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Cross-wind fatigue analysis of a full scale offshore wind turbine in the case of wind–wave misalignment
Engineering Structures 120 (2016) 147–157
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Cross-wind fatigue analysis of a full scale offshore wind turbine in the case of wind–wave misalignment Christina Koukoura a,⇑, Cameron Brown b, Anand Natarajan a, Allan Vesth a a b
Technical University of Denmark, DTU Wind Energy, Building 118, PO Box 49, 4000 Roskilde, Denmark DONG Energy A/S, Wind Power, Nesa Alle 1, 2820 Gentofte, Denmark
a r t i c l e
i n f o
Article history: Received 18 September 2014 Revised 27 January 2016 Accepted 11 April 2016
Keywords: Offshore wind turbine Wind–wave misalignment Side–side fatigue Monopile foundation Damping estimation
a b s t r a c t Wind–wave misalignment is often necessary to consider during the design of offshore wind turbines due to excitation of side–side vibration and the low aerodynamic damping in that direction. The measurements from a fully instrumented 3.6 MW pitch regulated-variable speed offshore wind turbine were used for the estimation of the side–side fatigue loads at the tower bottom. The joint wind–wave distribution and the distribution of the wind–wave misalignment angles were considered. The side–side fatigue at the tower bottom and the damping from site measurements are presented as function of the misalignment angles. A model of the same wind turbine was set-up and simulations with the aero-hydro-servo-elastic code HAWC2 were performed to investigate the effect of damping on the side–side fatigue. Turbulent wind field, irregular waves and flexible soil are used in the simulations based on site-measurements. The aim of the current study is to examine the sensitivity of the side–side fatigue to the wind–wave misalignment and different values of additional offshore damping in the system. It was found that the additional offshore damping of the physical system may be higher than what is typically used in offshore wind turbine sub-structure design, due to the low sensitivity of the measured side–side fatigue loads to the misalignment angle. Choice of an accurate damping value implemented in the model during the design of the wind turbine sub-structure can lead to material and cost savings. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Cross-wind fatigue on offshore wind turbine monopile support structures due to wave loading misaligned with the wind can become a significant design driver, because of the low aerodynamic damping experienced in this direction. According to the DNV guidelines for offshore structures [1], the misalignment between the wind and wave directions should be included in the design if misalignment conditions are present in the site of installation. However, these cross-wind fatigue loads are difficult to predict due to uncertainty in the overall system damping. The choice of a conservative damping value can result in overdimensionalization of the substructure, high estimated fatigue loading and a design which is not economically feasible. In Ref. [2], the cross-wind aero-elastic damping is examined, and the sensitivity of the cross-wind loads to the damping, especially during wind–wave misalignment, is highlighted. In the same study, ⇑ Corresponding author at: DONG Energy A/S, Wind Power, Nesa Alle 1, 2820 Gentofte, Denmark. E-mail addresses: [email protected] (C. Koukoura), [email protected] (C. Brown), [email protected] (A. Natarajan), [email protected] (A. Vesth). http://dx.doi.org/10.1016/j.engstruct.2016.04.027 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
measurements from offshore wind turbines at Horns Rev 1 and the Burbo offshore wind farms, were used to estimate the damping and a logarithmic decrement d of about 10% was found (excluding aerodynamic damping). This analysis gave indications that the actual damping on offshore wind turbines is more than what is typically used in design calculations (d ¼ 6%) [2]. In Ref. [3], the logarithmic decrement considering only the non-aerodynamic damping (structural-, hydrodynamic-, soil-damping) is estimated as 14–15% (2.25% damping ratio). The effect of misalignment angles on the fatigue of the structure is examined in Ref. [4]. A study conducted by Fischer et al. [5] considering all load cases described in IEC 61400-3 [6] and misalignment angles from 0 to 360 demonstrated the importance of wave directionality during the design process. The bending moment in the fore–aft direction was 30% higher in the case of waves perpendicular to the wind, while the side–side loading is 5 times larger when compared to aligned wind and wave results. In Ref. [7], the equivalent loads and fatigue damage at the tower and monopile bottom were examined for different cases of wind–wave misalignment, considering both linear and non-linear waves. The effect of misalignment on the simulated fatigue, including the probability density function of misalignment angles has
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been investigated in Ref. [8]. For a misalignment distribution with a peak close to 0 the fatigue damage in the tower bottom was increased by 3:6% between the misaligned and the collinear cases. For the case where the highest probability of occurrence is for an angle of 60 the increase in the fatigue damage is up to 15%. An increase in the fatigue damage accumulation due to waves perpendicular to the wind direction is also reported in Ref. [9], where a non-linear irregular wave model is implemented in the analysis. In the current study the target is to investigate the sensitivity of the cross-wind fatigue loading to the different wind–wave misalignment angles, for various values of the net damping of the system. In the analysis the misalignment distribution is considered. The outline of this paper is as follows: firstly the site and the measurements calibration are described in Sections 2 and 3. Secondly the joint wind–wave distribution and the misalignment distribution based on site observations are presented in Section 4. Thirdly the calculation of the damage equivalent loads of the measured cross-wind vibration at the tower bottom for each wind– wave bin and misalignment sector are discussed. Finally the sensitivity of the cross-wind fatigue to the different misalignment angles, for different damping values is examined.
2. Site description A 3.6 MW Siemens pitch regulated-variable speed wind turbine with a 107 m rotor is installed at the Walney Offshore Wind farm 1 (Fig. 1a). The wind turbine is located at the west coast of England, 15 km from the shore, in the Irish Sea and has been fully instrumented for load measurements. The turbine is mounted on a monopile structure at a water depth of 26 m. Strain gauges and accelerometers are installed at 4 different heights throughout the whole length of the tower (4 gauges per height). The sampling rate of the data acquisition system is 35 Hz. The data has been obtained from the wind turbine manufacturer (Siemens Wind Power) and DONG Energy and is presented in this paper in normalized terms. A nacelle mounted cup-anemometer provides wind speed measurements in time series of 10 min and a buoy installed close to the foundation measures the wave characteristics every 30 min (including significant wave height, peak crossing period and wave direction). Turbine yaw angles, blade pitch angles and power production are obtained as 10 min averages from the SCADA data. The mean yaw angle provided by the SCADA data was used to estimate
the wind direction and the mean wave direction from the buoy are compared to identify cases of wind–wave misalignment (Fig. 1b). 3. Measurements calibration Before the post-processing of the measurements a calibration of the raw data from the strain gauges is required. The time series data are divided up into files each corresponding to 10 min of measurements and the signals are in voltage. Four strain gauges are installed per height placed one across from the other at 150 —330 for the measurement of the North–South and 60 —240 for the East–West bending (Fig. 3a). In the same figure, the sign of the moments from the coordinate system definition is also presented. The tower measurements were calibrated using the mass and offset center of gravity of the nacelle, where the nacelle is slowly rotated 360 around the yaw axis. Fig. 2 presents the coordinate system of the support structure used for the measurements calibration, along with the location of the nacelle center of gravity (CoG). The moment induced by the nacelle weight is defined as a negative moment in the x direction. The subscript T denotes tower. The offset of the CoG creates a moment, which is captured by the strain gauges during the yaw test as a sinusoidal curve. Fig. 3b presents an example of the strain signal versus the yaw angle. The range of the sinusoidal curve from the yaw test is equal to twice the expected moment due to the nacelle weight. This allows the gain of the bridge to be estimated as shown in Eq. (1a). The bridge offset is the mean value of the sinusoidal curve, calculated by Eq. (1b). minðVÞ denotes the minimum strain value in voltage observed during the test, Massnacelle is the mass of the nacelle, g is the acceleration due to gravity, d is the distance of the nacelle center of gravity (CoG) from the tower axis and rangeðVÞ is the range of the sinusoidal curve in voltage. The transformation to the rotating system that follows the wind turbine is performed through Eq. (2), where a is the angle between the strain gauge position and bridge north (30 ) and y is the yaw angle at each time step.
2 Massnacelle g d ; rangeðVÞ offset ¼ Massnacelle g d gain min
gain ¼
M x;rot ¼ MNS cosða yÞ M EW sinða yÞ M y;rot ¼ MNS sinða yÞ þ M EW cosða yÞ
Fig. 1. Walney offshore wind farm 1.
