements, a rigid foundation; hence the elasticity of the of the soil was nottapered considered in thisconnected paper. Thetomass of the nacelle and rotor are concentrated pile and of the soil was not considered in this paper. The mass of the nacelle and rotor are concentrated at the top node, while the tower mass is concentrated at each corresponding node of the cantilever atbeam, the top node, while towermodel mass is each corresponding node of model the cantilever representing thethe flexible ofconcentrated the tower. A at pattern of the tower structural and of beam, representing the flexible of the tower. A pattern of theinput towerisstructural model 5. and of the external loads applied to it, model consisting of rotor thrust and seismic shown in Figure The the external loads applied to it, consisting of rotor thrust and seismic input is shown in Figure 5. equation of motion for the tower can be expressed as: The equation of motion for the tower can be expressed as: (4) MTF ẍ + CTF ẋ + KTF x = FRotor (t) - MTF I ẍg(t)
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MTF x¨ + CTF x˙ + KTF x = FRotor (t) - MTF I x¨ g (t)
(4)
where MTF , CTF and KTF , are the tower mass, damping and stiffness matrices, respectively; x¨ , x˙ and x areSustainability the time-dependent acceleration, velocity, and displacement vectors, respectively; FRotor 2017, 9, 1525 9 of 16(t) is the rotor thrust load vector, whose only non-nil component is that applied at the top node, MTF I x¨ g (t) MTFforce , CTF and KTF, wherein are the tower mass, damping stiffness matrices, respectively; ẋ and x the is thewhere seismic vector, I = [1,1,1, . . . ..,1]T and is the influence coefficient vectorẍ,and x¨ g (t) are the time-dependent acceleration, velocity, and displacement vectors, respectively; FRotor (t) is the ground acceleration time history. The total damping in the model is the sum of structural damping, rotor thrust load vector, whose only non-nil component is that applied at the top node, MTF I ẍg(t) is assumed to be 1% of critical, and aerodynamic damping calculated for each parked/operational the seismic force vector, wherein I = [1,1,1,…..,1]T is the influence coefficient vector and ẍg(t) the condition using the closed form solution proposed by Valamanesh and Myers [18]. As mentioned ground acceleration time history. The total damping in the model is the sum of structural damping, above, this decoupling canaerodynamic be applied because loadsfor and seismic excitation can be assumed to be 1% ofapproach critical, and dampingwind calculated each parked/operational seen condition as independent phenomena. Aerodynamic damping is accounted for as an additional structural using the closed form solution proposed by Valamanesh and Myers [18]. As mentioned damping thedecoupling Finite Element (FE)can model of thebecause supporting Figure 6). An accurate above,inthis approach be applied wind structure loads and (see seismic excitation can be seen as of independent phenomena. Aerodynamic damping isdamping accountedwas for ascarried an additional structural estimation the fore-aft and side-to-side aerodynamic out here using the dampingsolution in the Finite Element of the supporting Figure 6). theory, An accurate closed-form proposed in(FE) [18].model This solution, startingstructure from the(see blade BEM bases its estimation of the fore-aft and side-to-side aerodynamic damping was carried out here using the derivation on several simplifying assumptions, most notably a rigid rotor and a steady, uniform closed-form solution proposed in [18]. This solution, starting from the blade BEM theory, bases its of wind oriented perpendicular to the rotor plane. This approach permits the accurate consideration derivation on several simplifying assumptions, most notably a rigid rotor and a steady, uniform wind aerodynamic damping within software with more refined structural analysis features. The trends of oriented perpendicular to the rotor plane. This approach permits the accurate consideration of the aerodynamic damping ratio, here estimated for the case of the NREL 5-MW HAWT in fore-aft aerodynamic damping within software with more refined structural analysis features. The trends of direction and in side-to-side the above-mentioned and HAWT assuming air density the aerodynamic dampingdirection, ratio, hereusing estimated for the case of theapproach NREL 5-MW in fore-aft 3 values of 1.25 and kg/m , are presented in Figure 7. the These estimates are provided a function direction in side-to-side direction, using above-mentioned approach as and assumingofairwind 3, are presented speed for both parked operational conditions. InThese the fore-aft direction, the as predictions of the density values of 1.25and kg/m in Figure 7. estimates are provided a function of aerodynamic damping result in a maximum value of 0.1% for the parked condition, and in a mean wind speed for both parked and operational conditions. In the fore-aft direction, the predictions of result in aand maximum value of 0.1% for the parked condition, and in a mean valuethe ofaerodynamic 3.7% (rangedamping between 2.0% 5.2%) for operational conditions. The predictions for the value of direction 3.7% (range between 2.0% aerodynamic and 5.2%) for operational Thevalue predictions for the sideside-to-side result in lower damping, conditions. with a mean of 1% (range between direction result in lower aerodynamic 0.3%to-side and 1.5%) for the operational condition. damping, with a mean value of 1% (range between 0.3%
Aerodynamic Damping (%)
and 1.5%) for the operational condition.
