Introduction
Although the share of offshore wind energy in overall energy production has
been steadily growing over the last years, the cost of offshore wind energy
is still high compared to other renewable energies . In order
to achieve potential cost reductions of about 30 % in the next 10 years
, a realistic and accurate simulation of offshore
wind turbines and their substructures is beneficial. On the one hand, for
realistic simulations, the knowledge of scattering environmental conditions
is a central point. In this context, scattering conditions are non-constant
parameters that exhibit stochastic variations and aleatoric uncertainties,
and therefore should be modelled as statistically distributed. On the other
hand, carefully chosen simulation constraints, like the simulation length or
the time of initial transients, are essential to obtain accurate results.
Here, the simulation length is defined as the usable time for the
post-processing. The time of initial transients is the time that is removed
from each simulation to exclude initial transients resulting from starting a
calculation with a set of initial turbine conditions (like rotor speed).
Simulation length plus initial transient time make up the overall length.
Regarding the first point, current guidelines already define
that simulations should mirror the changing environmental conditions at the
precise site of a wind turbine. However, for academic research, real site
data are rarely available, and, even for industrial purposes, data quality might
be poor for some parameters or long-term data might be missing. As a result,
various research projects have characterised environmental conditions at specific
sites or entire areas and published statistical distributions as a
reference. Probably the most frequently used example is the UpWind
design basis . Further examples are the work of
, the PSA-OWT project
, and the investigations by
. All these reference conditions have some limitations.
The design basis of is only for deep-water
sites off the coasts of the United States of America. The wave state of deep-water sites is not comparable to shallow-water conditions in the North Sea,
as significant wave heights generally increase with the water depth
. Additionally, wind speeds are not measured
at hub height and therefore have to be extrapolated, which increases
uncertainties. For the UpWind design basis, the wind speed is just
given at a reference height of 10 m and not at hub height as well.
Furthermore, no statistical distributions for conditional parameters (e.g.
the wave height Hs depends on the wind speed vs) are given, only
scatter plots. In the PSA-OWT project, data of the research platform
FINO1 in the North Sea are used. Here, the wind speed is measured at hub
height, but shadow effects can occur if sensors are positioned behind the
measuring mast. use data of the research platform FINO3,
which has several sensors at each height to reduce shadow effects. However,
only five environmental parameters (wind speed and direction, wave height,
period and direction) are analysed, and the data period is only 5 years.
Hence, the need for a comprehensive database, covering several sites and
the most important parameters, becomes obvious in order to enable future
research that is based on realistic data. Missing conditions are, for
example,
the turbulence intensity, the wind shear, or ocean currents.
As to the second point, simulation constraints are frequently chosen based on
experience, literature values, or recommendations in current standards.
However, considering the simulation length and time of initial transients,
recommendations in the guidelines are mainly fairly vague . Simulation lengths of 10 min for fatigue calculations (FLS), and
1 h or less for ultimate loads (ULS) are frequently recommended. For the
initial transients, it is advised to discard lengths of 5 s or more.
Literature values partly differ significantly. To reduce the effects of
initial transients, the first 20, 30, or 60 s are discarded, for example
(), and simulation lengths of 10 min
and 1 h are common practice . However, longer
simulation lengths are partly used as well, especially in the oil and gas
industry or for floating substructures . Still, all these
recommendations are not underpinned with detailed analyses. For floating
offshore wind turbines, such investigations were conducted for the simulation
length by , and
. It is shown that simulation lengths of 10 min are
sufficient for ULS and FLS loads. The observation that ULS and FLS loads tend
to be higher for longer simulations is not for physical reasons but due to
unclosed cycles in the rainflow counting for the FLS case and a result of the
averaging technique in the case of ULS loads. Both can be handled by adapting
the algorithms. Concerning the time of initial transients,
recommend 60 s and the utilisation of initial conditions. This
recommendation is based on an analysis which has not been further specified.
For a jacket foundation, conducted a study investigating
lengths of simulations and initial transients and also concluded that 10 min
is sufficient, as long as
10 min time series are merged before the rainflow counting is applied. The
required time of initial transients is determined by checking the rotor speed
to reach a steady state. However, the initial conditions are not applied, and
a steady speed does not guarantee that all transients are damped out.
Therefore, the need for well-founded guidance on simulation lengths and times
of initial transients for bottom-fixed substructures becomes clear. For the
simulation length, useful preliminary work is available, but it is limited to
jacket substructures. Concerning initial transients, extensive studies are
rare and do not concentrate on the convergence of the relevant loads (FLS and
ULS). Furthermore, scattering environmental conditions are not taken into
account. This is a simplification especially in the case of the initial
transients, as this variation might lead to more pronounced resonance effects
(e.g. rarely occurring low wave peak periods that are close to the natural
frequency of the structure; see Sect. ) and therefore
to more pronounced initial transients.
After all, the listed shortcoming in state-of-the-art modelling assistance
motivated the current work that focuses on the following aspects:
deriving an open-access database for various scattering environmental conditions at different sites to enable more realistic
modelling;
giving well-founded guidance on simulation length requirements and the time needed to exclude initial transients,
when these realistic conditions are applied, to improve accuracy of numerical simulations.
