ESTIMATION OF FATIGUE LOAD ON FLOATING OFFSHORE WIND TURBINE AT
TOWER BASE DURING POWER PRODUCTION
12Danupon Subanapong , Atsushi Yamaguchi and Takeshi Ishihara
1,22Department of Civil Engineering, The University of Tokyo, 113-8656 Japan

Following results were obtained.
The measurement data of wind, wave and tower base moment at Fukushima Offshore site is investigated.
Firstly, the analysis of full-scale measurement data is performed. Then, the Damage Equivalent Fatigue Load (DEFL) iscalculated based on 1 year measurement data and used as the benchmark. The effect of direction of wind and wave,
wave height and wave on fatigue load is discussed in this research. The methods to reduce number of wind and wave
direction and wave height and wave period is proposed and then validated by the load calculated from measurement data.
Keywords: Damage Equivalent Fatigue Load, Wind and Wave Misalignment, Floating Offshore Wind Turbine

INTRODUCTION
For the fatigue design of offshore wind turbines, thejoint probability distribution of wind speed, wave heightand wave period has to be considered [1]. The
combination of those parameters leads to large numbersof numerical simulations. In addition, the applicability of
the approach for bottom mounted offshore wind turbine, tothe floating offshore wind turbines (FOWT) are unknown.
Several studies have been carried out on the fatigue
load analysis of floating offshore wind turbines wang et al.
[2] studied the effect of wind and wave misalignment on
the short-term fatigue damage. It is pointed out that theco-directional wind and wave gives relatively larger
fatigue damage compared to other misalignment cases
and it is conservative to use only co-directional condition.
Roberson et al [3] concludes that to consider only thealigned wind and wave condition the side-side tower
fatigue damage is underestimated by approximately 50%,
and fore-aft tower fatigue is overpredicted for 5%.
However, these studies only relied on simulation andthere is no validation between simulation and full-scalemeasurement. Also, there is no conclusion on how toreduce number of computation. Therefore, a method toreduce number of considered wind and wave direction
should be proposed.
Kvittem and Moan [4] pointed out the effect of wave
period on fatigue damage. It is discussed that at the samewind speed and wave height condition, the smaller wave
period gives larger fatigue damage. The reason is thatsmaller wave period causes higher frequency response
which finally leads to larger number of cycle in fatigue
calculation. However, this study only use simulation andthere is no validation between simulation and full-scalemeasurement.
In this study, the effect of wind and wave
misalignment is clarified and the method to reduce
number of wind and wave considered in calculation isproposed. By using the tower base moment measurement
data of Fukushima floating offshore wind turbines, 1-year
damage equivalent fatigue load (DEFL) calculated basedon proposed method is compared to the fatigue load
calculated from 1-year measurement data. The effect ofwave height and wave period is also discussed. The
parametric study of wave height shows that the higher
wave height is used, the larger fatigue damage while it is
no clear tendency for wave period effect on fatigue load.
Then, the method to reduce number of wave height andwave period is proposed and validated by measurement
data. Finally, the combination of two proposed methods:
to reduce number of wind and wave direction and toreduce number of wave height and wave period is used tocompute 1-year DEFL and compared with measurement
data.
ANALYSIS OF MEASUREMENT DATA
Environmental site condition
The measurement data was collected from
01/01/2015 to 12/31/2015. 10 minutes average windspeed, 10 minutes significant wave height and period, andtower base moment, and floater motion were used in thisstudy. The number of 10 minutes data is showed in Table.
1. エラー! 参照元が見つかりません。 illustrates the windrose and waver rose when wind turbine is in operation.
Table 1. Wind Turbine Status.
No. of cases
Operational34140
Parked
18429
Total
52560

Available
33731
15925
36022

be used to reduce number of wind and wave direction.
Table 2. Number of case for each direction

The damage equivalent fatigue loads [5] areemployed to calculate fatigue load in this study. The
advantage of calculating the equivalent fatigue load
instead of the regular fatigue value is that it reduces along history of random fatigue loads into one number,which make it easier to compare different load situations.
The equation for equivalent fatigue load is expressed asbelow.
𝑚∑ 𝑆 𝑚 𝑛𝑖

