WESWind Energy ScienceWESWind Energ. Sci.2366-7451Copernicus PublicationsGöttingen, Germany10.5194/wes-3-173-2018Assessment of wind turbine component loads under yaw-offset conditionsLoads under yaw-offsetDamianiRickrick.damiani@nrel.govDanaScotthttps://orcid.org/0000-0002-8292-8675AnnoniJenniferFlemingPaulhttps://orcid.org/0000-0001-8249-2544RoadmanJasonhttps://orcid.org/0000-0003-2280-5996van DamJeroenDykesKatherineNational Renewable Energy Laboratory, Golden, CO 80401, USARick Damiani (rick.damiani@nrel.gov)13April2018311731896September201712September201727November201719December2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://wes.copernicus.org/articles/3/173/2018/wes-3-173-2018.htmlThe full text article is available as a PDF file from https://wes.copernicus.org/articles/3/173/2018/wes-3-173-2018.pdf
Renewed interest in yaw control for wind turbine and power plants for wake
redirection and load mitigation demands a clear understanding of the effects
of running with skewed inflow. In this paper, we investigate the physics of
yawed operations, building up the complexity from a simplified analytical
treatment to more complex aeroelastic simulations. Results in terms of damage
equivalent loads (DELs) and extreme loads under misaligned
conditions of operation are compared to data collected from an instrumented, utility-scale
wind turbine. The analysis shows that multiple factors are responsible for
the DELs of the various components and that airfoil aerodynamics, elastic
characteristics of the rotor, and turbulence intensities are the primary
drivers. Both fatigue and extreme loads are observed to have relatively
complex trends with yaw offsets, which can change depending on the wind-speed
regime. Good agreement is found between predicted and measured trends for
both fatigue and ultimate loads.
Introduction
Despite numerous studies on the skewed inflow and wake of wind turbines
e.g.,, uncertainties still remain on the loading effects experienced
by their mechanical components under misaligned operation. Whereas new
interest is directed at maximizing plant power performance via wake steering
and yaw control e.g.,, understanding and managing
their effects on operation and maintenance (O&M) costs are critical for the
success of the strategy. For this reason, a clear understanding of the short-
and long-term consequences of operating in skewed conditions, or with yaw
offsets, is necessary to assess whether maintenance costs could change, and to
facilitate intelligent ways to improve power performance that mitigate any
negative O&M impacts.
It can be argued that a certain degree of yaw error is always present during
turbine operation, in part because of wind turbulence and in part because of
mechanical errors in the turbine alignment and during yaw transients
cf. . Here we are concerned with the systematic,
skewed-inflow operation. The resulting wake redirection could significantly
alleviate the cyclic loads of wind turbines located downwind of those
operating off axis. show that the increase in turbulence
associated with operation in waked inflow can increase fatigue loads by up to
15 % with respect to clean inflow. However, aerodynamic processes and
loading effects on the upwind turbines are, to a degree, uncertain. A few
studies have shown a reduction in blade load levels for turbines operating
under certain yaw offsets, accompanied by an increase in loads for other
components e.g., drivetrain and tower;.
Some focus has also been given to the load variations under cyclic variations
of angle of attack (α) and relative air velocity at the airfoil of
interest (Urel), but conflicting information still exists. On the
one hand, industry experts have either advised against yaw-offset operation
or devised technology and algorithms to
minimize yaw misalignment while maximizing power production at the individual
turbines in a plant . On the
other hand, control system scholars recommend adopting strategies that can
redirect wakes away from downwind turbines to increase the plant power
production as a whole e.g.,, or even suggest the use of continuous yaw control
to increase damping and reduce loads e.g.,. In the
middle, the owners and operators are left with the unsatisfying conundrum of
increasing power production and associated revenues while taking the risk of
accelerated machine damage and associated repair costs.
Data from wind tunnel experiments e.g.,
show load and performance trends under yawed conditions and emphasize the
importance of dynamic stall and unsteady-aerodynamics (UA) effects; yet these
tests do not capture the impact of realistic atmospheric turbulence on the
loads of key wind-power-plant components. Some data from full-scale turbines
are available e.g.,, but they are generally associated with
involuntary yaw errors rather than a systematic measurement campaign with
prescribed yaw offsets and comparison to aeroelastic simulations.
In this paper, we examine the problem of skewed wake and inflow for one
utility-scale turbine configuration. The analysis starts from a theoretical
standpoint and builds up in complexity, going from a simplified, analytical
model for the α and Urel azimuthal variations under
different yaw offsets to a fully aeroelastic realization of the turbulent
operation. At one end of the complexity spectrum, the analytical model is an
aid to the designer, as it predicts load and performance outcomes under
steady-state conditions and sheds light on the physics by highlighting the
effects of shaft tilt, inflow shear, and yaw error. The aeroelastic model
results, at the other end, account for turbulence effects and nonlinearities
of the entire system and therefore provide more clarity about the
system-dynamics response under realistic conditions. For practical
predictions, the aeroelastic model should be validated; hence extensive data
were collected on a 1.5 MW turbine under several different yaw-offset
conditions and compared to the model results.
In Sect. , we provide a description of the methods used
in this study, the load channels of interest, and the turbine under analysis.
In Sect. , the analytical model is presented.