ð1aÞ ð1bÞ ð2Þ
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mean wind speed for the Walney site. The wind turbine D01 is 80% of the time in the wake, so the apparent average wind speed was expected to be lower. Another reason for the discrepancy between the expected site conditions and the estimated wind from the joint wind–wave distribution, is due to the short measurement period of six months, which might not be representative of the site (wind index). The uncertainty of the measurement period should be considered in a more detailed analysis. The probability of each combination of wind speed and significant wave height for the joint distribution (Fig. 4a), was then based on the number of observations in each bin (Eq. (3)), where the index i represents the wind bins, the index j the wave bins and N the number of observations.
Ni;j pi;j ¼ P9 P8 i¼1
Fig. 2. Support structure coordinate system.
4. Environmental conditions 4.1. Wind–wave joint distribution The mean wind speed measurements provided by the SCADA system of the instrumented wind turbine D01 were used to calculate the Weibull probability density function of the wind speed P U . A 2-parameter Weibull distribution is suggested as the conditional distribution of the significant wave height for a given wind speed P Hs jU [10]. The measured wind speed is separated in bins of 2 m/s and the Weibull scale and shape parameters a and b for the wave heights within each bin are estimated. For the calculation of the joint wind–wave distribution, the 10 min mean wind speed U is separated in bins of 2 m/s in such a way that the bin for U = 6–8 m/s covers all the wind speeds in the interval 6 m=s 6 U < 8 m=s. The significant wave height Hs is separated in bins of 0.5 m. For the generation of the contour surface of the local joint wind–wave probability density function, shown in Fig. 4, 6 months of measurements have been used. Due to limited data availability, in Fig. 4a the average wind speed on the site appears to be 8 m/s. This is lower than the annual average
ð3Þ
j¼1 N i;j
As an alternative method of estimating the joint wind–wave distribution, the fitted conditional wave height distribution is combined with the fitted wind speed distribution. The wind distribution is based on measurements from the wake sector, since the wind turbine is mostly on the wake. Fig. 4b presents the contour surface of the fitted joint wind–wave distribution. Using this methodology, the average wind speed is 9 m/s. The time weighting used for the estimation of the lifetime accumulated fatigue are calculated from this fitted joint wind–wave probability multiplied with the hours obtained from the free wind Weibull distribution (hoursfree wind , Eq. (4)). The reduced mean wind speed, seen by the wind turbine due to the wake, should not be considered in the analysis, as the Sten Frandsen model was used for the estimation of the effective turbulence intensity [11]. 90% availability of the wind turbine due to maintenance is considered in the calculation of the operating hours.
life hours ¼ PHs jU P U hoursfree
wind
ð4Þ
4.2. Wind–wave direction probability The directional influence of the spreading on the wave direction measured by the buoy is identified by comparing the mean wave direction with the peak wave direction (i.e. the direction that results in the highest energy from the directional spectrum). Fig. 5 compares the peak and the mean wave direction measurements from the buoy; on the y axis is the mean wave direction, while the peak direction is presented on the x axis. It seems that there are no multi directional sea states from the swell contributions, which could cause differences between the mean and peak
Fig. 3. Strain gauges on the support structure.
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Fig. 4. Local and fitted joint wind–wave probability.
speed increases the misalignment probability decreases. This is because the waves are mainly generated by the wind, especially in sheltered areas like the Irish sea. So the wind–wave correlation at high wind speeds is higher and the probability that the waves are aligned with the wind is larger, since the waves are generated by the local wind conditions.
Buoy Mean Wave Direction (o)
400 350 300 250 200
5. Fatigue analysis/measurements
150 100 50 0 −50
0
50
100
150
200
250
300
350
400
Buoy Peak Wave Direction (o) Fig. 5. Confidence interval of 93% of the mean wave direction measured by the buoy.
The equivalent fatigue load corresponds to the cyclic load that if applied neq times in the structure, it will result in the same damage as the variable load fluctuations experienced over the lifetime of the wind turbine [12]. The measured time series binned as described in Section 4.1, were combined to calculate the 1 Hz equivalent load (Eq. (5)) for each mean wind speed-significant wave height combination. N i are the number of cycles for a given stress range Si , in all measured time series. m is the Wöhler exponent equal to 4 in the present study for the steel components, hi;j is the total measurement time of each bin in seconds and n is the number of stress range bins.
Pn wave directions. Therefore the mean wave direction is a good estimate of the wave direction, with an uncertainty of 30 (93% confidence interval). For the construction of the wind and wave roses shown in Fig. 6 the directions are separated in 12 bins of 30 each. The main wind and wave directions have a difference of 10 . In this analysis we are interested in the relative angle between wind and waves (misalignment) and not their absolute direction. Therefore all wind sectors are included in the study. The misalignment angles are separated in bins of 10 from the minimum to the maximum observed angle for a given mean wind speed and significant wave height combination. The cumulative distribution function (CDF) is then used to calculate the probability of occurrence of each misalignment angle. Table 1 presents the probability of occurrence of nine wind speeds and sea states along with the misalignment probability between the wind and wave directions based on six months of measurements. The probability of occurrence of misalignment angles larger than j 50j is very small and therefore not presented in the table. For all mean wind speeds the wave direction misalignment of 10 has the highest probability of occurrence. It can also be observed that as the mean wind
S1Hz ¼
m ð1=mÞ i¼1 N i Si
hi;j
ð5Þ
Fig. 7a presents the 1 Hz equivalent load for the cross-wind fatigue at the tower bottom as a function of the mean wind speed (all misalignment angles are taken into account). The different lines correspond to the different significant wave heights and the values are normalized with the maximum load for U ¼ 14 m=s. The equivalent load has the tendency of increasing with the wind speed and the wave height. Taking into account the joint wind–wave distribution, the fatigue damage contribution Df of each bin, to the lifetime fatigue of the wind turbine support structure is estimated. Under the assumption of linear cumulative damage, the fatigue damage accumulation is given by Eq. (6), where N tot;i are the number of cycles to failure for a given stress Si and a is the intercept of the S–N curve with the log N axis [13]. The result with respect to the mean wind speed is presented in Fig. 7b. The different curves illustrate the different significant wave heights. It can be observed that the greatest contribution to the lifetime fatigue is not due to the most severe cases but due to bins with higher probability of occurrence, even though the wind and wave conditions are milder.
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Fig. 6. Wind and wave roses with 12 bins of 30 .
Table 1 Probability of occurrence of nine wind-significant wave height combinations along with the observed misalignment probability between their directions. The mean wind speed, significant wave height and misalignment angles represent the center of each bin. U (m/s)
Hs (m)
pi;j
50
40
30
20
10
0
10
20
30
40
50
6 8 8 10 12 12 14 16 18
0.75 0.75 1.25 1.25 1.25 1.75 1.75 2.25 2.75
0.183 0.135 0.074 0.078 0.075 0.054 0.051 0.021 0.009
0.031 0.029 0.014 0.023 0.006 0.009 0.043 0.046 0.033
0.070 0.072 0.048 0.057 0.025 0.033 0.077 0.099 0.065
0.125 0.133 0.105 0.109 0.074 0.086 0.111 0.141 0.116
0.175 0.190 0.171 0.165 0.153 0.161 0.143 0.162 0.148
0.195 0.206 0.209 0.194 0.223 0.216 0.155 0.166 0.173
0.167 0.170 0.194 0.180 0.220 0.210 0.144 0.128 0.153
0.112 0.107 0.134 0.130 0.161 0.148 0.116 0.081 0.113
0.062 0.051 0.070 0.069 0.083 0.073 0.077 0.037 0.065
0.026 0.019 0.025 0.032 0.031 0.025 0.044 0.013 0.000
0.008 0.005 0.008 0.008 0.006 0.008 0.017 0.000 0.000
0.002 0.001 0.000 0.002 0.000 0.000 0.008 0.002 0.000
This observation demonstrates the importance of the joint wind– wave distribution in the calculation of the fatigue of the structure and indicates that it is not only the severeness of the operating conditions that contribute to the fatigue but their probability of occurrence as well.
Df ¼
n n X Ni 1X Ni ¼ m N a S tot;i i¼1 i¼1 i
ð6Þ
wind–wave misalignment for the combinations of wind speed and wave heights presented in Fig. 8. Considering the probability density function of the misalignment angles and using it as a weight to calculate the relative damage of every misalignment angle to the lifetime fatigue of the wind turbine support structure (Eq. (6)), it can be observed that the highest damage contribution is given for the misalignment angle with the highest probability, namely 10 .