FORE AFT DIRECTION SIDE TO SIDE DIRECTION
6.0
5.0 Cut in Wind Speed
4.0
Cut out Wind Speed
3.0 Rated Wind Speed
2.0 Operational
1.0
Parked
0.0 0
5
10 15 Vw (m/s)
20
25
Figure 7. Aerodynamicdamping damping in in the the fore-aft fore-aft and during parked and and Figure 7. Aerodynamic and side-to-side side-to-sidedirections directions during parked operational conditions for 5-MW land-based HAWT. operational conditions for 5-MW land-based HAWT.
These values are quite consistent with the recommendations by ASCE/AWEA RP2011, which These values aredamping quite consistent recommendations by ASCE/AWEA which state that the total should bewith set tothe 1% during parked conditions and 5% during RP2011, operational stateconditions, that the total damping should be set to 1% during parked conditions and 5% during operational regardless of the direction of vibration. Given the aerodynamic damping in the fore-aft conditions, regardless of theofdirection of vibration. Givendamping the aerodynamic damping the fore-aft and side-to-side direction the HAWT, the aerodynamic in any direction can beinobtained using a transformation and side-to-side direction matrix. of the HAWT, the aerodynamic damping in any direction can be obtained
using a transformation matrix.
7. Aerodynamic and Seismic Response of Wind Turbine
7. Aerodynamic and Seismic Response Wind Turbine The aerodynamic response of theofHAWT rotor blades was evaluated in the time domain calculating the time histories thrust at therotor rotorblades using Q-Blade for each mean The aerodynamic responseofofthethe HAWT was evaluated in thewind timespeed domain considered (parked and operational conditions), producing fifteen rotor thrust time histories. An calculating the time histories of the thrust at the rotor using Q-Blade for each mean wind speed example of the rotor thrust time history for each operational and parked condition is depicted in considered (parked and operational conditions), producing fifteen rotor thrust time histories. Figure 8. Each thrust time history is then applied to the top of the tower structural model, so as to evaluate the corresponding tower-base bending moment time-history in the fore-aft direction.