Section provides results attained with simulations of
the turbine operation under steady winds. Turbulent-inflow simulation results
are compared to field-collected data in Sect. . A summary of
the observations is offered in Sect. .
Methods and load channels of interest
Our analysis was focused on the General Electric (GE)
1.5sle 1.5 MW wind turbine (GEWT)
installed at the National Wind Technology Center (NWTC),
which is owned by the U.S. Department of Energy (DOE) and operated by the
National Renewable Energy Laboratory (NREL). The turbine is instrumented with
an extensive set of load and performance sensors per ,
which is described in the next section. An original GE aeroelastic model was
modified to be used with NREL's aero-hydro-servo-elastic tool for wind
turbine design (FAST) version 8 (FASTv8) . FAST is a
widely used industry and academic tool for load estimation.
(a) Convention used in this paper for positive yaw and yaw
offset. (b) View of the test turbine and meteorological tower, NREL
25911.
One of the underlying goals of this paper was to link the observed results to
the physics of the blade aerodynamics and structural dynamics. Therefore, we
started with a simplified model of the aerodynamics under steady, but
sheared, wind conditions and examined the azimuthal variation of the lift. An
analytical model based on the variance of the lift out-of-plane component as
a function of yaw offset was produced. The lift standard deviation, i.e., the
square root of its variance and hence the associated blade load standard
deviation, was used as an indicator of oscillating fatigue loads. We then
examined how this model performed under different hub-height wind speeds and
then increased complexity by first using AeroDyn 15 (AD15), FASTv8's aerodynamics
module, in stand-alone mode and then using a fully aeroelastic model of the
turbine within FASTv8. We demonstrated the effects of UA and of the
structural response on the blade-root bending moments by turning on and off
FASTv8's UA module and the relevant structural degrees of freedom. This
initial analysis was done based on two wind speeds, in turbine power regions
2 and 2.5. Finally, the model was further refined by accounting for turbulent
inflow and was compared to data from the field for several wind speeds up to
rated power wind speed. Twenty turbulent seeds were considered, using the
normal turbulence model (NTM), and the calculated loads
were compared to those extracted from wind-speed binned data coming from the
field. For the sake of brevity, results for only two wind speeds are shown,
which, however, are representative of conditions at and below rated power.
Seven output channels of interest were selected: blade-root edgewise bending
moment (EBM) and flapwise bending moment (FBM) and their resultant
root-bending moment (RBM); low-speed-shaft torque (LSSTq); tower-top bending
moment (TTBM, resultant of the fore–aft and side–side components); tower-top
torque (TTTq); and tower-base bending moment (TBBM, resultant of the fore–aft
and side–side components). Initially, the focus was on the FBM because
conflicting information exists in the literature and in the industry
experience , and because it is also associated
with thrust loads responsible for structural stresses on downstream components. The analysis
was mainly carried out on fatigue loading, and the results are given in terms
of short-term damage equivalent loads (DELs) via rain flow counting . Note that we
also provide some insights on ultimate loading, but they do not include
parked and fault conditions. Simulations and field data are based on 10 min
interval sets. In the next section, we describe the field instrumentation
setup.
Field instrumentation
The field-test campaign was carried out at the NWTC near Boulder, Colorado,
and occurred over 6 months, during which the test turbine was operated with
discrete yaw offsets over a range of wind speeds and atmospheric conditions.
The test turbine and its dedicated meteorological tower are shown in
Fig. . Details of the turbine are provided in
Table .
Test turbine details.
Brand and modelGE 1.5sle ESSparametervalueRated power (kW)1500Hub height (m)80Nominal rotor diameter (m)77Rated wind speed (m s-1)14
The turbine was instrumented in accordance with IEC 61400-13
for mechanical-load measurements. All measurement
methods and load processing were in conformance with this standard.
Specifically, the tower base, tower top, and blade roots were instrumented
for measurement of bending loads. In addition, the tower top and main shaft
were instrumented for torque measurements. Encoders were used to measure yaw
position, blade pitch, and rotor azimuth. The turbine was also instrumented
for independent power measurements per. All
signals were collected with a time-synchronous deterministic EtherCAT
protocol and stored at a sample rate of 50 Hz.
The meteorological tower is located 161 m (∼ 2 rotor diameters) in the
predominant upwind direction of the turbine and was instrumented in
accordance with IEC 61400-12-1 . The meteorological
tower measurement signals were time-synchronously recorded with the turbine
loads signals. For the analysis presented in this paper, the 80 m cup
anemometer and the 87 m wind vane signal were used for the reference mean
wind speed, direction, and turbulence intensity (TI). Test data were limited to a
sector of directions in which the meteorological tower is largely upwind of
the turbine. This measurement sector avoids any turbine wake influence on the
meteorological tower instrumentation or influence of other turbines at the
test site. More details on the instrumentation setup can be found in
.
The turbine nacelle's wind vane signal was modified using a frequency
modulation device with a dedicated user interface for programming yaw-offset
schedules of discrete offset values and durations. In no other way was the
turbine or its controller manipulated. The turbine was set to cycle at 1 h
intervals between the baseline setting, i.e., a 0∘ yaw offset, and a
nonzero offset. The offset values included -25, -18, -12.5, 0, 12.5,
18.0, and 25.0∘. However, not all offset value data could be used for
analysis because of wind speeds or directions outside of the acceptance
ranges selected for this study and discussed below.