Pn S1Hz;misal ¼
m ð1=mÞ i¼1 N i Si
hmisal;mes
ð7Þ
6. Fatigue analysis for different misalignment sectors (measurements) 7. Fatigue analysis/simulations In order to examine the effect of the misalignment angles on the fatigue of the structure, the equivalent load for different misalignment sectors within each wind–wave bin is calculated. The misalignment angles are separated in bins of 10 in such a way that the bin for mis ang ¼ ð15 Þ ð5 Þ covers all the misalignment angles in the interval 15 6 mis ang < 5. The 1 Hz equivalent load for each misalignment sector is calculated by Eq. (7), where hmisal;mes are the measured hours of a specific misalignment sector. The relative damage is estimated accounting for the probability density function of each misalignment angle as was shown in Section 4.2. The loads as a function of the misalignment angle are presented in Fig. 8. The 1 Hz equivalent loads are normalized with 0 misalignment. The 1 Hz equivalent load has a small tendency to increase with the increased absolute value of the misalignment angle. However, the trend is not clear and the side–side 1 Hz equivalent load does not appear to have a high sensitivity to the
In the following two sections the effect of the misalignment angle in the loading of the structure for different damping values is examined. To investigate this, aero-elastic simulations were performed. In Section 7 the estimated fatigue derived from the simulations is compared with the fatigue from the measured loads, to validate the accuracy of the model. In Section 8 the accumulated fatigue is estimated for various values of the damping and the sensitivity of the relative damage in the side–side direction to the misalignment angles is presented. Simulations were performed with the aero-elastic software HAWC2 [14]. The structural wind turbine model is based on a multi-body formulation, where each body is a Timoshenko beam. The 3 bladed 3.6 MW pitch-regulated-variable speed wind turbine model is developed and implemented in HAWC2. The model is described and validated in Refs. [15,16]. Fatigue loads are
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Fig. 7. 1 Hz equivalent load and relative damage at the tower bottom in the side–side direction.
simulated under 9 mean wind speeds, 8 significant wave heights (presented in Section 4.1) and 11 misalignment angles from 50 to 50 are used in the analysis. The turbulence intensity applied in the simulations is based on the wind speed measurements provided by the nacelle cup-anemometer. Fig. 9a presents the scattered wind turbulence intensity, along with the fitted exponential distribution (y ¼ a ebx þ c edx ) representing the 90th percentile of the data. The simulation of the wind turbulence was then made based on the Mann wind turbulence model as described in IEC 61400-1 [11].
The air density used in the simulations is equal to 1:225 kg=m3 . For the calculation of hydrodynamic forces the linear irregular wave theory combined with the Wheeler stretching method to account for loads above the mean sea level is implemented in the aero-elastic code. The hydrodynamic loads are based on the Morison’s equation [17]. The hydrodynamic forces above the mean sea level due to surface elevation are accounted for by applying the Wheeler stretching method [18,19]. The JONSWAP spectrum is fitted to the wave elevation, measured by a buoy installed near to the offshore wind turbine (Fig. 9b). Time series of surface elevation and directional spectrum
Fig. 8. 1 Hz equivalent load and relative damage contribution to the side–side fatigue at the tower bottom based on the probability of occurrence of different misalignment sectors for various wind–wave combinations (measurements). The values are normalized with the equivalent load at 0 misalignment.
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153
Fig. 9. Wind and wave direction distributions.
Fig. 10. 1 Hz equivalent load and relative damage at the tower bottom in the side–side direction, based on the joint wind–wave distribution (measurements vs. simulations), scaled to a lifetime of 25 years.
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Fig. 11. The total accumulated fatigue damage for measurements and simulations normalized with the simulations’ fatigue.
are measured by the buoy, providing a view of the sea state every 30 min. The parameters of the fitted spectrum are given as inputs to the HAWC2 simulations, for the generation of the wave field. Due to very low current velocities, the influence of the current can be neglected in the fatigue analysis [12]. For the loading of the pile-sand, the commonly used p–y curve method is employed, where the soil stiffness is modeled by distributed nonlinear springs along the subsoil portion of the support structure [1]. The soil characteristics used in the simulations are based on geotechnical measurements. The soil consists of different layers (first 7 m is clay/sand/ silt and the rest is sand). Fig. 9c presents the p–y curve for three different soil depths in the site. The lifetime equivalent load is based on the joint wind–wave distribution calculated from the measurements (Eq. (4)), scaled to a lifetime of 25 years. Fig. 10 presents the 1 Hz equivalent load and the relative damage of each bin to the fatigue of the structure with respect to the mean wind speed both for simulations and measurements (dashed lines correspond to simulations and solid to measurements). For each of the 46 mean wind speedsignificant wave height combinations 12 turbulence seeds of 600s and 11 misalignment angles were used in HAWC2, which
resulted in a total of 6072 simulations. The illustrated 1 Hz equivalent load data are normalized with the simulation maximum equivalent load for U ¼ 14 m=s. The simulated equivalent loads seem to follow satisfactorily the measurements. Discrepancies are mainly attributed to differences in the blade aerodynamics and uncertainties in the soil modeling. The accumulated fatigue load for the whole lifetime of the structure (25 years) is calculated both for measurements and simulations. Fig. 11 presents the accumulated fatigue damage at the tower bottom in the fore–aft and side–side directions. The illustrated data are normalized with the simulated load. The agreement between measurements and simulations is satisfactory. The higher simulated accumulated fatigue is due to the lower damping present in the simulations as was shown in Ref. [16]. Due to the low aerodynamic damping in the side–side direction, the modeling of the other sources of damping becomes very important. Uncertainties in the soil damping and the presence of a tower damper in the real wind turbine, but not taken into account in the model are responsible for the discrepancies in the damping estimation and thus the loading between measurements and simulations.
Fig. 12. Overall damping in normal operation from simulations using the Enhanced Frequency Domain Decomposition method. Three different non-aerodynamic damping values are examined from the simulations (stars correspond to d ¼ 12%, circles to d ¼ 6% and crosses to d ¼ 13:8%) and compared to the measurements (blue x). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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155
Fig. 13. The total accumulated fatigue damage from simulations with different values for the non-aerodynamic damping. Normalized with the fatigue from the model tuned to the measured damping for U ¼ 6 m=s and Hs ¼ 0:75 m.
Rayleigh coefficients in the model and applying an impulse to estimate the non-aerodynamic damping from the decaying response. The stars in the figure correspond to d ¼ 12%, the circles to nonaerodynamic damping of d ¼ 6% and the crosses to d ¼ 13:8%. It can be observed that the lowest non-aerodynamic damping (d ¼ 6%), results in much lower overall damping in both the fore–aft and side–side directions. However, as was shown in Ref. [16], using the same methodology, the damping estimated from the measurement data on the real structure was found to be higher. The x in the diagram correspond to the estimated damping from the measurements. These damping estimates from the measurements result in a logarithmic decrement similar to the simulations using higher non-aerodynamic damping (d ¼ 12% or 13:8%).
Damping ratio Side−side 1
U = 6m/s, H = 0.75m
0.9
U = 8m/s, H = 0.75m
logarithmic decrement
0.8
s s
U = 8m/s, H = 1.25m s
U = 10m/s, H = 1.25m s
0.7
U = 12m/s, H = 1.25m
0.6
U = 12m/s, H = 1.75m
0.5
U = 14m/s, H = 1.75m
0.4
U = 16m/s, Hs = 2.25m
s s s
U = 18m/s, Hs = 2.75m
0.3
8.2. Effect of damping on the cross-wind fatigue
0.2 0.1 0 −60
−40
−20
0
20
40
60
misalignment angle (deg) Fig. 14. Logarithmic decrement in the side–side direction from site-measurements as a function of the misalignment angle for different wind speed – significant wave height conditions.