(Figure 7), while the structural damping is assumed to be equal to 1% of critical for all directions. The time-history response to wind was calculated for 300 s, and the ground motion was applied after 200 s of simulation. In so doing, the transient behavior of the turbine at the beginning of the simulation did not affect the seismic response. The impact of the seismic effects on the operational wind turbine was analyzed in terms of bending moment fluctuations at the tower base section. For example, the Sustainability 2017, 9, 1525 10 of 16 results in terms of tower base bending moment in operational conditions at 11.4 m/s with and without the seismic effects are shown in Figure 9. In particular, the blue line indicates the tower base bending moment without considering thetime seismic effects, whileoperational the red lineand incorporates the seismic loads due An example of the rotor thrust history for each parked condition is depicted in to an artificial scaled to peak groundtoacceleration of 0.4 g. Instructural this case,model, the maximum Figure 8. Eachseismic thrust input time history is athen applied the top of the tower so as to bending of 166 MN· m corresponds to an increase of 118% with the maximum evaluatemoment the corresponding tower-base bending moment time-history in therespect fore-afttodirection. value due to the wind action alone. Sustainability 2017, 9, 1525
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1.2
Parked - U=3 m/s
Cut-in - U=3 m/s
Rated - U=11.4 m/s
Cut-out - U=25 m/s
Rotor Thrust [MN]Bending Moment [MN·m]
Rotor Thrust [MN]
1.0 The structural model was then analyzed under the fifteen artificial accelerograms mentioned above. Each ground motion is applied either as a fore-aft or a side-to-side acceleration boundary 0.8 condition at the base of the tower, and linear dynamic time-history analyses are carried out to 0.6 evaluate the corresponding seismic response. The magnitude of the aerodynamic damping for the 0.4 time-history analyses was set for each parked and operational condition at values calculated here for 0.2 side-to-side directions using the closed-form solution proposed by Valamanesh the fore-aft and (Figure 7), while 0.0 the structural damping is assumed to be equal to 1% of critical for all directions. The 0 100 for 300150 200 250 was applied 300 after 200 time-history response to wind50was calculated s, and the ground motion t [s] s of simulation. In so doing, the transient behavior of the turbine at the beginning of the simulation Figure 8.8.Samples fore-aft direction for conditions. did not affect the seismic response. Theininimpact the seismic effects onand theparked operational wind turbine Figure Samplesof ofthrust thrustforce force fore-aftof direction foroperational operational and parked conditions. was analyzed in terms of bending moment fluctuations at the tower base section. For example, the 200 Wind Thrust results in terms of tower base bending moment in operational conditions at accelerograms 11.4 m/s with and without The structural model was then analyzed under the fifteen artificial mentioned Wind Thrust the +acceleration Earthquake the seismic effects are motion shown in 9. either In particular, the blue indicates tower baseboundary bending above. Each ground is Figure applied as a fore-aft or line a side-to-side 150 moment without considering the seismic effects, while the red line incorporates the seismic loads due condition at the base of the tower, and linear dynamic time-history analyses are carried out to evaluate to artificial 100 seismic input scaled toThe a peak groundof acceleration of 0.4 g. In this case, thetime-history maximum theancorresponding seismic response. magnitude the aerodynamic damping for the bending moment of 166 MN· m corresponds to an increase of 118% with respect to the maximum analyses was set for each parked and operational condition at values calculated here for the fore-aft value due to the50wind action alone. and side-to-side directions using the closed-form solution proposed by Valamanesh (Figure 7), while
Bending Moment [MN·m]
the structural 1.2 dampingParked is assumed to be equal to 1% ofRated critical for all directions. The time-history - U=3 m/s Cut-in - U=3 m/s - U=11.4 m/s Cut-out - U=25 m/s 0 response to wind was calculated for200 300 s, and applied after s of simulation. 1.0 190 195 205the ground 210 motion 215 was 220 225 200 230 In so doing, the transient behavior of the turbine at the beginning of the simulation did not affect the t [s] 0.8 seismic response. The impact of the seismic effects on the operational wind turbine was analyzed in 0.6 Figure 9. Bending moment variations at the tower base section: thrust force in operational conditions terms of bending moment fluctuations at the tower base section. For example, the results in terms due to wind speed of 11.4 m/s with and without seismic load (scaled to a PGA of 0.4 g). of tower base 0.4 bending moment in operational conditions at 11.4 m/s with and without the seismic 0.2 effects are shown in Figure 9. In particular, the blue line indicates the tower base bending moment 8. Probabilistic Assessment of Peak Response without considering the seismic effects, while the red line incorporates the seismic loads due to an 0.0 According methodology presented, the structural response the 5 MW HAWT tower 0the scaled 50a peak 100 acceleration 150 of 0.4 200In thisof 250the 300 bending artificial seismicto input to ground g. case, maximum t [s] against the combined effects of wind and seismic actions was evaluated. In particular, for every moment of 166 MN·m corresponds to an increase of 118% with respect to the maximum value due to working condition (parked/operational) the maximum of the bending moment at the tower Samples of thrust force in fore-aft directionvalue for operational and parked conditions. the windFigure action8.alone. base cross-section was evaluated for each combination of wind load (acting in fore-aft direction) and 200 in fore-aft direction or in side-to-side one. TheWind seismic load acting probabilistic assessment of peak Thrust response of the wind turbine supporting structure was evaluatedWind using Monte Carlo simulations. Thrust + Earthquake 150 Specifically, each wind response time history was then combined with each seismic response timehistory, so to obtain a total of 2 × 225 response time histories for each scenario (1 parked and 3 100
50
0 190
195
200
205
210
215
220
225
230
t [s] Figure Figure 9. 9. Bending Bending moment moment variations variations at at the the tower tower base base section: section: thrust thrust force force in in operational operational conditions conditions due to wind speed of 11.4 m/s with and without seismic load (scaled to a PGA due to wind speed of 11.4 m/s with and without seismic load (scaled to a PGAof of0.4 0.4g). g).