As visible in Fig. , the convention employed for
the sign of the yaw misalignment implies that with positive yaw offset the
hub center is to the right of the tower centerline when looking downwind.
α (lines with no markers) and Urel (lines with
markers) calculated by the simplified analytical model as a function of
ψ for the 75 % blade-span station under yaw misalignments (γ)
as shown in the legend; Uhub=12 m s-1. In the legend, the
<> and Δ denote mean and range (max–min) of the argument.
Analytical simplification
Fundamentally, the dominant loads during turbine operation originate from the
aerodynamic forces and moments on the rotor blades. The largest contributor
to the design loads on the blades and the downstream components is the lift
distribution acting on the blade airfoils. Examining how the out-of-plane
(rotor axial) component of the lift varies as a function of azimuth under
different yaw angles can help explain the cyclic out-of-plane loading at the
blade root and therefore the associated variation of several component loads
(e.g., tower, drivetrain). The axial component (l^) of the 2-D airfoil
lift can be written as
l^=12ρaUrel2cl(α)ccosϕ,
where ρa is the air density, c is the chord, cl(α)
is the 2-D lift coefficient, α is the angle of attack, ϕ is the
inflow angle, and effects on cl due to Reynolds and Mach numbers are
ignored. In an initial approximation, within the linear region of the airfoil
lift polar, one could assume
cl(α)≃c1α,
where c1 is an airfoil constant (≃2π for thin airfoils). As we
are interested in fatigue loads, the standard deviation of l^ can be
used as a surrogate for the load oscillation significance. Besides a
constant, this translates to the standard deviation of the product between
clcosϕ(≃c1αcosϕ) and Urel2. To this
end, through basic trigonometry, α and Urel can be written
as in Eqs. ()–():
αψ,r,θ,Uhub,ω,γ=ϕ-θ=arctan(U(ψ,r,Uhub)cos(γ)cos(δ))/(vt(ω,r)-U(ψ,r,Uhub)cos(γ)sin(δ)sin(ψ)+sin(γ)cos(ψ))-θ,Urelψ,r,Uhub,ω,γ=U(ψ,r,Uhub)cos(γ)cos(δ)2+[vt(ω,r)-U(ψ,r,Uhub)cos(γ)sin(δ)sin(ψ)+sin(γ)cos(ψ)]2‾,
where ψ is the rotor azimuth angle, r is the blade station radial
position; θ is the airfoil aero-twist plus pitch setting; δ is
the shaft tilt; ω is the rotor rotational speed; γ is the rotor
yaw offset; vt(ω,r) is the airfoil tangential (in-plane) velocity;
and U(ψ,r,Uhub) is the wind speed at the elevation identified
by ψ and r station, and a function of the Uhub, where
Uhub is the hub-height mean wind speed. Note that a power-law
shear is included in U(ψ,r,Uhub). Under the hypothesis of
constant and uniform induction in region 2 of the turbine power-production
curve, we ignore induction and tip effects that would translate into a constant
bias in α and cl for most of the power-producing blade span.
In Fig. , α and Urel calculated
by this analytical model are plotted as a function of ψ for the 75 %
blade-span station under various yaw offsets and for Uhub=12 m s-1 with a power-law shear exponent value of 0.2
The
sign convention adopted for the yaw offset is shown in
Fig. .
. It can be seen that the impact of yaw
offset reflects primarily on increasing the amplitude of the oscillations for
both α and Urel, with little change in the mean values. Of
special note are the azimuthal loci of maxima and minima of the two
quantities, which are shifted away from ψ=0 and 180∘,
demonstrating an asymmetry in the distribution of lift between the left and
right halves of the rotor plane. The asymmetry is present even under aligned
conditions, indicating that tilt and shear, beside yaw offset, are also
contributing factors.
As shown by Eqs. ()–() and
Fig. , α and Urel are two
quantities well correlated; thus we can use basic statistics
e.g., to find the covariance of the product
clcosϕUrel2 as in Eq. ():
σ2clcosϕ⋅Urel2≃σ2αcosϕ⋅Urel2=σαcosϕ⋅Urel22=σαcosϕ2,Urel42+σαcosϕ2+αcosϕ‾2⋅σUrel22+Urel2‾2-σαcosϕ,Urel22+αcosϕ‾Urel2‾2.
In Eq. (), σ2 denotes the covariance or variance of
the argument, and overbars indicate the means of the variables; furthermore,
the constant c1 is omitted with no loss of generality.
In Fig. , the model-calculated standard deviations for the
75 % span airfoil's clcosϕ, Urel2, and their
product are shown for different values of yaw offsets and hub-height wind
speeds of 8 and 14 m s-1 with a wind shear exponent of 0.2. The
standard deviations were normalized by the means of their respective
variables and are indicated as σ^clcosϕ,
σ^Urel2, and σ^clcosϕ⋅Urel2, respectively. The rotor rotational speed was set at the
average value obtained from aeroelastic simulations and verified against
actual turbine field data for that wind speed.
Standard deviations of clcosϕ (crosses), Urel2
(triangles), and their product (circles) for the airfoil at ∼75 % of
the blade span for two Uhub wind speeds of
8 m s-1(a)
and 14 m s-1(b), wind shear exponent value of 0.2, and mean rotor
rotational speed of ω=16.4(a) and 18 rpm (b). The standard
deviations are normalized by the means of the respective arguments.