8. Fatigue for various damping values 8.1. Damping in normal operation During a yaw test performed for the calibration of the support structure strain gauges, a boat hit the structure, causing an impulse response to the turbine. The non-aerodynamic damping (structural-, hydro-, soil-damping and tower damper) was estimated from the exponential curve fitted to the decaying time series of the tower top accelerations [16]. The measured damping was found equal to d ¼ 12:2%. Fig. 12 presents the overall damping of the first two modes in normal operation, estimated with the Enhanced Frequency Domain Decomposition method [20,21]. Three different values of the non-aerodynamic damping have been used in the simulations (6% a typical value used for design, 12% tuned damping from the boat incident, 13.8%, 15% higher damping than the tuned). The damping is implemented by modifying the
Fig. 13 compares the accumulated fatigue load using four different damping values during different combinations of wind–wave conditions. The illustrated data are normalized with the fatigue from the model tuned to the measured damping of d ¼ 12% (reference model) for U ¼ 6 m=s and Hs ¼ 0:75 m. In the fore–aft direction the different damping values have small impact on the fatigue. When the non-aerodynamic damping decreased to half of the reference damping (i.e. 6%-points from d ¼ 12% to d ¼ 6%), the accumulated fatigue only increases by 6% (relative to the reference model). However, in the side–side direction, due to the little aerodynamic damping, the effect of the non-aerodynamic damping is more pronounced. By increasing the damping by 15% (i.e. 1.8%points from d ¼ 12% to d ¼ 13:8%), the reduction change in fatigue is up to 17%. While, when the non-aerodynamic damping is decreased to the lowest damping value (i.e. 6%-points from d ¼ 12% to d ¼ 6%), the fatigue in the cross-wind direction is up to 86% higher than the reference model. The damping in the side–side direction during normal operation for different misalignment angles, estimated with the Enhanced Frequency Domain Decomposition method is presented in Fig. 14. The illustrated data correspond to site measurements. Due to the low contribution of hydrodynamic damping, the overall damping seems to be invariant to the different misalignment angles. It is on a small extent though affected by the higher wind speed, due to the aerodynamic damping introduced to the side– side vibration from the blade pitching.
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Fig. 15. 1 Hz equivalent simulated load as a function of the misalignment angles. Results for four different non-aerodynamic damping values (simulations) are presented, normalized with the equivalent load of the reference model at 0 .
Figs. 15 and 16 present the 1 Hz equivalent load and the fatigue damage contribution respectively in the side–side direction at the tower bottom for different damping values as a function of the
misalignment angle. The sensitivity of the estimated equivalent load to the misalignment angles decreases with increased nonaerodynamic damping. Due to little aerodynamic damping in the
Fig. 16. Simulated relative damage as a function of the misalignment angles. Results for four different non-aerodynamic damping values (simulations) are presented, normalized with the damage of the reference model at 0 .
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side–side direction, the loading is more influenced by the structural damping and the damping due to soil, waves and tower dampers. The equivalent load from the measured time series is less sensitive to the misalignment angle, due to higher damping in the side–side direction of the full scale wind turbine and the spreading of the sea state that is not accounted for in the simulations (Fig. 8). For example at a misalignment of 20°, all the waves are coming from this direction in the simulations and therefore the excitation due to waves is all focused in a single direction. In reality the sea state is more spread, and waves are coming from different directions. This will average out the influence of misalignment in the measurements; therefore the sensitivity to the misalignment angle will not be so apparent. 9. Conclusions The side–side tower-bottom fatigue of a 3.6 MW offshore wind turbine is estimated from measurements on the Walney 1 offshore wind farm. The joint wind–wave distribution and the wind and wave direction distribution based on 6 months of measurements are included in the analysis. The implementation of the joint wind–wave probability scaled to 25 years lifetime, showed that the largest contributors to the accumulated fatigue damage on the sub-structure is from the most probable combinations of wind speed, significant wave height, and misalignment angle; rather than those combination which resulted in the highest 1 Hz equivalent loads. A 3.6 MW pitch regulated-variable speed offshore wind turbine model on a monopile foundation was built in the aero-elastic code HAWC2. Simulations with HAWC2 show good agreement with the measurements in the estimation of the equivalent load for each wind–wave combination and the accumulated fatigue throughout the whole lifetime of the structure. The side–side fatigue loads at the tower bottom were shown to be extremely sensitive to the damping applied in the HAWC2 model; especially in the case of wind–wave misalignment. Increasing values of the non-aerodynamic (to d ¼ 12%) result in a reduction in the side–side accumulated fatigue of up to 46%, compared to simulations with a damping value of d ¼ 6% (a typical value used for design of the sub-structure). Additionally, at a typical design damping of 6%, the simulated side–side fatigue loads are very sensitive to the wind–wave misalignment angle; however, this sensitivity decreased when higher damping values were applied. Therefore, an accurate choice of this damping value is necessary in order to accurately predict the side–side fatigue loads on the sub-structure. On the other hand, the measured side–side fatigue loads were shown to be relatively insensitive to the misalignment angle. The damping in the side–side direction estimated from the measurements during normal operation also seems to be insensitive to the misalignment angle. Additionally, the damping value estimated from the measurements of 12% was significantly higher than the typical design damping of 6%. These finding indicate that there may be significantly more non-aerodynamic damping than is typically considered in the design of wind turbine sub-structures. Since the side–side fatigue loads are highly sensitive to the choice of damping, the use of a conservative damping value in the wind farm design phase may result in significant overprediction of the lifetime side–side fatigue loads. These overpredicted
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loads may result in a significantly overdesigned sub-structure. Choice of an appropriate damping value can therefore result in significant material and cost savings during the design of offshore wind turbine sub-structures. Acknowledgments The work presented is part of the Danish Energy Agency EUDP project titled, Offshore wind turbine reliability through complete loads measurements project no. 64010-0123. The financial support is greatly appreciated. References [1] DNV. Design of offshore wind turbine structures. In: Offshore Standard DNVOS-J101; 2012. [2] Tarp-Johansen NJ, Andersen L, Christensen ED, Morch C, Kallesoe B, Frandsen S. Comparing sources of damping of cross-wind motion. In: European wind energy conference EOW, Stockholm, Sweden; 2009. [3] Damgaard M, Andersen JK, Ibsen LB, Andersen LV. Natural frequency and damping estimation of an offshore wind turbine structure. In: International offshore and polar engineering conference, ISOPE, Rhodes, Greece. [4] Norton E. Wind and wave misalignment effects on fatigue loading. Tech. Rep. 10084. Garrad Hassan, iEC Working Group 3 (Wind Turbine Offshore Standard); 2003. [5] Fischer T, Rainey P, Bossanyi E, Kühn M. Study on control concepts suitable for mitigation of loads from misaligned wind and waves on offshore wind turbines supported on monopiles. Wind Eng, vol. 35. Multi-Science; 2011. p. 561–74. [6] International Electrotechnical Commission (IEC). IEC 61400-3. Wind turbines Part 3: Design requirements for offshore wind turbines. In: International standard; 2009. [7] Schløer S. Fatigue and extreme wave loads on bottom fixed offshore wind turbines. Effects from fully nonlinear wave forcing on the structural dynamics Ph.D. thesis. Technical University of Denmark; 2013. [8] Norton E, Quarton D. Recommendations for design of offshore wind turbines (RECOFF). Tech. rep.; 2003. [9] van der Meulen MB, Ashuri T, van Bussel GJW, Molenaar DP. Influence of nonlinear irregular waves on the fatigue loads of an offshore wind turbine. The science of making torque from wind, Oldenburg, Germany 2012:1–10. [10] Johannessen K, Meling TS, Haver S. Joint distribution for wind and waves in the northern north sea. In: International offshore and polar engineering conference, Stavanger, Norway. [11] International Electrotechnical Commission (IEC). IEC 61400-1. Wind turbines Part 1: Design requirements. In: International standard; 2005. [12] Veldkamp D. A probabilistic approach to wind turbine fatigue design Ph.D. thesis. Technical University of Delft; 2006. [13] DNV. Fatigue design of offshore steel structures. In: DNV recommended practice DNV-RP-C203; 2012. [14] Larsen T, Hansen A. How 2 HAWC2, the user’s manual. Denmark: Forskningscenter Risø, Risø National Laboratory; 2007. [15] Koukoura C, Natarajan A, Krogh T, Kristensen OJ. Offshore wind turbine foundation model validation with wind farm measurements and uncertainty quantification. In: 23rd international offshore and polar engineering conference, ISOPE, Anchorage, Alaska, USA. p. 119–25. [16] Koukoura C, Natarajan A, Vesth A. Identification of support structure damping of a full scale offshore wind turbine in normal operation. Renew Energy 2015;81:882–95. [17] Sumer BM, Jorgen F. Hydrodynamic around cylindrical structures. World Scientific; 2006. [18] Wheeler J et al. Method for calculating forces produced by irregular waves. Journal of petroleum technology, vol. 22. Society of Petroleum Engineers; 1970. p. 359–67. [19] Gudmestad OT. Measured and predicted deep water wave kinematics in regular and irregular seas. Mar Struct, vol. 6. Elsevier; 1993. p. 1–73. [20] Brincker R, Ventura C, Andersen P. Damping estimation by frequency domain decomposition. In: 19th international modal analysis conference. p. 698–703. [21] Jacobsen NJ, Andersen P, Brincker R. Using enhanced frequency domain decomposition as a robust technique to harmonic excitation in operational modal analysis. In: Proceedings of ISMA2006: international conference on noise & vibration engineering. p. 18–20.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Cross-wind fatigue analysis of a full scale offshore wind turbine in the case of wind–wave misalignment Christina Koukoura a,⇑, Cameron Brown b, Anand Natarajan a, Allan Vesth a a b