8. 8. Probabilistic Probabilistic Assessment Assessment of of Peak Peak Response Response According According to to the the methodology methodology presented, presented, the the structural structural response response of of the the 55 MW MW HAWT HAWT tower tower against the combined effects of wind and seismic actions was evaluated. In particular, for every against the combined effects of wind and seismic actions was evaluated. In particular, for every working condition (parked/operational) the maximum value of the bending moment at the tower base cross-section was evaluated for each combination of wind load (acting in fore-aft direction) and seismic load acting in fore-aft direction or in side-to-side one. The probabilistic assessment of peak response of the wind turbine supporting structure was evaluated using Monte Carlo simulations. Specifically, each wind response time history was then combined with each seismic response time-
wind speed up to the cut-out condition (mean value of 51.94 MN·m). Moreover, for the wind speed value of 3 m/s, the difference between the tower base absolute maximum bending moment values observed in the parked and operational conditions (mean value of 1.89 MN·m and 22.05 MN·m, respectively) is due to the much lower rotor thrust calculated for the parked scenario with respect to Sustainability 2017, scenario. 9, 1525 11 of 16 the operational The empirical cumulative density function (CDF) of the tower base absolute maximum bending moment is again fitted to a Lognormal distribution for the tower model subjected to the seismic working condition (parked/operational) the maximum value of the bending moment at the tower base action, scaled to a peak ground acceleration of 0.5 g, acting in fore-aft direction (Figure 10b) or in sidecross-section was evaluated for each combination of wind load (acting in fore-aft direction) and seismic to-side direction (Figure 10c), without considering the wind action. The operational condition stated load acting in fore-aft direction or in side-to-side one. The probabilistic assessment of peak response in the legend of Figure 10b refers to the aerodynamic damping value assumed for the seismic of the wind turbine supporting structure was evaluated using Monte Carlo simulations. Specifically, analyses. In these cases, it is observed that the tower base bending moment values decrease as the each wind response time history was then combined with each seismic response time-history, so to wind speed increases, due to the increasing value of the corresponding aerodynamic damping ratio. obtain a total of 2 × 225 response time histories for each scenario (1 parked and 3 operational wind For a wind speed of 3 m/s and the seismic action in the side-to-side direction, the seismic effects for speed levels). The method adopted for the combination of the aerodynamic and seismic response of the parked and operational conditions are the same, because the aerodynamic damping is the same. wind turbine was described in Section 7. In Figure 11, the empirical and fitted CDF of the tower base absolute maximum bending moment are In Figure 10a, the empirical cumulative density function (CDF) of the tower base absolute shown for the combination of the wind and seismic action. Also in this case, the accelerograms were maximum bending moment M is fitted to the Lognormal distribution for all parked and operational scaled to a peak ground acceleration of 0.5 g. When the seismic action is in the fore-aft direction, the wind conditions without seismic actions. As expected, the values of the tower base bending moment operational rated scenario brings the largest values of the tower-base bending moment (mean value increase with the operational wind speed up to the rated value, where the maximum bending moments of 163.53 MN·m and standard deviation of 11.9 MN·m). For a wind speed of 3 m/s, the combined are reached (mean value of 134.82 MN·m), and then decrease with further increase in the wind speed effect of wind and seismic loads are larger for the parked condition if compared to the operational up to the cut-out condition (mean value of 51.94 MN·m). Moreover, for the wind speed value of 3 m/s, one, due to the lower aerodynamic damping. The parameters of the CDF (mean μ and standard the difference between the tower base absolute maximum bending moment values observed in the deviation σ) estimated for the wind load conditions (fore-aft direction), the seismic load conditions parked and operational conditions (mean value of 1.89 MN·m and 22.05 MN·m, respectively) is due to (fore-aft and side-to-side direction) and the combinations of wind and seismic loads presented here are the much lower rotor thrust calculated for the parked scenario with respect to the operational scenario. listed in Table 2.