The graphs show that, whereas σ^Urel2 displays a
minimum at 0∘ yaw, the σ^clcosϕ has a minimum
near -20∘. By examining other wind-speed cases (not shown), which
in general rendered similar trends to Fig. , it was observed
that the minima in σ^clcosϕ and σ^clcosϕ⋅Urel2 get closer to the γ=0∘
location with increasing wind speed. Both the σ^clcosϕ
and σ^Urel2 curves in Fig. show an
asymmetric behavior. The σ^Urel2 standard
deviation, for example, shows higher values for negative yaw offsets than for
the corresponding positive misalignments. In contrast, σ^clcosϕ exhibits larger variations for positive yaw offsets. The
σ^clcosϕ⋅Urel2 standard deviation,
however, decreases sharply, going from negative to positive misalignments,
with a reduction of some 66 % at γ=25∘ with respect to
the baseline case of γ=0∘. This simplified analysis suggests
that, at least in terms of aerodynamic load oscillations, positive yaw
misalignments could lead to a considerable load range reduction. Similar
trends were observed at other span locations (not shown).
Although this analysis only considered steady winds, rigid blades, steady
aerodynamics, and no induction, it brought forth results in agreement with
recent studies. , for example, suggest the existence of an
asymmetric behavior of blade and tower fatigue loads, hinting at the same
positive offset as load-favorable misalignment direction.
Blade aerodynamics and structural dynamics under steady winds
To better assess the physics responsible for fatigue loading under skewed-inflow
conditions, and to verify the existence of a preferred misalignment
direction for loads, we build up models of increasing complexity utilizing
AD15 and the full FASTv8 aeroelastic tool under steady winds.
Figure shows azimuthal trends for α and
Urel as calculated by AD15 for two GEWT blade-span stations
(near 50 and 75 % of the blade span) with aligned, sheared flow (0.2
power-law exponent) and no induction effects. It can be observed that
α achieves a maximum before reaching the azimuthal zenith and a
minimum affected by the tower shadow effects just before the 180∘
azimuth; Urel exhibits an analogous trend, though shifted by
180∘. The asymmetry is caused by the combination of the nonlinear
wind profile (power law) and the trigonometric contribution of the airfoils'
rotational speed to the relative air speed as a function of their positions
(advancing/retreating effect). Therefore, the sole presence of shear and tilt
causes an asymmetry in the variation of cl(α) and Urel
even under no-yaw-offset conditions, which can affect the performance of both
the individual machine and the entire plant. For example, it can be
speculated that under significant shear the optimum power performance could
occur under misaligned conditions. Furthermore, the asymmetric distribution
of α and Urel translates into an asymmetric azimuthal
distribution of the induction factors, which in turn offsets the wake axis. A
power increase under yaw-offset conditions is suggested by ,
and reports of skewed wake under aligned inflow conditions have been
presented in and . These aspects are
not further analyzed in this study, however.
α and Urel for two blade stations (denoted in the
legend by their spanwise fractions bf) as a function of ψ under
aligned conditions and a steady hub-height wind speed of 8 m s-1 as
calculated by AD15.
(a)cl vs. ψ for various blade stations (bf)
and for γ=10∘ offset as calculated by AD15 for a hub-height
wind speed of 12 m s-1. (b) As in (a) but with UA effects included.
By adding yaw offset, the asymmetry about the 0–180∘ azimuth is
still present (see also Fig. ), and whereas the
azimuthal mean α values slightly decrease with larger yaw offsets, the
α ranges (max–min, denoted by “Δ”) increase with increasing
offsets. Table shows the range for α, cl, and
Urel2 at different blade-span stations (given as spanwise
fractions, bf=0.28–0.92) for two hub-height wind speeds (8 and
12 m s-1) and for γ=0, -10, and 10∘. From the table,
it can be observed that, relative to the aligned cases, α ranges
reduce by 16–30 % with negative misalignments and increase by
14–70 % with positive ones. This is in agreement with the analytical
model predictions. Also, when compared to the aligned cases, the cl ranges
tend to be larger (smaller) for positive (negative) offsets. The
Urel2 ranges, however, increase for both directions of
misalignment but increase more under negative offsets. As these effects
oppose each other when generating aerodynamic loads, it is difficult to
ascertain whether one offset direction could lead to a more favorable load
response. Furthermore, as shown in Table , the reduced
frequencies (k=dαdtc/2Urel, where c is the chord length and t denotes time)
associated with the azimuthal α variations are largely above 0.02,
which is the commonly accepted threshold for unsteady aerodynamic effects to
take place . Given the expected higher values in angles
of attack under positive yaw offsets, dynamic stall effects should be more
prevalent with those misalignments.
Ranges (Δ) for α, cl, and Urel2 as
calculated by AD15 (without induction) for various blade stations (bf) and
hub-height wind speeds (Uhub) and for yaw offsets (γ) of
0, -10, and 10∘. A wind shear exponent of 0.2 was assumed. The
calculated reduced frequencies (k) for the various airfoil stations are
also given.
aΔ* denotes the relative difference in range
of the argument, with respect to the same quantity at 0∘ yaw offset.