Technical University of Denmark, DTU Wind Energy, Building 118, PO Box 49, 4000 Roskilde, Denmark DONG Energy A/S, Wind Power, Nesa Alle 1, 2820 Gentofte, Denmark
a r t i c l e
i n f o
Article history: Received 18 September 2014 Revised 27 January 2016 Accepted 11 April 2016
Keywords: Offshore wind turbine Wind–wave misalignment Side–side fatigue Monopile foundation Damping estimation
a b s t r a c t Wind–wave misalignment is often necessary to consider during the design of offshore wind turbines due to excitation of side–side vibration and the low aerodynamic damping in that direction. The measurements from a fully instrumented 3.6 MW pitch regulated-variable speed offshore wind turbine were used for the estimation of the side–side fatigue loads at the tower bottom. The joint wind–wave distribution and the distribution of the wind–wave misalignment angles were considered. The side–side fatigue at the tower bottom and the damping from site measurements are presented as function of the misalignment angles. A model of the same wind turbine was set-up and simulations with the aero-hydro-servo-elastic code HAWC2 were performed to investigate the effect of damping on the side–side fatigue. Turbulent wind field, irregular waves and flexible soil are used in the simulations based on site-measurements. The aim of the current study is to examine the sensitivity of the side–side fatigue to the wind–wave misalignment and different values of additional offshore damping in the system. It was found that the additional offshore damping of the physical system may be higher than what is typically used in offshore wind turbine sub-structure design, due to the low sensitivity of the measured side–side fatigue loads to the misalignment angle. Choice of an accurate damping value implemented in the model during the design of the wind turbine sub-structure can lead to material and cost savings. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Cross-wind fatigue on offshore wind turbine monopile support structures due to wave loading misaligned with the wind can become a significant design driver, because of the low aerodynamic damping experienced in this direction. According to the DNV guidelines for offshore structures [1], the misalignment between the wind and wave directions should be included in the design if misalignment conditions are present in the site of installation. However, these cross-wind fatigue loads are difficult to predict due to uncertainty in the overall system damping. The choice of a conservative damping value can result in overdimensionalization of the substructure, high estimated fatigue loading and a design which is not economically feasible. In Ref. [2], the cross-wind aero-elastic damping is examined, and the sensitivity of the cross-wind loads to the damping, especially during wind–wave misalignment, is highlighted. In the same study, ⇑ Corresponding author at: DONG Energy A/S, Wind Power, Nesa Alle 1, 2820 Gentofte, Denmark. E-mail addresses: [email protected] (C. Koukoura), [email protected] (C. Brown), [email protected] (A. Natarajan), [email protected] (A. Vesth). http://dx.doi.org/10.1016/j.engstruct.2016.04.027 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
measurements from offshore wind turbines at Horns Rev 1 and the Burbo offshore wind farms, were used to estimate the damping and a logarithmic decrement d of about 10% was found (excluding aerodynamic damping). This analysis gave indications that the actual damping on offshore wind turbines is more than what is typically used in design calculations (d ¼ 6%) [2]. In Ref. [3], the logarithmic decrement considering only the non-aerodynamic damping (structural-, hydrodynamic-, soil-damping) is estimated as 14–15% (2.25% damping ratio). The effect of misalignment angles on the fatigue of the structure is examined in Ref. [4]. A study conducted by Fischer et al. [5] considering all load cases described in IEC 61400-3 [6] and misalignment angles from 0 to 360 demonstrated the importance of wave directionality during the design process. The bending moment in the fore–aft direction was 30% higher in the case of waves perpendicular to the wind, while the side–side loading is 5 times larger when compared to aligned wind and wave results. In Ref. [7], the equivalent loads and fatigue damage at the tower and monopile bottom were examined for different cases of wind–wave misalignment, considering both linear and non-linear waves. The effect of misalignment on the simulated fatigue, including the probability density function of misalignment angles has
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been investigated in Ref. [8]. For a misalignment distribution with a peak close to 0 the fatigue damage in the tower bottom was increased by 3:6% between the misaligned and the collinear cases. For the case where the highest probability of occurrence is for an angle of 60 the increase in the fatigue damage is up to 15%. An increase in the fatigue damage accumulation due to waves perpendicular to the wind direction is also reported in Ref. [9], where a non-linear irregular wave model is implemented in the analysis. In the current study the target is to investigate the sensitivity of the cross-wind fatigue loading to the different wind–wave misalignment angles, for various values of the net damping of the system. In the analysis the misalignment distribution is considered. The outline of this paper is as follows: firstly the site and the measurements calibration are described in Sections 2 and 3. Secondly the joint wind–wave distribution and the misalignment distribution based on site observations are presented in Section 4. Thirdly the calculation of the damage equivalent loads of the measured cross-wind vibration at the tower bottom for each wind– wave bin and misalignment sector are discussed. Finally the sensitivity of the cross-wind fatigue to the different misalignment angles, for different damping values is examined.
2. Site description A 3.6 MW Siemens pitch regulated-variable speed wind turbine with a 107 m rotor is installed at the Walney Offshore Wind farm 1 (Fig. 1a). The wind turbine is located at the west coast of England, 15 km from the shore, in the Irish Sea and has been fully instrumented for load measurements. The turbine is mounted on a monopile structure at a water depth of 26 m. Strain gauges and accelerometers are installed at 4 different heights throughout the whole length of the tower (4 gauges per height). The sampling rate of the data acquisition system is 35 Hz. The data has been obtained from the wind turbine manufacturer (Siemens Wind Power) and DONG Energy and is presented in this paper in normalized terms. A nacelle mounted cup-anemometer provides wind speed measurements in time series of 10 min and a buoy installed close to the foundation measures the wave characteristics every 30 min (including significant wave height, peak crossing period and wave direction). Turbine yaw angles, blade pitch angles and power production are obtained as 10 min averages from the SCADA data. The mean yaw angle provided by the SCADA data was used to estimate
the wind direction and the mean wave direction from the buoy are compared to identify cases of wind–wave misalignment (Fig. 1b). 3. Measurements calibration Before the post-processing of the measurements a calibration of the raw data from the strain gauges is required. The time series data are divided up into files each corresponding to 10 min of measurements and the signals are in voltage. Four strain gauges are installed per height placed one across from the other at 150 —330 for the measurement of the North–South and 60 —240 for the East–West bending (Fig. 3a). In the same figure, the sign of the moments from the coordinate system definition is also presented. The tower measurements were calibrated using the mass and offset center of gravity of the nacelle, where the nacelle is slowly rotated 360 around the yaw axis. Fig. 2 presents the coordinate system of the support structure used for the measurements calibration, along with the location of the nacelle center of gravity (CoG). The moment induced by the nacelle weight is defined as a negative moment in the x direction. The subscript T denotes tower. The offset of the CoG creates a moment, which is captured by the strain gauges during the yaw test as a sinusoidal curve. Fig. 3b presents an example of the strain signal versus the yaw angle. The range of the sinusoidal curve from the yaw test is equal to twice the expected moment due to the nacelle weight. This allows the gain of the bridge to be estimated as shown in Eq. (1a). The bridge offset is the mean value of the sinusoidal curve, calculated by Eq. (1b). minðVÞ denotes the minimum strain value in voltage observed during the test, Massnacelle is the mass of the nacelle, g is the acceleration due to gravity, d is the distance of the nacelle center of gravity (CoG) from the tower axis and rangeðVÞ is the range of the sinusoidal curve in voltage. The transformation to the rotating system that follows the wind turbine is performed through Eq. (2), where a is the angle between the strain gauge position and bridge north (30 ) and y is the yaw angle at each time step.
2 Massnacelle g d ; rangeðVÞ offset ¼ Massnacelle g d gain min
gain ¼
M x;rot ¼ MNS cosða yÞ M EW sinða yÞ M y;rot ¼ MNS sinða yÞ þ M EW cosða yÞ
Fig. 1. Walney offshore wind farm 1.
ð1aÞ ð1bÞ ð2Þ
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mean wind speed for the Walney site. The wind turbine D01 is 80% of the time in the wake, so the apparent average wind speed was expected to be lower. Another reason for the discrepancy between the expected site conditions and the estimated wind from the joint wind–wave distribution, is due to the short measurement period of six months, which might not be representative of the site (wind index). The uncertainty of the measurement period should be considered in a more detailed analysis. The probability of each combination of wind speed and significant wave height for the joint distribution (Fig. 4a), was then based on the number of observations in each bin (Eq. (3)), where the index i represents the wind bins, the index j the wave bins and N the number of observations.