𝐷𝐸𝐹𝐿 = √ 𝑖 𝑖𝑁0Wave

Fig. 1. Wind rose and wave rose during power production
DAMAGE EQUIVALENT FATIGUE LOAD

030
60
90
120
150
180
210
240
270300
330

0169
883
1045
1231
1358
750
157
0000430
28
294
635
691
539
388
150
0000060040
341
300
208
91
13000009000132
272
430
64
500000120020101
144
227982700000Wind
150
180
00
2352
186
515
194865341 1526
198
964
75
740
0
120
0000000

210
0
39
421
744
1475
1207
972
110000

240
1
7144
167
163
233
198
150
100

270
135
113
464
375
246
396
434
39
11
67
45
60

300
688
375
781
629
495
428
246
60
1115
107

330
761
863
1043
831
996
544
128
0
6
1
464(1)

where 𝑆𝑖 is the stress range, 𝑛𝑖 is the number of cycle ineach range, 𝑁𝑖 is the total cycle for the whole fatigue load
period calculation and m is the fatigue exponential, for thiscase m=3 for welded steel, is used.
Fig. 2. Misalignment effect on DEFL for fore-aft direction
PROPOSED MODEL FOR WIND AND WAVE
DIRECTION
Effect of wind and wave alignment on DEFL
To study the effect of wind and wave misalignment on
fatigue load, the number of case for each wind and wave
direction are analyzed. The same degree of misalignmentis then grouped into the same color as shown in Table. 2.
The damage equivalent fatigue (DEFL) for each degree ofmisalignment are compared in Fig. 2 for fore-aft direction
and Fig. 3 for side-side direction. It can be seen that when
the degree of misalignment is 0⸰ and 180⸰ the DEFL forfore-aft direction is maximum. However, there is no clear
tendency for side-side moment.

Fig. 3 Misalignment effect on DEFL for side-side direction

Proposed method for the wind and wave direction
To reduce the number of wind and wave directions
concerned for the fatigue load calculation, 4 of the mostfrequently occurred wind and wave direction are used: 0 ⸰,180⸰, 210⸰, and 330⸰ for wind directions and 60⸰, 90⸰,120⸰, 150⸰ for wave directions. The DEFL are calculated
for each combination of wind and wave direction. The
1-year DEFL is computed by summarizing all fatigue loadof each wind and wave direction by weighting theprobability of their wind and wave direction. Then, the1-year DEFL computed by proposed method is comparedto the 1-year DEFL calculated from all 1-year
measurement data and the conventional case(co-directional wind and wave condition) as shown in Fig.
4 and Fig. 5. It is found that the proposed method gives
small underestimation about 10% for fore-aft direction and15% for side-side direction which is acceptable while theconventional case gives relatively large overestimation
about 25% for fore-aft and 20% for side-side direction.
Therefore, it is concluded that this proposed method canFig. 4 1-year DEFL calculated by proposed method(fore-aft)Fig. 5 1-year DEFL calculated by proposed method (side-side)

PROPOSED MODEL FOR WAVE PERIOD AND
WAVE HEIGHT
Effect of wave height and wave period on DEFL
To study the effect of wave height and wave period,210 wind direction and 60⸰ wave period is selected. Theprobability distribution of wave height and wave period isshown in Fig. 6. The DEFL for fore-aft and side-side
direction is shown in Fig. 7 and Fig. 8. Then, bycomparing the DEFL for the same wave period and windspeed with different wave height the effect of wave heighton fatigue load can be obtained. Fig. 9 shows the effect ofthe wave height on DEFL. Higher wave height causes
larger fatigue load. The effect of wave period on DEFL isshown in Fig.10. As seen in Fig. 10, there is no clear
tendency for the effect of wave period. Therefore, it isconcluded that the effect of wave height on DEFL isimportant to be concerned.