In order to address these topics, firstly, a database for all significant
environmental conditions is derived from real data of the FINO research
platforms. In this work, the data source is introduced, the analysis is
described, and the resulting distributions and some interesting findings are
presented. Secondly, required simulation lengths and times of initial
transients are determined. For this purpose, the probabilistic simulation
approach and the simulation model are explained. Then, studies of convergence
are conducted for the simulation length and the time of initial transients. A
monopile and a jacket substructure, FLS and ULS loads, and different wind
speeds are considered. Recommendations are summarised. Lastly, the benefits
and limitations of the current approach are summarised, and a conclusion is
drawn.
Environmental conditions (wind speed vs, significant
wave height Hs, wave peak period Tp, and turbulence
intensity TI) of the K13 shallow-water site (UpWind design basis;
). The wind shear exponent is α=0.14, and
wind and wave directions are usually set to zero, but scatter plots are
available.
vs (m s-1)
2
4
6
8
10
12
14
16
18
20
22
24
26
TI (%)
29.2
20.4
17.5
16.0
15.2
14.6
14.2
13.9
13.6
13.4
13.3
13.1
13.0
Hs (m)
1.07
1.10
1.18
1.31
1.48
1.70
1.91
2.19
2.47
2.76
3.09
3.42
3.76
Tp (s)
6.03
5.88
5.76
5.67
5.74
5.88
6.07
6.37
6.71
6.99
7.40
7.80
8.14
Positions of the three FINO platforms in the North and Baltic Sea,
adapted from OpenStreetMap.
Comprehensive database
Raw data
Environmental conditions can vary significantly among various turbine sites.
As these states affect loads, and therefore the design of offshore wind
turbines, precise data of specific turbine location are valuable. Real site
data are scarce, which is the reason for the previously mentioned reference
databases
.
These databases define conditional, statistical distributions for some of
the most important environmental conditions: wind speed and direction, wave
height, direction, and peak period. However, other conditions are fixed for
each wind speed or are set completely constant. The states of the frequently
used UpWind design basis are summarised in Table as
an example.
In this study, scattering conditions are derived directly from offshore
measurement data. The raw data are taken from the three FINO platforms, and
conditional distributions for the following 13 environmental parameters are
determined: wind speed and direction, wave height, peak period and direction,
turbulence intensity, wind shear exponent, speed and direction of the sub-
and near-surface current, and air and water density. The FINO measurement
masts are located in the North Sea and Baltic Sea and are operated on behalf
of the German Federal Ministry for the Environment, Nature Conservation,
Building and Nuclear Safety (BMUB).
for details. The locations of the three FINO sites are marked in Fig. .
For all three sites, maximum, minimum, mean, and standard deviation values of
the wind speed, measured at different heights between 30 and 100 m above
mean sea level, are available for 10 min intervals. Wind speeds are measured
with cup and ultrasonic anemometers. In this study, cup anemometers are used,
as these sensors are available at more different heights. For FINO1 and 2,
the anemometers are positioned on jibs in secondary wind directions to reduce
shadow effects. For FINO3, three anemometers are installed around the mast to
minimise shadow effects. Sensors at different heights allow a detailed
analysis of shear effects. Wind direction, air pressure, temperature, and
humidity are measured at different heights as well. Buoys in the immediate
vicinity of the research platforms (about 150 m) measure the wave
conditions. Mean values of significant wave heights, wave directions, wave
peak periods and water temperatures are measured every 30 min. Furthermore,
acoustic Doppler current profilers (ADCPs) close to the platforms measure
ocean current velocities and directions at different water depths using the
Doppler effect of sound waves. The platforms FINO1, 2, and 3 have been
measuring continuously since 2004, 2007, and 2009 respectively, resulting in 7
to 13 complete years of measurement data, and enabling at least some
long-term predictions. Data of incomplete years are not taken into account in
order not to introduce bias due to seasonal effects.
Conditional distributions
In this work, raw data of the FINO measurement masts are used to set up a database for correlated, scattering environmental conditions. As the post-processing of raw data is
time-consuming and it is unnecessary to repeat it each time environmental conditions are used, conditional probability
distributions (i.e. P(Y=y|X=x), with X being the independent random
variable, Y the dependent one, and P the probability function) for
environmental conditions are derived to make the database easy to use.
Firstly, post-processing is carried out to identify sensor failures (missing
data) and measurement failures (outliers). Missing data are not interpolated
but instead left out, in order not to introduce any bias. As sufficient data of
proper signal quality are available (e.g. more than 350 000 data points for
the wind speed even for FINO3), this approach is practicable. Wind speed data
are synchronised with the wind direction data. This enables a selection of the
anemometer in front of the mast for FINO3. For FINO1 and 2, wind speed values
are discarded if the jib is located directly in the tower shadow. The
turbulence intensity (TI) can be computed as the quotient of the standard
deviation of the wind speed in a 10 min interval (σv) and the mean
wind speed in this interval (vs) according to Eq. ():
TI=σvvs.
For the wind shear, Eq. () applies according to the standard
of
:
vs(z)=vs(z0)×zz0α,
where z is the height above mean sea level, z0 is a reference height,
vs(z) and vs(z0) are wind speeds at the specified heights, and α
is the wind shear exponent. At the FINO platforms, the wind speed is measured
at eight different heights. Therefore, it is possible to determine the wind
shear exponent for every 10 min interval by assuming z0=90m
and applying a non-linear regression. The air density can be calculated using
Avogadro's law in Eq. () and the measurements of humidity
(ϕ), air pressure (phumid), and temperature in degrees Celsius
(Tair):
ρair=phumidRhumidTair.