Ni;j pi;j ¼ P9 P8 i¼1
Fig. 2. Support structure coordinate system.
4. Environmental conditions 4.1. Wind–wave joint distribution The mean wind speed measurements provided by the SCADA system of the instrumented wind turbine D01 were used to calculate the Weibull probability density function of the wind speed P U . A 2-parameter Weibull distribution is suggested as the conditional distribution of the significant wave height for a given wind speed P Hs jU [10]. The measured wind speed is separated in bins of 2 m/s and the Weibull scale and shape parameters a and b for the wave heights within each bin are estimated. For the calculation of the joint wind–wave distribution, the 10 min mean wind speed U is separated in bins of 2 m/s in such a way that the bin for U = 6–8 m/s covers all the wind speeds in the interval 6 m=s 6 U < 8 m=s. The significant wave height Hs is separated in bins of 0.5 m. For the generation of the contour surface of the local joint wind–wave probability density function, shown in Fig. 4, 6 months of measurements have been used. Due to limited data availability, in Fig. 4a the average wind speed on the site appears to be 8 m/s. This is lower than the annual average
ð3Þ
j¼1 N i;j
As an alternative method of estimating the joint wind–wave distribution, the fitted conditional wave height distribution is combined with the fitted wind speed distribution. The wind distribution is based on measurements from the wake sector, since the wind turbine is mostly on the wake. Fig. 4b presents the contour surface of the fitted joint wind–wave distribution. Using this methodology, the average wind speed is 9 m/s. The time weighting used for the estimation of the lifetime accumulated fatigue are calculated from this fitted joint wind–wave probability multiplied with the hours obtained from the free wind Weibull distribution (hoursfree wind , Eq. (4)). The reduced mean wind speed, seen by the wind turbine due to the wake, should not be considered in the analysis, as the Sten Frandsen model was used for the estimation of the effective turbulence intensity [11]. 90% availability of the wind turbine due to maintenance is considered in the calculation of the operating hours.
life hours ¼ PHs jU P U hoursfree
wind
ð4Þ
4.2. Wind–wave direction probability The directional influence of the spreading on the wave direction measured by the buoy is identified by comparing the mean wave direction with the peak wave direction (i.e. the direction that results in the highest energy from the directional spectrum). Fig. 5 compares the peak and the mean wave direction measurements from the buoy; on the y axis is the mean wave direction, while the peak direction is presented on the x axis. It seems that there are no multi directional sea states from the swell contributions, which could cause differences between the mean and peak
Fig. 3. Strain gauges on the support structure.
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Fig. 4. Local and fitted joint wind–wave probability.
speed increases the misalignment probability decreases. This is because the waves are mainly generated by the wind, especially in sheltered areas like the Irish sea. So the wind–wave correlation at high wind speeds is higher and the probability that the waves are aligned with the wind is larger, since the waves are generated by the local wind conditions.
Buoy Mean Wave Direction (o)
400 350 300 250 200
5. Fatigue analysis/measurements
150 100 50 0 −50
0
50
100
150
200
250
300
350
400
Buoy Peak Wave Direction (o) Fig. 5. Confidence interval of 93% of the mean wave direction measured by the buoy.
The equivalent fatigue load corresponds to the cyclic load that if applied neq times in the structure, it will result in the same damage as the variable load fluctuations experienced over the lifetime of the wind turbine [12]. The measured time series binned as described in Section 4.1, were combined to calculate the 1 Hz equivalent load (Eq. (5)) for each mean wind speed-significant wave height combination. N i are the number of cycles for a given stress range Si , in all measured time series. m is the Wöhler exponent equal to 4 in the present study for the steel components, hi;j is the total measurement time of each bin in seconds and n is the number of stress range bins.
Pn wave directions. Therefore the mean wave direction is a good estimate of the wave direction, with an uncertainty of 30 (93% confidence interval). For the construction of the wind and wave roses shown in Fig. 6 the directions are separated in 12 bins of 30 each. The main wind and wave directions have a difference of 10 . In this analysis we are interested in the relative angle between wind and waves (misalignment) and not their absolute direction. Therefore all wind sectors are included in the study. The misalignment angles are separated in bins of 10 from the minimum to the maximum observed angle for a given mean wind speed and significant wave height combination. The cumulative distribution function (CDF) is then used to calculate the probability of occurrence of each misalignment angle. Table 1 presents the probability of occurrence of nine wind speeds and sea states along with the misalignment probability between the wind and wave directions based on six months of measurements. The probability of occurrence of misalignment angles larger than j 50j is very small and therefore not presented in the table. For all mean wind speeds the wave direction misalignment of 10 has the highest probability of occurrence. It can also be observed that as the mean wind
S1Hz ¼
m ð1=mÞ i¼1 N i Si
hi;j
ð5Þ
Fig. 7a presents the 1 Hz equivalent load for the cross-wind fatigue at the tower bottom as a function of the mean wind speed (all misalignment angles are taken into account). The different lines correspond to the different significant wave heights and the values are normalized with the maximum load for U ¼ 14 m=s. The equivalent load has the tendency of increasing with the wind speed and the wave height. Taking into account the joint wind–wave distribution, the fatigue damage contribution Df of each bin, to the lifetime fatigue of the wind turbine support structure is estimated. Under the assumption of linear cumulative damage, the fatigue damage accumulation is given by Eq. (6), where N tot;i are the number of cycles to failure for a given stress Si and a is the intercept of the S–N curve with the log N axis [13]. The result with respect to the mean wind speed is presented in Fig. 7b. The different curves illustrate the different significant wave heights. It can be observed that the greatest contribution to the lifetime fatigue is not due to the most severe cases but due to bins with higher probability of occurrence, even though the wind and wave conditions are milder.
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Fig. 6. Wind and wave roses with 12 bins of 30 .
Table 1 Probability of occurrence of nine wind-significant wave height combinations along with the observed misalignment probability between their directions. The mean wind speed, significant wave height and misalignment angles represent the center of each bin. U (m/s)
Hs (m)
pi;j
50
40
30
20
10
0
10
20
30
40
50
6 8 8 10 12 12 14 16 18
0.75 0.75 1.25 1.25 1.25 1.75 1.75 2.25 2.75
0.183 0.135 0.074 0.078 0.075 0.054 0.051 0.021 0.009
0.031 0.029 0.014 0.023 0.006 0.009 0.043 0.046 0.033
0.070 0.072 0.048 0.057 0.025 0.033 0.077 0.099 0.065
0.125 0.133 0.105 0.109 0.074 0.086 0.111 0.141 0.116
0.175 0.190 0.171 0.165 0.153 0.161 0.143 0.162 0.148
0.195 0.206 0.209 0.194 0.223 0.216 0.155 0.166 0.173
0.167 0.170 0.194 0.180 0.220 0.210 0.144 0.128 0.153
0.112 0.107 0.134 0.130 0.161 0.148 0.116 0.081 0.113
0.062 0.051 0.070 0.069 0.083 0.073 0.077 0.037 0.065
0.026 0.019 0.025 0.032 0.031 0.025 0.044 0.013 0.000
0.008 0.005 0.008 0.008 0.006 0.008 0.017 0.000 0.000
0.002 0.001 0.000 0.002 0.000 0.000 0.008 0.002 0.000
This observation demonstrates the importance of the joint wind– wave distribution in the calculation of the fatigue of the structure and indicates that it is not only the severeness of the operating conditions that contribute to the fatigue but their probability of occurrence as well.
Df ¼
n n X Ni 1X Ni ¼ m N a S tot;i i¼1 i¼1 i
ð6Þ
wind–wave misalignment for the combinations of wind speed and wave heights presented in Fig. 8. Considering the probability density function of the misalignment angles and using it as a weight to calculate the relative damage of every misalignment angle to the lifetime fatigue of the wind turbine support structure (Eq. (6)), it can be observed that the highest damage contribution is given for the misalignment angle with the highest probability, namely 10 .