(a)
(b)
(c)
Figure 10. Cumulative density function estimation of the HAWT base section maximum bending Figure 10. Cumulative density function estimation of the HAWT base section maximum bending moment: (a) for forwind wind parked operational conditions without earthquake; for earthquake moment: (a) parked andand operational conditions without earthquake; for earthquake condition condition scaled to 0.5g without wind action; (b) fore-aft direction; (c) side-to-side direction; scaled to 0.5g without wind action; (b) fore-aft direction; (c) side-to-side direction; (continuous (continuous line—empirical; dashed line—Lognormal). line—empirical; dashed line—Lognormal).
The empirical cumulative density function (CDF) of the tower base absolute maximum bending moment is again fitted to a Lognormal distribution for the tower model subjected to the seismic action, scaled to a peak ground acceleration of 0.5 g, acting in fore-aft direction (Figure 10b) or in side-to-side direction (Figure 10c), without considering the wind action. The operational condition stated in the legend of Figure 10b refers to the aerodynamic damping value assumed for the seismic analyses. In these cases, it is observed that the tower base bending moment values decrease as the wind speed increases, due to the increasing value of the corresponding aerodynamic damping ratio. For a wind speed of 3 m/s and the seismic action in the side-to-side direction, the seismic effects for the parked and operational conditions are the same, because the aerodynamic damping is the same. In Figure 11, the empirical and fitted CDF of the tower base absolute maximum bending moment are shown for the combination of the wind and seismic action. Also in this case, the accelerograms were scaled to a peak ground acceleration of 0.5 g. When the seismic action is in the fore-aft direction, the operational rated scenario brings the largest values of the tower-base bending moment (mean value of 163.53 MN·m and standard deviation of 11.9 MN·m). For a wind speed of 3 m/s, the combined effect of wind and seismic loads are larger for the parked condition if compared to the operational one, due to the lower
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aerodynamic damping. The parameters of the CDF (mean µ and standard deviation σ) estimated for the wind load conditions (fore-aft direction), the seismic load conditions (fore-aft and side-to-side Sustainability 2017,the 9, 1525 direction) and combinations of wind and seismic loads presented here are listed in Table 2. 12 of 16
(a)
(b)
Figure 11. Cumulative density function estimation of the HAWT base section maximum bending Figure 11. Cumulative density function estimation of the HAWT base section maximum bending moment for parked and operational conditions with earthquake scaled to 0.5g: (a) fore-aft direction; moment for parked and operational conditions with earthquake scaled to 0.5g: (a) fore-aft direction; (b) side-to-side direction; (continuous line—empirical; dashed line—Lognormal). (b) side-to-side direction; (continuous line—empirical; dashed line—Lognormal). Table 2. Estimated parameters of the cumulative function Lognormal distribution. Table 2. Estimated parameters of the cumulative function Lognormal distribution. Working
Working Condition Condition
Wind Action
Earthquake
Earthquake
Fore-Aft
Fore-Aft
Side-to-Side
Wind Action Fore-Aft
Earthquake Fore-Aft
μ
σ
μ µ
σ
Parked Parked
0.591 0.591
0.344 0.344
4.975 4.975
0.145 0.145
Operational cut-in Operational cut-in
3.093 3.093
0.046 0.046
4.714 4.714
0.095 0.095
µ
σ
σ
Earthquake
μ
µ
0.040 0.054
4.567 4.465
0.119 0.126
Operational cut-out 3.950
0.054
4.465
0.126
4.782
4.904
0.040
4.567
0.119
σ
σ
4.921 0.135 0.135 0.135 0.135
4.904 3.950
Operational rated
Wind + Earthquake
Fore-Aft
Side-to-Side
4.921 4.921 4.921 4.866 4.866 4.782
Operational rated Operational cut-out
Wind + Earthquake Wind + Earthquake Fore-Aft
μ
µ
4.978
Wind + Earthquake
Side-to-Side Side-to-Side
σ
σ
0.140
μ
µ
4.923
σ
σ
0.131
0.127 0.127 0.102
4.978 4.778 4.778 5.097 5.097 4.796
0.140 0.087 0.087 0.073 0.073 0.087
4.923 4.923 4.923 4.987 4.987 4.820