As humid air can be regarded as a mixture of ideal gases, the following
equation applies for Rhumid:
Rhumid=Rdry1-ϕpsatphumid1-RdryRvapour,
where Rdry=287.1 J kg-1 K-1 is the specific gas
constant for dry air, Rvapour=461.5 J kg-1 K-1 for
water vapour, and psat is the saturation vapour pressure that can,
for example, be calculated using the August–Roche–Magnus formula:
psat=6.1094hPa×e17.625×TairTair+243.04.
For the water density, a semi-analytical approach by of
the following form is applied:
ρwater=ATwater+BTwaterS+CTwaterS1.5+DS2,
where S is the salinity; Twater is the water temperature at the
surface; A, B, and C are polynomial functions of the water temperature;
and D is a constant. As constant salinity is assumed, the water density is
a function of the water temperature. For all wave parameters, 3 h mean
values are calculated, as wave conditions stay stationary for a duration of
about 3 h . For the speeds and directions of sub- and
near-surface currents, measured current values (vm and
θm) have to be converted in order to separate sub- and
near-surface components. According to, for example, , the
following two equations apply for sub- and near-surface currents
respectively:
vSS(z)=vSS(0m)d-zd17
and
vNS(z)=vNS(0m)20m-z20mforz<=00forz>0.
Here, vSS(z) and vNS(z) are the sub- and near-surface
current speeds at a position z below the water surface, and d is the
water depth. For reasons of clarity, the following notation is introduced:
vSS(z)=vSS,z. The velocity profiles are shown in
Fig. . Obviously, the near-surface current does not exist
below a reference depth of 20 m. Hence, it is possible to use measurement
data of a depth of 20 m (or more) to directly get the sub-surface direction
(θSS,20=θm,20) and to calculate the speed, for
example for FINO2 (d=25 m):
vSS,0=vSS,2025m-20m25m-17.
For the near-surface current, measurements close to the surface (e.g.
vm,2) can be used. However, these measurements include sub- and
near-surface components, as shown in Fig. .
Velocity profiles of the sub- and near-surface currents according to
Eqs. () and () respectively, with a water depth of
25 m and normalised speeds (vSS,0=vNS,0=1).
Therefore, the sub-surface component at 2 m has to be calculated using Eq. (), and the sub-surface direction is assumed to be constant over
depth (θSS,20=θSS,2=θSS,0). Then,
trigonometrical relationships can be applied to calculate the near-surface
current at 2 m:
vNS,2=vSS,22+vm,22-2vSS,2vm,2cosθm,2-θSS,2,θNS,2=θm,2+arcsinvSS,2sinθm,2-θSS,2vNS,2.
Lastly, the reference near-surface current vNS,0 is given by
vNS,0=vNS,220m20m-2m.
A depth-independent near-surface direction is assumed, and therefore
θNS,0=θNS,2.
After having post-processed the measurement raw data, maximum likelihood
estimations are applied to the processed data of the regarded 13 environmental conditions in order to fit several statistical distributions.
In addition to unimodal distributions, and if several distinct peaks are
distinguishable, multimodal distributions are fitted as well, as it is
assumed that the peaks are due to physical phenomena. However, as multimodal
approaches have more degrees of freedom, they always fit the data better,
even in the case of a physically unimodal shape. Therefore, they have to be
chosen with care in order not to fit physically unimodal distributions with
multimodal approaches.
Dependencies, statistical distributions, and bin widths for
environmental conditions derived from FINO1–3 data.
Parameter
Statistical distributions
Dependencies
Bin sizes
Wind speed (vs)
Weibull
–
–
Wind direction (θwind)
Non-parametric KDE
Wind speed
2 ms-1
Turbulence intensity (TI)
Weibull, gamma
Wind speed
2 ms-1
Wind shear exponent (αPL)
Bimodal normal
Wind speed
2 ms-1
Air density (ρair)
Bimodal log-normal
–
–
Significant wave height (Hs)
Gumbel, Weibull
Wind speed
2 ms-1
Wave peak period (Tp)
Bimodal Gumbel
Wave height
0.5 m
Wave direction (θwave)
Non-parametric KDE
Wave height and wind direction
1.0 m and 30∘
Water density (ρwater)
Trimodal normal
–
–
Near-surface current (vNS)
Weibull
–
–
Sub-surface current (vSS)
Weibull, Gumbel
–
–
Deviation NS direction (ΔNS)
Bimodal normal
(Wind direction and NS direction)
–
SS direction (θSS)
Non-parametric KDE
–
–
Considering the example of wind speed and wave height, it is self-evident
that some environmental parameters are conditioned by others, and
dependencies have to be defined. For example, the case of a calm sea during a
storm is very unlikely. Analysing scatter plots of the environmental inputs
and taking a literature review into account, the dependencies in
Table are defined, although it is possible to define them
differently (see
), as mainly the correlation is significant, and
the determination of cause and effect is secondary.
Vectorial analysis of ocean current components at a depth of 2 m
(measured values (m), near- and sub-surface components (NS and SS)).
One of the most common ways to include dependencies in statistical
distributions is to split up the data of the dependent parameters into
several bins of the independent parameters (e.g.