Pn S1Hz;misal ¼
m ð1=mÞ i¼1 N i Si
hmisal;mes
ð7Þ
6. Fatigue analysis for different misalignment sectors (measurements) 7. Fatigue analysis/simulations In order to examine the effect of the misalignment angles on the fatigue of the structure, the equivalent load for different misalignment sectors within each wind–wave bin is calculated. The misalignment angles are separated in bins of 10 in such a way that the bin for mis ang ¼ ð15 Þ ð5 Þ covers all the misalignment angles in the interval 15 6 mis ang < 5. The 1 Hz equivalent load for each misalignment sector is calculated by Eq. (7), where hmisal;mes are the measured hours of a specific misalignment sector. The relative damage is estimated accounting for the probability density function of each misalignment angle as was shown in Section 4.2. The loads as a function of the misalignment angle are presented in Fig. 8. The 1 Hz equivalent loads are normalized with 0 misalignment. The 1 Hz equivalent load has a small tendency to increase with the increased absolute value of the misalignment angle. However, the trend is not clear and the side–side 1 Hz equivalent load does not appear to have a high sensitivity to the
In the following two sections the effect of the misalignment angle in the loading of the structure for different damping values is examined. To investigate this, aero-elastic simulations were performed. In Section 7 the estimated fatigue derived from the simulations is compared with the fatigue from the measured loads, to validate the accuracy of the model. In Section 8 the accumulated fatigue is estimated for various values of the damping and the sensitivity of the relative damage in the side–side direction to the misalignment angles is presented. Simulations were performed with the aero-elastic software HAWC2 [14]. The structural wind turbine model is based on a multi-body formulation, where each body is a Timoshenko beam. The 3 bladed 3.6 MW pitch-regulated-variable speed wind turbine model is developed and implemented in HAWC2. The model is described and validated in Refs. [15,16]. Fatigue loads are
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Fig. 7. 1 Hz equivalent load and relative damage at the tower bottom in the side–side direction.
simulated under 9 mean wind speeds, 8 significant wave heights (presented in Section 4.1) and 11 misalignment angles from 50 to 50 are used in the analysis. The turbulence intensity applied in the simulations is based on the wind speed measurements provided by the nacelle cup-anemometer. Fig. 9a presents the scattered wind turbulence intensity, along with the fitted exponential distribution (y ¼ a ebx þ c edx ) representing the 90th percentile of the data. The simulation of the wind turbulence was then made based on the Mann wind turbulence model as described in IEC 61400-1 [11].
The air density used in the simulations is equal to 1:225 kg=m3 . For the calculation of hydrodynamic forces the linear irregular wave theory combined with the Wheeler stretching method to account for loads above the mean sea level is implemented in the aero-elastic code. The hydrodynamic loads are based on the Morison’s equation [17]. The hydrodynamic forces above the mean sea level due to surface elevation are accounted for by applying the Wheeler stretching method [18,19]. The JONSWAP spectrum is fitted to the wave elevation, measured by a buoy installed near to the offshore wind turbine (Fig. 9b). Time series of surface elevation and directional spectrum
Fig. 8. 1 Hz equivalent load and relative damage contribution to the side–side fatigue at the tower bottom based on the probability of occurrence of different misalignment sectors for various wind–wave combinations (measurements). The values are normalized with the equivalent load at 0 misalignment.
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153
Fig. 9. Wind and wave direction distributions.
Fig. 10. 1 Hz equivalent load and relative damage at the tower bottom in the side–side direction, based on the joint wind–wave distribution (measurements vs. simulations), scaled to a lifetime of 25 years.
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Fig. 11. The total accumulated fatigue damage for measurements and simulations normalized with the simulations’ fatigue.
are measured by the buoy, providing a view of the sea state every 30 min. The parameters of the fitted spectrum are given as inputs to the HAWC2 simulations, for the generation of the wave field. Due to very low current velocities, the influence of the current can be neglected in the fatigue analysis [12]. For the loading of the pile-sand, the commonly used p–y curve method is employed, where the soil stiffness is modeled by distributed nonlinear springs along the subsoil portion of the support structure [1]. The soil characteristics used in the simulations are based on geotechnical measurements. The soil consists of different layers (first 7 m is clay/sand/ silt and the rest is sand). Fig. 9c presents the p–y curve for three different soil depths in the site. The lifetime equivalent load is based on the joint wind–wave distribution calculated from the measurements (Eq. (4)), scaled to a lifetime of 25 years. Fig. 10 presents the 1 Hz equivalent load and the relative damage of each bin to the fatigue of the structure with respect to the mean wind speed both for simulations and measurements (dashed lines correspond to simulations and solid to measurements). For each of the 46 mean wind speedsignificant wave height combinations 12 turbulence seeds of 600s and 11 misalignment angles were used in HAWC2, which
resulted in a total of 6072 simulations. The illustrated 1 Hz equivalent load data are normalized with the simulation maximum equivalent load for U ¼ 14 m=s. The simulated equivalent loads seem to follow satisfactorily the measurements. Discrepancies are mainly attributed to differences in the blade aerodynamics and uncertainties in the soil modeling. The accumulated fatigue load for the whole lifetime of the structure (25 years) is calculated both for measurements and simulations. Fig. 11 presents the accumulated fatigue damage at the tower bottom in the fore–aft and side–side directions. The illustrated data are normalized with the simulated load. The agreement between measurements and simulations is satisfactory. The higher simulated accumulated fatigue is due to the lower damping present in the simulations as was shown in Ref. [16]. Due to the low aerodynamic damping in the side–side direction, the modeling of the other sources of damping becomes very important. Uncertainties in the soil damping and the presence of a tower damper in the real wind turbine, but not taken into account in the model are responsible for the discrepancies in the damping estimation and thus the loading between measurements and simulations.
Fig. 12. Overall damping in normal operation from simulations using the Enhanced Frequency Domain Decomposition method. Three different non-aerodynamic damping values are examined from the simulations (stars correspond to d ¼ 12%, circles to d ¼ 6% and crosses to d ¼ 13:8%) and compared to the measurements (blue x). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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155
Fig. 13. The total accumulated fatigue damage from simulations with different values for the non-aerodynamic damping. Normalized with the fatigue from the model tuned to the measured damping for U ¼ 6 m=s and Hs ¼ 0:75 m.
Rayleigh coefficients in the model and applying an impulse to estimate the non-aerodynamic damping from the decaying response. The stars in the figure correspond to d ¼ 12%, the circles to nonaerodynamic damping of d ¼ 6% and the crosses to d ¼ 13:8%. It can be observed that the lowest non-aerodynamic damping (d ¼ 6%), results in much lower overall damping in both the fore–aft and side–side directions. However, as was shown in Ref. [16], using the same methodology, the damping estimated from the measurement data on the real structure was found to be higher. The x in the diagram correspond to the estimated damping from the measurements. These damping estimates from the measurements result in a logarithmic decrement similar to the simulations using higher non-aerodynamic damping (d ¼ 12% or 13:8%).
Damping ratio Side−side 1
U = 6m/s, H = 0.75m
0.9
U = 8m/s, H = 0.75m
logarithmic decrement
0.8
s s
U = 8m/s, H = 1.25m s
U = 10m/s, H = 1.25m s
0.7
U = 12m/s, H = 1.25m
0.6
U = 12m/s, H = 1.75m
0.5
U = 14m/s, H = 1.75m
0.4
U = 16m/s, Hs = 2.25m
s s s
U = 18m/s, Hs = 2.75m
0.3
8.2. Effect of damping on the cross-wind fatigue
0.2 0.1 0 −60
−40
−20
0
20
40
60
misalignment angle (deg) Fig. 14. Logarithmic decrement in the side–side direction from site-measurements as a function of the misalignment angle for different wind speed – significant wave height conditions.
8. Fatigue for various damping values 8.1. Damping in normal operation During a yaw test performed for the calibration of the support structure strain gauges, a boat hit the structure, causing an impulse response to the turbine. The non-aerodynamic damping (structural-, hydro-, soil-damping and tower damper) was estimated from the exponential curve fitted to the decaying time series of the tower top accelerations [16]. The measured damping was found equal to d ¼ 12:2%. Fig. 12 presents the overall damping of the first two modes in normal operation, estimated with the Enhanced Frequency Domain Decomposition method [20,21]. Three different values of the non-aerodynamic damping have been used in the simulations (6% a typical value used for design, 12% tuned damping from the boat incident, 13.8%, 15% higher damping than the tuned). The damping is implemented by modifying the
Fig. 13 compares the accumulated fatigue load using four different damping values during different combinations of wind–wave conditions. The illustrated data are normalized with the fatigue from the model tuned to the measured damping of d ¼ 12% (reference model) for U ¼ 6 m=s and Hs ¼ 0:75 m. In the fore–aft direction the different damping values have small impact on the fatigue. When the non-aerodynamic damping decreased to half of the reference damping (i.e. 6%-points from d ¼ 12% to d ¼ 6%), the accumulated fatigue only increases by 6% (relative to the reference model). However, in the side–side direction, due to the little aerodynamic damping, the effect of the non-aerodynamic damping is more pronounced. By increasing the damping by 15% (i.e. 1.8%points from d ¼ 12% to d ¼ 13:8%), the reduction change in fatigue is up to 17%. While, when the non-aerodynamic damping is decreased to the lowest damping value (i.e. 6%-points from d ¼ 12% to d ¼ 6%), the fatigue in the cross-wind direction is up to 86% higher than the reference model. The damping in the side–side direction during normal operation for different misalignment angles, estimated with the Enhanced Frequency Domain Decomposition method is presented in Fig. 14. The illustrated data correspond to site measurements. Due to the low contribution of hydrodynamic damping, the overall damping seems to be invariant to the different misalignment angles. It is on a small extent though affected by the higher wind speed, due to the aerodynamic damping introduced to the side– side vibration from the blade pitching.