Table offers similar results to
Table , but with induction, skewed wake correction
, and UA effects included. For most blade spans and wind
speeds, AD15 returned increased ranges of α with respect to the
no-induction, geometric calculations. Overall, however, the trends explored
under no-induction conditions still apply, with positive yaw offsets showing larger
variations in cl but smaller in Urel2, confirming that the
assumptions in the analytical model of constant and uniform induction are
reasonable. By enabling UA , higher peaks in cl's
especially inboard of the blade were noted. As visible in
Fig. , which portrays azimuthal traces for cl at four
blade-span stations with no UA (Fig. a) and with UA
(Fig. b) effects, the impact of UA is mostly associated with
a sharp stall transition for the inboard airfoils (at rotor radius
≤ 30 %), which is discussed below.
Ranges (Δ) for α, cl, and Urel2 as
calculated by AD15 (with induction) for various blade stations (bf) and
hub-height wind speeds (Uhub) and for yaw offsets (γ) of
0, -10, and 10∘. A wind shear
exponent of 0.2 was assumed. Results for Δ(cl) are given with (UA)
and without (nUA) unsteady aerodynamics effects included.
aΔ* denotes the relative difference in range
of the argument, with respect to the same quantity at 0∘ yaw
offset.
Figure a shows the basic statistics of the blade-root FBM
and EBM as calculated by a complete FASTv8 model of the turbine under
investigation for yaw offsets ranging from -25 to 25∘ and for 8 and
12 m s-1 hub-height wind speeds. The companion
Fig. b and c offer similar results, obtained by
excluding either UA or the rotor/tower flexibility, respectively. In the
plots, the 25th and 75th percentiles of the loads' distributions are marked
with the left and right sides of rectangular boxes, respectively; the line in
the middle of each box is the median, and the whisker lines show the
distances to the most extreme sample values within the 1.5 interquartile
range (i.e., 1.5 times the width of the box). Data beyond 1.5 times the
interquartile ranges are shown as outliers with red crosses.
Figure a shows little variation of the EBM statistics as
a function of yaw offset and wind speed; this outcome is to be expected, as
the EBM is mainly driven by gravity loads. The FBM median is seen to decrease
with nonzero yaw offsets, as one would expect given that the mean thrust load
reduces. The FBM distribution interquartile, and hence the variance and standard
deviation, however, get larger with nonzero offsets, and more pronouncedly so
for negative yaw offsets. Note that, in contrast to this result, the
analytical model of Sect. predicted an increase in
variance for negative yaw offsets but a decrease for positive misalignments.
Data associated with Fig. results demonstrate that the
standard deviations tend to increase (except at the highest yaw offset) when
UA is excluded from the computations. This indicates that UA acts as a
low-pass filter on the span-integral load. Furthermore, under rigid
conditions, the FBM values are generally associated with slightly lower
standard deviations, whereby it can be expected they would lead to lesser
fatigue loads. These observations are confirmed by an analysis of the load
variation as a function of azimuth (not shown for the sake of brevity), which
translate into smoother curves.
(a) Nondimensional FBM (top) and EBM (bottom) boxplot
statistics for the various cases of Uhub (8 and 12 m s-1)
and γ (-25 to 25∘) as indicated along the y axis, as
calculated by FASTv8 for a complete model of the GEWT. The loads are
normalized by the respective means at 8 m s-1 and 0∘ yaw
offset. (b) As in (a) but calculated excluding UA effects,
and (c) as in (a) but calculated with rigid blades and
tower.
In Fig. , the calculated short-term FBM DELs are
presented for Uhub=8 and 12 m s-1, and for three
different configurations: one including the entire model physics, one without
UA effects, and one without blade (and tower) flexibility. The complete model
results show a minimum of the DEL for the aligned conditions, although the
asymmetry in the loading persists, with negative yaw offsets rendering larger
loads than the positive counterparts. The second set of results in
Fig. is only slightly different from the first and thus
confirms that the dynamic stall effects are not so important for the trends
observed in blade-root loads, despite showing a noticeable effect on the
cl's as shown in Fig. . This result suggests that the
integral of the lift distribution along the blade span washes out the UA
contribution to the oscillating loads. Finally, with rigid blades and
Uhub=8 m s-1, the trend for the root FBM DEL is as
expected from the simplified variance model of Sect. .
Therefore, at this wind speed, the inertial forces associated with the
elastic response – of the rotor in particular – have a dominant effect on
the calculated DELs.
Blade-root FBM short-term DEL with yaw offsets from -25 to
25∘ as calculated by FASTv8 for Uhub=8 and
12 m s-1. Also shown are results obtained either by excluding UA
(denoted by “no UA”) or by removing structural rotor flexibility (denoted
as “rigid”).
At Uhub=12 m s-1, however, the DEL trend with yaw offset
reflects what is observed in the first set of Fig. ,
suggesting that the load variation with yaw offset at this wind speed is only
slightly affected by the structural response and therefore primarily driven
by pure aerodynamic loading
Note that the turbine controller
constantly varies the pitch of the blades at this speed and at all the yaw
errors examined thus far, but it was verified that disabling the controller
in the simulations does not significantly affect these observations.