0.131 0.131 0.131 0.097 0.097 0.094
0.102
4.796
0.087
4.820
0.094
9. Prediction of the Tower Failure Condition 9. Prediction of the Tower Failure Condition Globally, the wind turbine tower behaves as a simple cantilever beam. Locally, however, it behaves Globally, thecylindrical wind turbine behaves as a simple cantilever however, it as a thin-walled shell,tower and the local buckling condition needsbeam. to be Locally, considered in safety behaves as a thin-walled cylindrical shell, and the local buckling condition needs to be considered in evaluation. In this paper, the buckling limit state condition assessment was carried out deterministically safety evaluation. In this paper, the buckling limit state condition waswhich carried out by means of the stress design procedure proposed in Section 8.5 of ENassessment 1993-1-6 [22], is also deterministically by means of the stress design procedure proposed in Section 8.5 of EN 1993-1-6 [22], allowed within ASCE/AWEA RP2011 [17]. To this end, an S355 steel was considered of fabrication which is also allowed within ASCE/AWEA RP2011 [17]. To this end, an S355 steel was considered of tolerance quality Class C. Moreover, fixing an axial force value of 6.88 MN acting on the tower fabrication tolerance quality Class C. Moreover, fixing an axial force value of 6.88 MN acting on the base section, due to the gravity loads, and assuming that the tangential stress associated with the tower base section, due to the gravity loads, and assuming that the tangential stress associated with shear force has a negligible effect on the maximum von Mises stress, an ultimate bending moment the shear force has a negligible effect on the maximum von Mises stress, an ultimate bending moment value of 205.8 MN·m for the buckling condition was assessed. This latter condition is reached when value of 205.8 MN·m for the buckling condition was assessed. This latter condition is reached when the maximum meridional compressive stress equals the elastic critical meridional buckling stress. the maximum meridional compressive stress equals the elastic critical meridional buckling stress. In In particular, a partial safety factor for material γm equal to 1.2 was assumed, according to IEC [16] and particular, a partial safety factor for material γm equal to 1.2 was assumed, according to IEC [16] and ASCE/AWEA RP2011 [17]. It should be mentioned that this type of analysis generally results in rather ASCE/AWEA RP2011 [17]. It should be mentioned that this type of analysis generally results in rather conservative values, whereas more accurate calculations can be obtained through global numerical conservative values, whereas more accurate calculations can be obtained through global numerical analysis (e.g., using Linear Buckling Analysis and Materially Nonlinear Analysis) on a more refined analysis (e.g., using Linear Buckling Analysis and Materially Nonlinear Analysis) on a more refined FE model, according to the Section §8.6 of EN 1993-1-6. FE model, according to the Section §8.6 of EN 1993-1-6. 10. Fragility Curve Derivation 10. Fragility Curve Derivation Fragility analyses are commonly used in earthquake engineering for assessing the vulnerability Fragilitythrough analysesthe areprobability commonly of used in earthquake engineering for assessing the vulnerability of structures damage over a range of potential loading intensities. Some of structures through the probability of damage over a range of potential loading intensities. Some specific research has already been developed for onshore HAWT, considering the variability of ground motion intensity [30,31] and wind speed [32] separately, and for offshore HAWT under the combination of extreme wind and wave conditions [33]. Fragility is defined as the conditional probability of a damage measure (DM) attaining or exceeding a damage limit state for a given