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Fig. 15. 1 Hz equivalent simulated load as a function of the misalignment angles. Results for four different non-aerodynamic damping values (simulations) are presented, normalized with the equivalent load of the reference model at 0 .
Figs. 15 and 16 present the 1 Hz equivalent load and the fatigue damage contribution respectively in the side–side direction at the tower bottom for different damping values as a function of the
misalignment angle. The sensitivity of the estimated equivalent load to the misalignment angles decreases with increased nonaerodynamic damping. Due to little aerodynamic damping in the
Fig. 16. Simulated relative damage as a function of the misalignment angles. Results for four different non-aerodynamic damping values (simulations) are presented, normalized with the damage of the reference model at 0 .
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side–side direction, the loading is more influenced by the structural damping and the damping due to soil, waves and tower dampers. The equivalent load from the measured time series is less sensitive to the misalignment angle, due to higher damping in the side–side direction of the full scale wind turbine and the spreading of the sea state that is not accounted for in the simulations (Fig. 8). For example at a misalignment of 20°, all the waves are coming from this direction in the simulations and therefore the excitation due to waves is all focused in a single direction. In reality the sea state is more spread, and waves are coming from different directions. This will average out the influence of misalignment in the measurements; therefore the sensitivity to the misalignment angle will not be so apparent. 9. Conclusions The side–side tower-bottom fatigue of a 3.6 MW offshore wind turbine is estimated from measurements on the Walney 1 offshore wind farm. The joint wind–wave distribution and the wind and wave direction distribution based on 6 months of measurements are included in the analysis. The implementation of the joint wind–wave probability scaled to 25 years lifetime, showed that the largest contributors to the accumulated fatigue damage on the sub-structure is from the most probable combinations of wind speed, significant wave height, and misalignment angle; rather than those combination which resulted in the highest 1 Hz equivalent loads. A 3.6 MW pitch regulated-variable speed offshore wind turbine model on a monopile foundation was built in the aero-elastic code HAWC2. Simulations with HAWC2 show good agreement with the measurements in the estimation of the equivalent load for each wind–wave combination and the accumulated fatigue throughout the whole lifetime of the structure. The side–side fatigue loads at the tower bottom were shown to be extremely sensitive to the damping applied in the HAWC2 model; especially in the case of wind–wave misalignment. Increasing values of the non-aerodynamic (to d ¼ 12%) result in a reduction in the side–side accumulated fatigue of up to 46%, compared to simulations with a damping value of d ¼ 6% (a typical value used for design of the sub-structure). Additionally, at a typical design damping of 6%, the simulated side–side fatigue loads are very sensitive to the wind–wave misalignment angle; however, this sensitivity decreased when higher damping values were applied. Therefore, an accurate choice of this damping value is necessary in order to accurately predict the side–side fatigue loads on the sub-structure. On the other hand, the measured side–side fatigue loads were shown to be relatively insensitive to the misalignment angle. The damping in the side–side direction estimated from the measurements during normal operation also seems to be insensitive to the misalignment angle. Additionally, the damping value estimated from the measurements of 12% was significantly higher than the typical design damping of 6%. These finding indicate that there may be significantly more non-aerodynamic damping than is typically considered in the design of wind turbine sub-structures. Since the side–side fatigue loads are highly sensitive to the choice of damping, the use of a conservative damping value in the wind farm design phase may result in significant overprediction of the lifetime side–side fatigue loads. These overpredicted
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loads may result in a significantly overdesigned sub-structure. Choice of an appropriate damping value can therefore result in significant material and cost savings during the design of offshore wind turbine sub-structures. Acknowledgments The work presented is part of the Danish Energy Agency EUDP project titled, Offshore wind turbine reliability through complete loads measurements project no. 64010-0123. The financial support is greatly appreciated. References [1] DNV. Design of offshore wind turbine structures. In: Offshore Standard DNVOS-J101; 2012. [2] Tarp-Johansen NJ, Andersen L, Christensen ED, Morch C, Kallesoe B, Frandsen S. Comparing sources of damping of cross-wind motion. In: European wind energy conference EOW, Stockholm, Sweden; 2009. [3] Damgaard M, Andersen JK, Ibsen LB, Andersen LV. Natural frequency and damping estimation of an offshore wind turbine structure. In: International offshore and polar engineering conference, ISOPE, Rhodes, Greece. [4] Norton E. Wind and wave misalignment effects on fatigue loading. Tech. Rep. 10084. Garrad Hassan, iEC Working Group 3 (Wind Turbine Offshore Standard); 2003. [5] Fischer T, Rainey P, Bossanyi E, Kühn M. Study on control concepts suitable for mitigation of loads from misaligned wind and waves on offshore wind turbines supported on monopiles. Wind Eng, vol. 35. Multi-Science; 2011. p. 561–74. [6] International Electrotechnical Commission (IEC). IEC 61400-3. Wind turbines Part 3: Design requirements for offshore wind turbines. In: International standard; 2009. [7] Schløer S. Fatigue and extreme wave loads on bottom fixed offshore wind turbines. Effects from fully nonlinear wave forcing on the structural dynamics Ph.D. thesis. Technical University of Denmark; 2013. [8] Norton E, Quarton D. Recommendations for design of offshore wind turbines (RECOFF). Tech. rep.; 2003. [9] van der Meulen MB, Ashuri T, van Bussel GJW, Molenaar DP. Influence of nonlinear irregular waves on the fatigue loads of an offshore wind turbine. The science of making torque from wind, Oldenburg, Germany 2012:1–10. [10] Johannessen K, Meling TS, Haver S. Joint distribution for wind and waves in the northern north sea. In: International offshore and polar engineering conference, Stavanger, Norway. [11] International Electrotechnical Commission (IEC). IEC 61400-1. Wind turbines Part 1: Design requirements. In: International standard; 2005. [12] Veldkamp D. A probabilistic approach to wind turbine fatigue design Ph.D. thesis. Technical University of Delft; 2006. [13] DNV. Fatigue design of offshore steel structures. In: DNV recommended practice DNV-RP-C203; 2012. [14] Larsen T, Hansen A. How 2 HAWC2, the user’s manual. Denmark: Forskningscenter Risø, Risø National Laboratory; 2007. [15] Koukoura C, Natarajan A, Krogh T, Kristensen OJ. Offshore wind turbine foundation model validation with wind farm measurements and uncertainty quantification. In: 23rd international offshore and polar engineering conference, ISOPE, Anchorage, Alaska, USA. p. 119–25. [16] Koukoura C, Natarajan A, Vesth A. Identification of support structure damping of a full scale offshore wind turbine in normal operation. Renew Energy 2015;81:882–95. [17] Sumer BM, Jorgen F. Hydrodynamic around cylindrical structures. World Scientific; 2006. [18] Wheeler J et al. Method for calculating forces produced by irregular waves. Journal of petroleum technology, vol. 22. Society of Petroleum Engineers; 1970. p. 359–67. [19] Gudmestad OT. Measured and predicted deep water wave kinematics in regular and irregular seas. Mar Struct, vol. 6. Elsevier; 1993. p. 1–73. [20] Brincker R, Ventura C, Andersen P. Damping estimation by frequency domain decomposition. In: 19th international modal analysis conference. p. 698–703. [21] Jacobsen NJ, Andersen P, Brincker R. Using enhanced frequency domain decomposition as a robust technique to harmonic excitation in operational modal analysis. In: Proceedings of ISMA2006: international conference on noise & vibration engineering. p. 18–20.