. To
understand what is happening at 12 m s-1, we further examined the
blade cl-vs.-azimuth relationship. Figure shows how
blade structural flexibility affects the cl-vs.-azimuth trends for various
blade-span stations at γ=12.5∘ and for Uhub=8
and 12 m s-1. At the higher wind speeds, the inboard airfoils start
stalling, even at γ=0∘, and the abrupt drop in cl creates
a load forcing that contributes to the higher DELs. This can also be observed
in Fig. . By comparing Fig. a to b, one
can note the 100 % increase in the cl range for the station near the
30 % blade span when going from Uhub=8 m s-1 to
Uhub=12 m s-1. Furthermore, by comparing
Fig. a–b to Fig. c–d, one can see that,
at Uhub=12 m s-1, the lift curves are almost unchanged
when the blades are made rigid, as opposed to the case with 8 m s-1
hub-height wind speed, where the blade flexibility returns a more complex
cl response in the region of tower influence near the 180∘ azimuth
for the outboard airfoils, thus again leading to expected higher fatigue
loading. This analysis explains why, at the higher wind speeds, the impact of
flexibility is almost negligible on the FBM short-term DEL trend with yaw
misalignment but how suppressing elastic response at the lower wind speeds
can significantly change the fatigue loading level.
FASTv8 results with steady winds; (a)cl vs. ψ for
8 m s-1 wind speed and 12.5∘ yaw offset, (b) as
in (a) for a hub-height wind speed of 12 m s-1, and
(c, d) as in (a, b) but with rigid blades and tower. Note
that the legends provide mean (denoted by <>) and range (max–min) of
cl for the various span stations (bf).
Figure further demonstrates how the blade inboard stations
exhibit a sharp drop in lift near stall. The combination of higher α's
with higher wind speeds, and the sharper airfoil stall characteristics of the
inboard airfoils, causes the large variations in cl's, which in turn are
responsible for the increase in oscillating loads at the root.
Lift polar curve of the inboard to midspan airfoils normalized to
the respective maximum cl's.
This nonlinear aerodynamics explains why the simple variance model cannot
capture load trends at higher wind speeds and therefore indicates that the
airfoil characteristics and the associated UA, together with the elastic
response of the blades, contribute to the actual fatigue loading of the
blade and thus all the downstream turbine components. Given these
results, one can only rely on accurate, nonlinear, aeroelastic models of the
turbine and thorough loads analyses to assess the loading levels in the
various components when operating under yaw offsets. In the subsequent section, we carry out
a load analysis based on FASTv8 simulations with turbulent winds and
compare the predictions to field-measured loads.
Aeroelastic simulation and field data validation
To compare model predictions to actual field measurements, we ran aeroelastic
simulations for hub-height mean wind speeds ranging from 4 to 24 m s-1
in 2 m s-1 wind-speed bins, and with NTM inflow see
also with 20 turbulence seeds per wind-speed bin. However,
besides brevity, we limit the discussion to mean hub-height wind speeds of 10
and 14 m s-1 for three reasons. First, we intend to compare to data
bins from the field; thus we selected those that provided sufficient field
data points for statistical significance. Second, above rated wind speed,
pitch dynamics add more complexity to the interpretation of the results.
Lastly, low wind speeds (≤ 6 m s-1) gave rise to shutdowns in the
simulations, which we wanted to exclude for the sake of clarity. Furthermore,
the selected wind speeds are representative of conditions at or below rated
power, which is where wake steering is thought to be most effective
e.g.,.
The investigated yaw offsets ranged from -25 to +25∘, which have
been considered for wake redirection in wind farms. Because the field data
showed large variations in TI within individual
wind-speed bins (see Fig. ), a lower turbulence range was
selected for the simulations, with a mean TI = 15 % throughout the
wind-speed range. Accordingly, the field data were filtered to retain
measurements with TI ranging from 1 to 17 % to guarantee a statistically
significant number of samples. This was necessary because turbulence
intensity proved to have a larger effect than the sole yaw offset on the
magnitude of DELs, as can be seen, for example, in the blade-root FBM DELs
shown in Fig. .
Comparison between simulated (circles) and measured (squares) values
of TI as a function of yaw offset for two wind-speed bins of interest
(a: Uhub=10 m s-1; b: Uhub=14 m s-1). The field data are shown when including all data (label
“All” in the legend) and when filtering for TI below 17 % (label “TI
1–17 %” in the legend). The simulated data are shown for class IA
turbulence (label “FAST TI Class IA” in the legend) and
for TI = 16 % at 15 m s-1 (label “FAST TI 16 %”).
TI effect on the blade FBM DEL. Comparison between simulated
(circles) and measured (squares) values of the loads for various TI levels,
as a function of yaw offset and for Uhub=10 m s-1(a) and Uhub=14 m s-1(b). The loads are normalized by the mean value at
0∘ yaw offset from the field data filtered to a TI range of 1 to
17 %. Labels in the legend are the same as in Fig. .
Fatigue loads
Figure offers a summary comparison between predicted
and measured short-term DELs for the various channels of interest and for 10
and 14 m s-1. The bars represent mean values from simulation results,
and the square symbols are the corresponding values derived from the field
measurements. For each channel, the mean values are given as a function of
yaw offset, with all DELs normalized by the field value at the zero yaw
offset. Because field data at γ=-12.5∘ were scarce, they were
not included in the plots. In Appendix ,
Figs. – show detailed
comparisons between the predicted and the measured DELs for the various load
channels of interest as a function of yaw offset and including error bars
representing ±1 standard deviations. The spread comes from multiple seeds
in the FAST results and from multiple data points (10 min records) in the
field datasets.