Fig. 9. Effect of wave height on DEFL

⸰Fig. 10. Effect of wave period on DEFL
Proposed method for the wind and wave direction

Fig. 6. Probability Distribution

Fig. 7. Distribution of DEFL (Fore-aft)

As it is seen that the effect of wave height isimportant to be concerned. The 90 percentile of wave
height is selected as the equivalent wave height. For thewave period, 25 percentile, 50 percentile, and 75
percentile of wave height are selected. To verify if thismethod is applicable, the DEFL at specific wind and wave
direction is computed and compared with measurement
data. Fig. 11 and Fig. 12 illustrate the comparison of DEFL
calculated by proposed method and by using the all themeasurement data in fore-aft and side-side direction. The
total fatigue load is computed by summarizing DEFL ofeach wind speed bins by weighting the probability of theirwind speeds as shown in Fig. 13. It is found that theproposed method gives very accurate prediction for bothfore-aft and side-side direction. Therefore, it is concludedthat the proposed method is applicable to reduced
number of wave height and wave period considered incalculation.

Fig.8. Distribution of DEFL (Side-side)

Fig. 6 DEFL of each wind speed (fore-aft)Fig. 9 Total fatigue load (fore-aft)

Fig.

Fig. 10 Total fatigue load (side-side)

7 DEFL for each wind speed (side-side)

Table 3. The number of simulation cases
Wind/wave
direction

Windspeed

Wave
heightWave
periodTotal

All

144(12x12)

12677257

Conventi
onal

12126766048

Propose16(4x4)

121

3576

CdFig. 8 Total fatigue load at specific wind/wave direction
OMBINATION OF PROPOSED METHOD FOR WIND
AND WAVE DIRECTION AND WAVE HEIGHT AND
WAVE PERIOD
The applicability of the combination of the proposed
method for wind and wave direction, and the wave heightand period, is investigated. Firstly, the wind and wave
directions are selected as mentioned in the previous
section: 0⸰, 180⸰, 210⸰, and 330⸰ for wind directions and60⸰, 90⸰, 120⸰, 150⸰ for wave directions. Secondly, forthe computation of the DEFL at each wind speed andwind and wave direction, 90 percentile of wave height isused while 25, 50 and 75 percentile of wave period areused. The total fatigue loads computed by the proposed
method are compared to the load calculated from 1-year
measurement data and the conventional method(co-direction of wind and wave direction) in Fig.11 andFig.12. It is found that the conventional method gives
relatively large overestimation compared to the proposed
method for both fore-aft and side-side direction and thecomputed load by the proposed method is appropriate forthe fatigue load prediction. Table.2 shows how theproposed method can significantly reduce the number ofconditions required to calculate fatigue load.

CONCLUSION
In this study, the 1 year measurement data of wind, wave
and tower base moment at Fukushima Offshore site isinvestigated. Following results were obtained.
1)

To reduce number of wind and wave direction, 4 mostfrequent wind directions and 4 most frequent wave
directions are selected. The DEFL calculated based
on 4x4 wind and wave direction gives around 10%
underestimation for fore-aft direction, while it is about
5% underestimation for side-side direction.

2)To reduce number of wave height and wave period,
90 percentile of wave height with 25 , 50, 75
percentile of wave period are selected. The
differences between actual DEFL and proposed
method are 1.5 % and 4.2% for fore-aft and side-sidedirection.

3)

The combination of two methods to reduce number ofwind and wave direction and wave height and wave
period gives accurate fatigue load calculation.
REFERENCES[1] IEC61400-3: Wind Turbine – Part3: Design requirements for offshore wind turbines, 2009[2] Wang, K., Ji, C., Xue, H. and Tang, W. (2016).
Fatigue
DamageCharacteristics
ofaSemisubmersible-type Floating Offshore Wind Turbine atTower Base. Journal of Renewable and SustainableEnergy.

[3] Robertson, A., Lackner, M., Matha, D. and Stewart, S.
W. (2014). Wind/Wave Misalignment in the Loads
Analysis of a Floating Offshore Wind Turbine.
ResearchGate.
[4] Kvittem, M. I. and Moan, T. (2015). Time Domain
Analysis Procedures for Fatigue Assessment of a
Semi-submersible Wind Turbine. Marine Structures.
[5] H. B. Hendriks and B.H. Bulder (1995), Fatigue
Equivalent Load Cycle Method. ECN-C-95-074