). To illustrate this
approach, for example, the wave peak period is fitted in several bins of
0.5 m wave height (e.g. P(Tp)=P(Tp|1.5m≤Hs<2m)). The bin widths for the dependent parameters
are summarised in Table as well. For highly correlated
parameters, an alternative to the binning procedure is to model only the
deviation between the parameters. Here, the direction of the near-surface
current that is highly dependent on the wind direction is an example.
Therefore, by modelling the deviation ΔNS according to
Table , the following applies:
θNS=ΔNS+θwind
Visual inspections and objective criteria using Kolmogorov–Smirnov tests (KS
tests) and chi-squared tests (χ2 tests) are used to select the best
fitting distribution for each environmental condition. Although the KS test
is less powerful than other statistical tests, it is still used due to its
suitability for small samples (occurring, for example, for dependent variables
and high wind speeds), where χ2 tests are not applicable. For one
parameter, it is attempted to chose only one distribution for all bins and
sites in order to keep the database easy to use. However, as noted in Table , in some cases several distributions are selected to
increase the accuracy of the fits.
Directional parameters like θwind are treated differently, as
classical, parametric distributions can hardly fit several peaks in
continuous distributions (0∘ = 360∘). Therefore, a non-parametric
kernel density estimation (KDE) is used to fit directional parameters.
Resulting distributions
In order to establish a full database, statistical distribution and their
parameters for all 13 environmental conditions, the three sites and all
bins (if necessary) have to be provided. Furthermore, for non-parametric
distributions the underlying data are needed. The main ideas are explained
here; however, due to the comprehensiveness of the data, detailed and
additional information is provided in an easily applicable form, in the
Supplement. At this point, only two examples are shown in Figs.
and .
Special findings
In this section, some noteworthy findings of this database, mainly
resulting from the consideration of scattering, are pointed out. Three
examples are presented: the importance of wave peak periods, the high
scattering of wind shear exponents, and the behaviour of the turbulence
intensity.
Weibull distributions for the wind speeds for all three sites.
Wave loads are of particular importance if the wave frequency is close to
the first natural frequency of the structure. Standard offshore wind turbines
have first bending frequencies of about 0.25 to 0.3 Hz
corresponding to eigenperiods of less than 4 s. If state-of-the-art databases are used (see Table ), there will be no resonance.
However, real data suggest that resonance effects are problematic even for
higher wind speeds, as wave peak periods of less than 4 s occur (see Fig. ).
Concerning the wind shear exponent, in the standards and most current databases (e.g. ), constant values for all wind
speeds are proposed. However, this assumption is a massive simplification.
showed that the wind shear exponent significantly depends
on the wind speed. Here, it is shown (see Fig. ) that it does
not only vary between wind speeds but also scatters remarkably within each bin as
well, and might even be negative.
Distribution of the significant wave height for different wind
speeds and the FINO1 site. For vs≤10 m s-1, Gumbel
distributions are applied. For higher wind speeds, Weibull distributions fit
the data more accurately.
For the turbulence intensity, this database reveals that state-of-the-art
approaches are mainly conservative, as too high turbulence intensities are
assumed. This is shown in Fig. , where the turbulence intensity
for all three sites is compared to a standard database
and to current standards . All
three sites exhibit similar mean turbulence intensities and 90th percentile
values (Q0.9). For the comparison with literature values, the 90th
percentile is of importance, as standards require simulations with this
percentile value. However, even for the 90th percentile, the
UpWind database is very conservative. The least conservative case
(category C) in fits the Q0.9 values relatively well,
but it predicts slightly higher turbulence intensities for wind speeds above
about 10 m s-1. Considering the fact that using the 90th
percentile is a conservative assumption and that the measurements include
some wake effects due to wind farms near to all measurement masts, it can be
concluded that state-of-the-art assumptions for turbulence intensities are
probably unnecessarily conservative. The wake effects are depicted in Fig. , where turbulence intensity measurements of FINO1 from 2011 to
2016 are shown. In this period, the wind farm Alpha Ventus was operating on
the east side of FINO1. Therefore, west wind leads to free stream conditions
and east wind to wake conditions. Obviously, free stream conditions lead to
even lower turbulence intensities, whereas wake conditions increase the
turbulence, especially for smaller wind speeds, as also detected by
.
Probability distribution of the wave peak period for
vs = 11–13 m s-1 for the FINO3 site.
Distribution of the wind shear exponent for different wind speeds
for the FINO2 site.
Simulation assistance
In the previous section, a comprehensive database for scattering
environmental offshore conditions was developed. However, even with realistic
input parameters the accuracy of numerical simulations is significantly
influenced by constraints like their lengths and the time eliminated to
exclude initial transients. Therefore, in this section, efficient simulation
lengths and times of initial transients for varying wind speeds and different
types of loading and substructures are determined. This is achieved by
analysing the convergence of relevant quantities (i.e. FLS and ULS loads).
Before conducting these studies, the overall probabilistic simulation
approach is explained, as it differs from the approach in the standards.
Subsequently, the utilised simulation model and the chosen environmental
conditions are briefly presented.
Turbulence intensity (mean value and 90th percentile
(Q0.9)) for different wind speeds compared to the literature.
Probabilistic simulation approach
For the design of offshore wind turbines, several design load cases (DLC1.1
to 8.3) have to be simulated according to the standards .