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specific research has already been developed for onshore HAWT, considering the variability of ground motion intensity [30,31] and wind speed [32] separately, and for offshore HAWT under the combination of extreme wind and wave conditions [33]. Fragility is defined as the conditional probability of a damage measure (DM) attaining or exceeding a damage limit state for a given intensity measure (IM) of the combined environmental conditions. The conditional probability of failure Pf,i can be evaluated as (e.g., [32,34]): Pf ,i = P[ DMi | EDP = edp ] P[ EDP = edp| I M = im ] (5) where DMi refers to damage measure according to the ith damage state and EDP is the engineering demand parameter. Lower-case symbols indicate the values of the random variables. P [DMi|EDP = edp] is the probability that the structures reaches the ith damage state, given the EDP value, i.e., the fragility curve. The EDP value in turn comes from the IM, probabilistically as P [EDP = edp|IM = im]. The fragility function is then obtained by calculating Pf for a convenient number of intensity values. In this paper, the achievement of the tower base ultimate bending moment Mu (equal to 205.8 MN·m), corresponding to the buckling failure condition, is considered to be the only damage limit state; therefore, it is the only EDP considered. Thus, the fragility curves are defined as follows: Pf ,i = P M ≥ Mu U = Ui ; a g
(6)
where Mu is the structural capacity corresponding to the above-mentioned failure limit state, M is the demand corresponding to the intensity measure of the combined wind scenario and earthquake intensity. Thus, the fragility curves are calculated for the four different wind scenarios (parked and operational, defined as U = Ui ) combined with the seismic loads acting in fore-aft or side-to-side direction (Table 3 and Figure 12). The most common form of a seismic fragility function is the lognormal cumulative distribution function (CDF), and can be also expressed as: Pf ,i a g
! ln a g − µ =Φ σ
(7)
where Φ is the standardized normal distribution function; µ and σ are the natural logarithm of the mean and logarithmic standard deviation, respectively. The results obtained for the seismic loads acting in the fore-aft direction show that fragility increases with increasing operational wind speed up to the rated condition and decrease for further increase of wind speed up to the cut-out condition. The results obtained for the seismic loads acting in fore-aft direction show that the multi-hazard fragility is higher for the parked condition, whose fragility curve is very close to that corresponding to the operational rated speed condition. This is due to the lowest value of the aerodynamic damping being related to the fore-aft parked condition. In these cases, the probability of failure is equal to 50% for Peak Ground Acceleration (PGA) values of 0.71 g and 0.72 g. Moreover, these conditions show the same PGA value of 0.78 g for a probability of failure of 76%. On the other hand, the fragility curves carried out for the seismic loads acting in the side-to-side direction for cut-in and rated conditions are very close to one another. In particular, these conditions show the same peak ground acceleration value of 0.73 g for a probability of failure of 41%. While a minor fragility is observed for the operational cut-out condition due to the highest value of the aerodynamic damping. Finally, for the parked and cut-in operational conditions the fragility curves in the side-to-side direction are coincident since for both cases the same value of aerodynamic damping is used.
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Table 3. Estimated parameters of the Lognormal distribution for fragility curves. Wind + Earthquake
Wind + Earthquake
Fore-Aft
Side-to-Side
Working Condition
Parked Operational cut-in rated Sustainability 2017,Operational 9, 1525 Operational cut-out
µ
σ
µ
σ
−0.343 −0.117 −0.328 −0.008
0.140 0.093 0.120 0.121
−0.288 −0.288 −0.289 −0.161
0.131 0.131 0.123 0.100
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Figure 12. Fragility curves for parked and operational conditions with earthquake: fore-aft Figure 12. Fragility curves for parked and operational conditions with earthquake: fore-aft direction– direction–continuous line; side-to-side direction – dashed line. continuous line; side-to-side direction – dashed line.