Comparison between predicted (FAST, bars) and measured (field,
square symbols) mean DELs as a function of yaw offsets for mean
Uhub=10 m s-1(a) and
14 m s-1(b). DELs are normalized by their respective mean
values at 0∘ yaw offset as calculated from the field measurements for
the respective wind-speed bins.
Overall, good agreement was observed between predicted and measured data both
in absolute terms and as far as yaw-offset trends are concerned. For example,
the FBM values predicted at the blade root are very close to the
corresponding field-derived data. A minimum is seen under aligned conditions
as was also shown under steady-state wind conditions in
Sect. . The previously observed asymmetry in the mean
loading as a function of yaw offset is still visible, with negative yaw
errors giving rise to larger loads, though at 14 m s-1 this effect is
not confirmed by the field-derived data.
Both the calculated and measured blade-root EBM display a mostly monotonic,
decreasing trend with increasing yaw offset, although less pronounced at
14 m s-1. This decreasing trend is in line with the decrease in
standard deviations observed in Fig. a under steady
conditions and is attributable to the aerodynamics partially relieving the
gravity loading when going from negative to positive yaw offsets.
To assess the effective fatigue load on the blade root, the resultant
unsymmetric RBM must be analyzed via load roses, wherein multiple
circular sectors of the root cross section are considered, in addition to the
0∘ (FBM) and 90∘ (EBM) components. Eight sectors, each
22.5∘ wide, were analyzed, and the data from the largest contributing
sector from each yaw offset were selected and normalized with respect to the
field value under aligned conditions. The calculated results demonstrate that
the resulting fatigue loading decreases with increasing yaw offset and that
negative misalignments appear more detrimental than the aligned conditions.
The field-derived results generally confirm this trend, but not as clearly.
The LSSTq DELs also showed good agreement between predicted and measured
data, especially at 14 m s-1. Note, however, the reversal in the trend
with yaw misalignments for different wind speeds. For wind speeds below
14 m s-1 and near γ=0∘, in fact, FAST results
exhibited a maximum in torque DEL, whereas they showed a minimum for a wind
speed of 14 m s-1. The field-derived data confirm this reversal,
although an outlier can be noted at γ=-25∘ and
10 m s-1.
Comparison between predicted (FAST, bars) and measured (field,
square symbols) mean extreme loads as a function of yaw offsets for mean
Uhub=10 m s-1(a) and 14 m s-1(b). The
loads are normalized by their respective mean measured values at 0∘
yaw offset and Uhub=14 m s-1.
A more significant discrepancy was observed for the mean resultant TTBM DEL.
The load-rose analysis of field data (conducted in the same fashion as for
the blade-root loads above) exhibits an increase in the short-term fatigue
damage for nonzero yaw offsets. FAST predictions, however, render a much
smaller effect of the yaw misalignment. The largest discrepancy between field
and FAST results (∼ 40 % relative error) can be seen at γ=25∘ and 14 m s-1, but it is also accompanied by very large
standard deviations in the field data (see Fig. ).
The TTTq DEL from measurements at tower top is, on average, overestimated by
the simulations. Large variations in the loading levels, however, can be seen
for positive yaw offsets and higher wind speeds both in the field data and in
the predictions (see Fig. ). Notwithstanding this
discrepancy (up to 17 % relative error), the increase in torque with
increasing yaw misalignment is confirmed by both simulation- and
field-derived data.
At the tower base, FAST predicts that the resultant TBBM DELs (calculated
through load roses) have a maximum between 0 and -12.5∘ yaw
offsets. Measurements from the field, however, lead to a significant increase
of the DELs with negative yaw offset (-25∘) and a somewhat lesser
increase for positive yaw offsets except at the higher wind speeds. The
field-derived data at -25∘ still appear to be outliers. The largest
relative error in the calculated DEL was 50 % under aligned conditions
and 14 m s-1.
Extreme loads
To complete this gallery of results, we offer a comparison between the
FAST-predicted extreme loads and those measured in the field. Note that these
loads are not necessarily the highest loads the various components would
encounter throughout the turbine lifetime, but they give an idea of what to
expect in a relative sense when the turbine is operated under misaligned
conditions.
Similarly to what was done for the DELs, a summary graph for the mean load
values is given in Fig. for all the main channels of
interest. The extreme loads were normalized by the mean recorded in the field
at 14 m s-1 wind speed and 0∘ yaw. Detailed trends and graphs
for individual load channels are given in .
Except for the tower-top resultant moment (which yielded a maximum relative
error of 40 % at 14 m s-1 wind speed), good agreement exists
between predicted and measured extreme loads.
For the RBM, the maximum values are seen at 14 m s-1, where the mean
values of the load peaks increase with nonzero yaw offsets, and the
largest values are predicted and measured at γ=-25∘. Note that
the FAST underprediction of the loads is likely caused by the remaining
difference in turbulence values between simulations and field data.
The LSSTq also shows the largest loads around rated wind speed, where both
FAST and field data show limited to no effect of yaw offset.