These load cases cover ultimate and fatigue loads during power production,
idling and fault conditions, and several special cases like start-up or
shut-down. Stochastic inputs for turbulent wind and irregular wind are
included. Nevertheless, the DLCs remain quasi-deterministic, as environmental
conditions like turbulence intensities and wind shear do not scatter. In
order to guarantee safe designs despite the deterministic approach, several
ULS load cases, covering extreme environmental conditions (e.g. DLC1.3 for
turbulence or DLC1.5 for wind shear), are needed.
Shadow effects on the turbulence intensity for FINO1 and free stream
(western) and wake (eastern) conditions.
In this work, statistically scattering environmental conditions are applied,
and therefore a probabilistic simulation approach is used. This
probabilistic approach differs from the deterministic load-case-based
approach. For the probabilistic approach or “real-life” approach, it is not
necessary to simulate any load cases of extreme environmental conditions
(e.g. DLC1.3 to 1.6), but the use of scattering conditions leads directly to
simulations that represent the real lifetime of the turbine (without fault,
start-up, or other special situations). Hence, simulations (e.g. 10 000 simulations) cover a realistic period of power production and idling, leading
to about 2.3 months of turbine lifetime (for 10 000 simulations). As
environmental conditions scatter, effects like high turbulences, extreme wind
shear, high waves, small wave periods, and others are covered and do not
have to be considered separately. Load cases are not simulated explicitly,
but are covered implicitly by conducting probabilistic simulations.
That is why the two approaches do not differ significantly for FLS. The
“real-life” approach covers DLC 1.2 and 6.4. For ULS, the “real-life”
approach covers all power production cases (DLC 1.1–1.6) and DLC 6.1 by
applying scattering environmental conditions. As the “real-life” approach
cannot simulate 20 years of turbine lifetime (or even a return period of 50
years), a load extrapolation, as required for DLC 1.1, is needed in order to
calculate an ULS design. However, this extrapolation is not needed here, as
it does not influence the investigated simulation constraints.
As common in academia, only power production and idling is simulated. Fault
cases, start-up, etc. are not taken into account due to several reasons.
Firstly, at least for the jacket, fault cases are less relevant
. Secondly, these load cases are very controller and design
dependent and need special treatment (e.g. there is no need of removing
initial transients for start-up load cases). Thirdly, this work is not
intended to calculate exact fatigue damages or ultimate loads for the whole
turbine lifetime, as no turbine design or optimisation is done. The exclusion
of some load cases does not affect the recommendations on simulation
constraints that are given for power production and idling conditions. As
there is no need of exact FLS and ULS lifetime loads in this study, an
assessment of the probabilistic approach concerning accordance with the
standards is neither conducted nor needed, but this would be valuable for further
applications of probabilistic approaches.
Simulation setup
As environmental conditions vary for various turbine sites, a database
being used for the studies of convergence has to be chosen. The basis
developed in this work is appropriate, and the FINO3 site is chosen. Some
conditions, like air and water density, are kept fixed, as it was shown that
their variation is of minor importance . An attempt is made to
keep the convergence study as simple as possible, and to focus on the most
relevant parameters. Hence, for the probabilistic approach, statistically
scattering values according to the determined distributions of wind speed and
direction, wave height, direction and period, turbulence intensity, and wind
shear exponent are used in all simulations. In addition, the following
assumptions are made for all simulations:
The turbulent wind field is computed according to the Kaimal model and using the software TurbSIM with a different wind seed for each simulation.
Irregular waves are calculated according to the JONSWAP spectrum using varying wave seeds for all simulations.
Soil conditions of the OC3 model are applied.
The current, second-order and breaking waves, wave spreading effects, marine growth, local vibration effects of braces, joint stiffnesses, and degradation effects are neglected.
The time domain simulations of the convergence study are conducted using the
aero-servo-hydro-elastic simulation framework FASTv8 . A soil
model applying linearised soil-structure interaction
matrices enhances this code. The NREL 5 MW reference wind turbine
with two different substructures is investigated: Firstly,
the OC3 monopile and secondly, the OC4 jacket .
The outcomes of the FAST simulations are, inter alia, time series of forces,
moments, and stresses for each element of the substructure.
Since the convergence of fatigue and ultimate loads is investigated in the
next step, the calculation concept of these two loads is briefly explained.
For the jacket, the procedure of the fatigue analysis in accordance with
is the following: for each connection of each joint (K joints,
Y joint, butt welds, etc.), eight hotspot stresses around the circumference
of the intersection have to be calculated using the time series. The needed
stress concentration factors (SCFs) depending on the joint geometry are
calculated according to Appendix B of . The fatigue damage is
calculated with a fatigue limit of 52.6 MPa at 107 cycles. This
corresponds to the DNV-GL S-N curve 90 (for cathodic protection) as used in
the original design . For all stresses, rainflow counting
evaluates the stress cycles. As recommended by the current standards, the
conservative damage accumulation according to the Palmgren–Miner rule is
assumed using a slope of the S–N curve of 3 before and 5 after the
fatigue limit for both substructures. The separated fatigue calculation (and
summation over all simulations) for each connection of each joint is
necessary, as damages in each connection and joint are different for each
simulation, and the highest values do not always occur in the same joint (for
example due to the probabilistic variation of the wind direction). Finally,
the decisive damage for the jacket is the highest accumulated value of all
connections of all joints.
For the monopile, the fatigue procedure is similar, but is done according to
, where a detail of 71 MPa for transverse butt welds and an
additional reduction due to the size effect (t>25 mm) is recommended.