11. 11. Conclusions Conclusions The a probabilistic framework for the and assessment of land-based The preliminary preliminaryresults resultsofof a probabilistic framework for design the design and assessment of landhorizontal axis wind turbines (HAWTs) subjected to combined wind and seismic actions are presented. based horizontal axis wind turbines (HAWTs) subjected to combined wind and seismic actions are The aerodynamic and seismic effects on theeffects structural model of the HAWT decoupling presented. The aerodynamic and seismic on the structural model were of theassessed HAWT by were assessed the aerodynamic behavior of the rotor from the dynamic response of the support structure. was by decoupling the aerodynamic behavior of the rotor from the dynamic response of theThis support first achieved evaluating the aerodynamic response of a rotor with rigidofblades to structure. Thisby was first achieved by evaluating the aerodynamic response a rotorwhen withsubjected rigid blades wind loads through the nonlinear Lifting Line Free Vortex Wake algorithm implemented in Q-Blade when subjected to wind loads through the nonlinear Lifting Line Free Vortex Wake algorithm software. Then, structural response of the wasresponse assessed of bythe applying wind thrust by of implemented inthe Q-Blade software. Then, the HAWT structural HAWTthe was assessed the rotor and seismic to the tower FE model, therebyto neglecting applying the the wind thrustexcitation of the rotor and the seismic excitation the toweraeroelastic FE model,feedback. thereby The aeroelastic interaction was taken into account through the addition of aerodynamic damping neglecting aeroelastic feedback. The aeroelastic interaction was taken into account through the to the model; the latter was evaluated using the closed-form solution proposed by Valamanesh and addition of aerodynamic damping to the model; the latter was evaluated using the closed-form Myers (2014). The probabilistic assessment of the(2014). peak response of the tower structure,of against the solution proposed by Valamanesh and Myers The probabilistic assessment the peak combined effect of wind and seismic actions, was evaluated by calculating the maximum value of the response of the tower structure, against the combined effect of wind and seismic actions, was bending moment at the tower for each combination of windmoment load (fifteen wind timebase histories for evaluated by calculating the base maximum value of the bending at the tower for each each operational/parked condition) and seismic load (fifteen artificial accelerograms) acting in both combination of wind load (fifteen wind time histories for each operational/parked condition) and fore-aft directions. In particular, the empirical and theand estimated CDFsdirections. of the tower seismic and loadside-to-side (fifteen artificial accelerograms) acting in both fore-aft side-to-side In base maximum bending moment are evaluated for the combination of the wind and seismic action. particular, the empirical and the estimated CDFs of the tower base maximum bending moment are The fragility curves for theoftower buckling limit state were finally obtained from Monte Carlo evaluated for the combination the wind and seismic action. simulations of the curves tower subjected to different wind and seismic scenarios, and using the tower The fragility for the tower buckling limit state wereload finally obtained from Monte Carlo base bending moment as a deterministic limit state parameter representative of the structural capacity. simulations of the tower subjected to different wind and seismic load scenarios, and using the tower For purpose, the failure of thelimit tower structure was estimated according to structural the stress basethis bending moment as acondition deterministic state parameter representative of the design procedure by EC3 forcondition buckling limit assessment. vulnerability capacity. For this proposed purpose, the failure of thestate tower structure Consequently, was estimatedthe according to the assessment of HAWTs to wind and seismic actions is carried out in terms of probability of failurethe of stress design procedure proposed by EC3 for buckling limit state assessment. Consequently, the supporting tower structure as a function of the PGA for both parked and operational conditions. vulnerability assessment of HAWTs to wind and seismic actions is carried out in terms of probability The resultsofhighlight a probability failure of 50% for of PGA greater thanand 0.7 operational g when the of failure the supporting tower of structure asover a function ofvalues the PGA for both parked
conditions. The results highlight a probability of failure of over 50% for values of PGA greater than 0.7 g when the rotor is in parked or operational rated conditions, and for seismic loads acting in the fore-aft direction. The fragility is slightly lower for parked, cut-in and rated conditions combined with seismic loads acting in the side-to-side direction.
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rotor is in parked or operational rated conditions, and for seismic loads acting in the fore-aft direction. The fragility is slightly lower for parked, cut-in and rated conditions combined with seismic loads acting in the side-to-side direction. Author Contributions: Alberto Maria Avossa, Cristoforo Demartino and Francesco Ricciardelli proposed the main idea of the paper; Alberto Maria Avossa and Cristoforo Demartino have constructed the numerical model, made the calculation and analyzed the results; All authors contributed to the writing and revising of the article; All authors approved the paper final version. Conflicts of Interest: The authors declare no conflict of interest.
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20.
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