Differing from the recommendations in , the same slopes of the
S–N curves as for the jacket are used.
For the ULS analysis, maximum stresses are decisive and extracted from the
time series. For the monopile, is used to analyse the
plastic limit state, cyclic plasticity limit state, and buckling limit state
(LS1–3). For the jacket, NORSOK N-004 is applied for tubular members and
joints, which takes combined axial, shear, bending, and hydrostatic loadings
into account. In both cases, the yield stress is 355 MPa.
Additionally, ultimate limit state proofs for the foundation piles are
performed including axial and lateral soil proofs according to GEO2
and a plastic limit state proof (LS1) for the steel pile
below mudline. Especially for the monopile, the last proof might be decisive
as the bending moment frequently reaches its maximum below mudline. For all
ULS proofs, utilisation factors, being the percentage of the maximum loads,
are the outcomes.
Simulation length
The simulation length significantly influences the
overall computing time of the load assessment. However, there is no
conclusive consensus concerning the length needed. Current standards
recommend, for example, 10 min or 1 h calculations. The offshore oil
and gas industry prefers simulation lengths of 6 h to cover all
low-frequency hydrodynamic effects.
The use of 10 min simulations can potentially reduce the computing time by
a factor of about 36 compared to 6 h simulations. Hence, a study of
convergence for bottom-fixed offshore wind turbines is conducted here. For
floating wind turbines, it is referred to , who
showed that for floating structures all physical effects can be covered with
10 min simulations.
The presented outcomes of this study focus on the monopile substructure, but
a jacket is analysed as well and results (not shown) are generally
comparable. For several wind speed bins, 500 simulations with a total length
of 10 h are conducted. As the initial transient behaviour is analysed
subsequently, a clearly sufficient time, being discarded to exclude the
initial transients, of 4 h is chosen. With elimination of these 4 h of
initial transients, the total length of 10 h reduces to a maximum available
length (simulation length) of 6 h for the convergence study. In a first
step, the convergence of FLS loads is analysed. Afterwards, the ULS case is
investigated.
The procedure to calculate the mean fatigue damage for each wind speed bin is
the following: from the basis of the 500 ten-hour simulations having different
random seeds and varying environmental conditions, 500 cases are selected
(with replacement). For each simulation, the fatigue damage is calculated and
weighted with the simulation length. The mean value of all cases is
calculated. This procedure is repeated 10 000 times (bootstrapping) to
assess the associated uncertainty.
Figure displays the normalised mean fatigue damages for
different wind speeds and simulation lengths between 10 min and 6 h. The values are normalised with the 6 h values, and error bars
show the ±σ confidence intervals (68 %) that are estimated using
a bootstrap procedure with 10 000 resamplings.
It is apparent that due to scattering environmental conditions and the
limited number of simulations the uncertainty is relatively high. A detailed
investigation of the fatigue load uncertainty, when scattering environmental
conditions are applied, is valuable but out of the scope of this work (see
Sect. ). Nevertheless, from Fig. it
is apparent that there are no pronounced trends for changing simulation
lengths. A slight increase in fatigue loads for higher simulation lengths
might be suspected given the fact that such behaviour was observed for
floating substructures by . In order to focus on
the simulation length effects, the variation of environmental conditions is
neglected in a second step (only varying random seeds). This reduces the
uncertainty, making it possible to clearly identify a slight increase in FLS
loads of about 5 % for higher simulations lengths (see Fig. , non-merged case). However, as shown by
for floating substructures, the increasing
fatigue loads are not due to any physical effect (all important low-frequency
effects of waves are already covered by 10 min simulations), but can be
explained by the effect of unclosed cycles in the rainflow counting. Cycles
that are not completed at the end of the simulation are approximated by
counting them as half cycles. The longer the simulation, the less influential
this approximation is, as the number of half cycles compared to the number of
full cycles reduces. A quite straightforward approach to reduce the problem
of half cycles is to merge several shorter simulations (e.g. 10 min
simulations) into a longer one (e.g. 6 h simulation). This means fatigue
damages are not calculated for each time series separately but rather for longer
time series consisting of several shorter ones that are just appended to each
other. It is possible to either append different 10 min time series to
each other or each time series is duplicated and appended several times to
itself. If scattering environmental conditions are assumed, in some
simulations, fairly different load levels occur. In these cases, load levels
of the simulations might not fit, and additional cycles can be introduced by
merging different time series, leading to unreasonably increased fatigue
damages. Merging each time series with itself guarantees fitting load
levels. A downside of this is that the computing time of the post-processing is
slightly increased. The effect of merging several shorter simulations with
themselves to generic and repetitive 6 h time series (e.g. each 10 min
time series is duplicated 36 times and is appended to itself to create a
6 h time series) is demonstrated in Fig. . It can
be seen that the simulation error of about 5 % too low FLS loads for non-merged 10 min simulations can be compensated for by merging time series in the
post-processing.
Normalised mean fatigue damage (500 simulations) for increasing
simulation lengths and different wind speeds.
Normalised mean fatigue damage (500 simulations) for increasing
simulation lengths and vs = 9–11 m s-1. Environmental
conditions are kept constant to demonstrate the effect of merging time series
more clearly.
For the ULS loads, the calculation procedure is similar. From the basis of
the 500 ten-hour simulations, 500 cases are selected (with replacement). The
maximum value of all simulations is taken as decisive utilisation factor.
This procedure is repeated 10 000 times (bootstrapping) to assess the
associated uncertainty.
The convergence is shown in Fig. . Obviously, ULS loads
are higher for longer simulations. Again, this increase is not due to any
physical phenomenon, but a result of different overall computing times.
Clearly, 500 ten-minute simulations should not be compared to 500 six-hour
simulations but instead to about 14 six-hour simulations .
Therefore, in a second step, the ULS calculation procedure is slightly
adapted. Now, 500 cases are only selected for 10 min simulations. For all
other simulations length, the number of cases is reduced to keep the over
simulation length constant at 5000 min (i.e. 250 cases for 20 min
simulation, for example). This comparison is displayed in Fig.
and makes clear that ULS loads do not depend on the simulation length but
instead on the overall computing time. A second fact being visible in Fig. are the higher uncertainties for longer simulation
lengths. Since 10 min simulations lead to a higher number of cases than
6 h simulations for the same total length (i.e. 500 and 14), shorter
simulations better cover rare cases, and therefore scattering environmental
conditions leading to less uncertainty.
After all, the investigations of this section suggest that simulations of
10 min length are sufficient independent of the type of load or investigated
substructure, or wind speed. At this point, it has to be noted that only two
types of substructures are analysed and environmental conditions typical for
the North Sea. For significantly different substructures or locations, the
validity might be limited. Notwithstanding the above, for ULS loads, the same
overall time has to be compared in order to achieve reliable results. By
keeping the simulation length short, more simulations can be conducted in the
same overall computing time leading to a better convergence of ULS loads. For
FLS loads, simulation errors due to the simulation length can be reduced by
merging the time series.
Normalised mean ULS utilisation factor (500 simulations) for
increasing simulation lengths and different wind
speeds.
Normalised mean ULS utilisation factor for increasing simulation
lengths (constant overall length of 500×10 min, leading to 500 to
14 simulations) and different wind speeds.
Initial transients
For the analysis of the simulation length, the first 4 h of each simulation
were discarded to guarantee a steady-state operation of the turbine. However,
removing 4 h of initial transients and only using 10 min of simulation is
computationally very expensive. Therefore, the convergence of FLS and ULS
loads with respect to the time of initial transients is analysed. As initial
conditions, like an initial rotor speed, influence the initial transient
behaviour , initial rotor speeds and blade pitches
depending on the wind speed are set here. These initial conditions are
quasi-static states determined using prior simulations.
As the initial transient behaviour is affected by the type of substructure
and the load condition, the time that has to be removed is analysed in each
wind speed bin for FLS and ULS loads and for both types of substructures
separately. Commonly, time series are investigated to estimate times of
initial transients (). Although this is a
straightforward approach, here it is considered to not be expedient. For a
fatigue assessment, the convergence of the fatigue damage has to be analysed,
and for the ULS analysis, maximum loads or utilisation factors have be
considered.
For each wind speed bin, 10 000 simulations for the monopile and 500 for the
jacket were conducted according to the simulation setup in Sect. . This means that each simulation has its own random seed for
irregular waves and turbulent wind, and in addition, different wind speeds
and directions, wave heights, directions and periods, turbulence intensities
and wind shear exponents according to the FINO3 data are applied. The high
and unequal number of simulations is needed to exclude effects of the number
of simulations, mentioned in the previous section and addressed in Sect. , as well as possible. For the monopile, each simulation at
operating conditions is 900 s long (600 s simulation length plus 300 s of
initial transients) and 1800 s at idling conditions. When the turbine is
idling, the aerodynamic damping is lower, leading to more pronounced initial
transients. For the jacket, all simulations are 720 s long. Using this
simulated database, it is possible to analyse the effect of different
initial simulation times removed on the fatigue damage and utilisation
factors in order to determine optima. The analysed simulation length is kept
constant at 600 s, while the removed length varies between 0 and 300 s
(1200 s for idling; 120 s for the jacket).
Initial transient behaviour of the operating wind turbine with a
monopile substructure for different wind speeds. Percentage difference in the
fatigue damage compared to the “converged” value (300 s).
Figure displays the convergence of the fatigue damage of
the monopile substructure at operating conditions. Here, 300 s or 120 s
values are used as a reference, the so-called “converged value”. The 10 h
simulations in Sect. were used determine these values,
where the error due to initial transients can be neglected and is much
smaller than the error due to the number of simulations. For idling
conditions (not shown), the initial transient behaviour takes longer, as the
aerodynamic damping is lower. For the same reason, the transients are shorter
for higher wind speeds. For the jacket substructure displayed in Fig. , the transients decay much faster in all wind speed
bins. As jackets are less influenced by wave loads, being not always aligned
with the wind, the aerodynamically marginally damped side-to-side modes are
less excited, leading to a shorter transient behaviour. This interpretation
is supported by the fact that for the jacket, idling conditions, where the
hydrodynamic behaviour dominates, have shorter initial transients.
Recommended times that should be discarded to exclude initial
transients for simulations with OC4 jacket and OC3 monopile substructures for
different wind speeds to achieve errors below 5 %.
vs in m s-1
Case
<3
3–5
5–7
7–9
9–11
11–13
13–15
15–17
17–19
19–21
21–23
23–25
>25
Monopile
FLS
720 s
240 s
240 s
240 s
240 s
240 s
240 s
150 s
120 s
60 s
60 s
60 s
360 s
Jacket
40 s
30 s
50 s
40 s
50 s
50 s
50 s
50 s
50 s
60 s
50 s
50 s
10 s
Monopile
ULS
< 10 s
< 10 s
< 10 s
< 10 s
10 s
10 s
10 s
10 s
10 s
10 s
10 s
10 s
< 10 s
Jacket
< 10 s
20 s
20 s
20 s
20 s
20 s
20 s
20 s
20 s
20 s
20 s
20 s
< 10 s
The convergence of ULS utilisation factors for both substructures is shown in
Figs. and . It becomes apparent that
initial transients are short independent of the type of substructure and wind
speed. The cycles with high amplitudes occurring at the beginning of each
simulation are damped out within a few seconds, and hence are not
influencing the ULS behaviour. More problematic are less damped cycles with
smaller amplitudes leading to the previously presented, higher times of
initial transients for FLS loads.
Initial transient behaviour of the wind turbine with a jacket
substructure for different wind speeds. Percentage difference in the fatigue
damage compared to the “converged” value (120 s).
The recommended times that should be discarded to exclude initial transients
for both substructures, being always a compromise between computing time and
accuracy (here, errors below 5 %), are summarised in
Table . It has to be mentioned that the general validity is
limited, as these times of initial transient might vary, for example, for
different aero-elastic codes, numerical solvers, time constants of the
aero-elastic models, or substantially different substructures. For example,
jackets for 10 MW turbines might behave differently due to larger diameters
of legs and braces increasing wave effects. However, for similar applications
(e.g. FASTv8, NREL 5 MW turbine, OC3 monopile, or OC4 jacket) that are not
rare in academia (e.g. or
), the given values represent a well-founded
guidance for simulation setups. Furthermore, these results should sensitise
the research community to the problem of initial transients especially in the
case of fatigue. For fatigue, the time of initial transients might be higher
than frequently presumed in the literature. This is due to weakly damped
cycles with small amplitudes that cannot directly be identified when looking
at time series.
Initial transient behaviour of the wind turbine with a monopile
substructure for different wind speeds. Percentage difference in the
utilisation factor (ULS) compared to the “converged” value (120 s).
Initial transient behaviour of the wind turbine with a jacket
substructure for different wind speeds. Percentage difference in the
utilisation factor (ULS) compared to the “converged” value (120 s).
Benefits and limitations
The benefit of the current work is twofold. Firstly, a comprehensive database for scattering environmental conditions was set up, which is freely
available and easy to use. Secondly, two simulation constraints (simulation
length and time of initial transients) were analysed, and well-founded
recommendations are given.
The main advantages over existing databases are the following: the database
covers several different sites situated in different oceans. It has to be
admitted that the sites are fairly similar, as they are all in shallow-water
conditions. Additionally, the database contains statistical distribution for
much more environmental conditions than existing ones. As was shown, for
example, by that not only main conditions like
the wind speed are influencing the dynamic behaviour of offshore wind
turbines, knowledge of additional parameters is beneficial. Current databases
consist frequently of raw data that need to be post-processed, which is a
time-consuming process. Here, on the one hand, easily applicable statistical
distributions are given. On the other hand, the complexity of dependent
environmental conditions is still covered by utilising conditional
distributions and multimodal and non-parametric approaches. In contrast to
many existing databases, the raw data are of good quality. For example, wind
speeds are measured at heights comparable to hub heights of current turbines,
and there is no need for extrapolations, as is the case for buoy measurements.
Still, more data would be valuable in order to achieve more reliable
distributions in high-wind-speed bins that rarely occur. After all, the
developed database is capable of improving offshore wind turbine modelling by
providing more realistic inputs for simulations in academia, where real site
data are scarce. One example of improved offshore wind turbine modelling is
given in Sect. and . The inclusion of
probabilistic inputs leads to a significant and realistic increase in fatigue
damage scattering requiring high numbers of simulations. Hence, deterministic
inputs underestimating this scattering can lead to biased fatigue values.
Detailed analyses of the effect of scattering environmental conditions on
fatigue damage, and therefore of the needed number of simulations, are part
of upcoming work of the authors.
Concerning the second benefit, the simulation constraints, it has to be kept
in mind that not only realistic modelling but also small simulation errors
are important in order to model accurately. In this context, the chosen
simulation length and time of initial simulation transients matter. So far,
these values are frequently chosen without profound knowledge. Some
approaches to gain a deeper insight into these constraints
(; )
concentrate on simulation lengths or specific types of substructures and are
not taking realistically scattering environmental conditions into account. In
this work, the scattering of the conditions is addressed and different
bottom-fixed substructures are analysed. This enables recommendations for
simulation lengths and times of initial transients depending on the wind
speed, the type of substructure, and the considered load case (ULS or FLS).
However, the general validity of the current results has to be slightly
restricted, as only one design of each type of substructure was investigated.
Therefore, the initial transient behaviour might be slightly different for
significantly different designs. Furthermore, for the time being removed to
exclude initial transients, the values might also differ between different
simulation codes and are only tested for the FASTv8 code. Different numerical
solver or time constants of the aero-elastic models might also influence the
time of initial transients. Nevertheless, even in these cases, firstly, the
given recommendations can be regarded as a well-founded starting point for
further investigations. Secondly, and even more important, they clarify the
challenge of a well-founded choice.