At tower top, a distinctive increase of peak TTBM with increasing yaw offset
can be observed in Fig. , and this trend persists in
both the model and measured data. For the TTTq extremes, FAST predicts a
minimum under aligned conditions, but field data show even smaller values at
γ=-25∘. Very good agreement exists for positive yaw offsets,
however.
Finally, calculated TBBM extremes (highest values at 14 m s-1 wind
speed) are seen to slightly decrease with increasing yaw offset. Whereas this
trend is confirmed by the measurements at 10 m s-1 wind speed, at
14 m s-1 the field data are noisier and show less influence of the
yaw misalignment.
Conclusions
In this paper, we presented an analytical treatment, numerical
investigations, and field data analyses to explore the effects of yaw-offset
operation on the loads of a commercial-grade wind turbine.
The results of models of increasing complexity were presented for the rotor
aerodynamics under different yaw misalignments to shed some light on the
physics and load predictions. It was shown that, under the presence of
vertical wind shear, asymmetric conditions exist in the azimuthal
distributions of the angle of attack and relative air velocity even under
aligned inflow, which complicates the intuitive picture of the turbine
response and might have further consequences on wake dynamics and control
strategies. When turning the attention to the cl distributions, rapid
changes in values obtained under both steady and unsteady aerodynamics at the
inboard sections of the blades were noted for wind speeds in power region
2.5, which are likely the responsible factors for the standard deviations
noted in the blade-root FBMs. These effects were mostly attributed to the
crossing of the stall region of the airfoil polars, which was seen as rather
abrupt. At lower wind speeds (power region 2), these effects were partially
eliminated by assuming rigid blades, thus demonstrating that, besides
aerodynamics, the stiffness characteristics of the turbine play a significant
role in the calculated DELs. A simple analytical model for the standard
deviation of the out-of-plane component of the blade lift was presented and
shown to be a valid proxy for DELs only under quasi-steady-state and
rigid-rotor conditions. In fact, it was shown how stiffness characteristics
and aerodynamics specific to the actual wind turbine model have a dominant
role in the determination of the load statistics and therefore the fatigue
response.
Furthermore, by considering more realistic turbulent wind fields, via both
simulations and field data records, it was shown that the turbulence
intensity distribution for the various mean wind-speed bins can significantly
mask the effects caused by skewed inflow, and care must be given to the
actual site conditions to assess their effects on the loads. Only dedicated
aero-servo-elastic simulations can capture the actual trends in loading as a
function of yaw offset, and only if the proper turbulent inflow conditions
are matched.
Aeroelastic simulations can predict well the blade-root FBM and
EBM DELs, and it was shown how these, on average, exhibit
different trends with yaw offsets. Whereas the FBM increased with nonzero
misalignment, the EBM decreased with increasing yaw offsets. To assess the
actual impact of misaligned operation on blade-root fatigue, the combined
bending, or resultant moment, was analyzed via load roses. On average, the
blade-root bending moment DEL decreased for positive yaw offsets and
increased for negative offsets. Fairly large variations can be attributed to
different turbulence seeds and data records, making generalization more
difficult.
More complex trends were observed in shaft torque and tower-top bending
moment DELs. For example, trend reversals in shaft torque from the
simulation-derived data were noted when the wind speed increased toward power
region 3. The initial DEL reduction with nonzero yaw offset seen for wind
speeds below 10 m s-1 is replaced by a slight increase at higher wind
speeds. Some of these effects are a direct consequence of the controller
dynamics and therefore difficult to generalize to multiple turbine models.
The resultant moment DEL at tower top increased sharply with nonzero yaw
offsets in the field-derived data, whereas the FAST predictions showed little
or no influence of yaw misalignment.
Tower-top torque – which, together with the tower-top bending, can be
responsible for the reliability of the yaw drive components – generally showed
an increase in loading with positive misalignments, exhibiting good agreement
between predictions and field measurements. To reiterate, however, standard
deviations were fairly large and grossly dependent on turbulence
characteristics, which tended to override the effects of yaw misalignment.
For the tower-base bending moment, the mean DELs derived from aeroelastic
simulation decrease with positive yaw offsets, whereas measurement-derived
data generally indicate a slight increase. Standard deviations of the
predicted DELs are, however, quite large.
Extreme loads were also compared between field-measured and predicted values
under operational conditions and skewed inflow. The results of the analysis
showed that, for the resultant moment at the blade root, an increase can occur
under misaligned conditions. The shaft torque extreme load does not
significantly change with nonzero yaw offsets. Tower-top bending moments
increase with increasing yaw offset, whereas tower-top torque peaks increase
with nonzero misalignment. At the tower base, the resultant bending moment
tends to decrease slightly with increasing yaw error.
The current dichotomy between the desire of wind power plant production
optimization and the conservatism toward reliability due to load increase
concerns is corroborated by the results presented in this research. In
contrast to what was reported in previous studies, the fatigue load
components do not necessarily decrease with increasing yaw offsets, and we
offered justifications as to why that might be happening. Whereas blade-root
loads can be said to decrease, large standard deviations of the mean results
also point to caution and to the need to carefully assess the site
conditions. Even more attention should be paid to the yaw drive system, given
the measured increase in tower-top extreme loads. The turbine controller,
however, can significantly impact these results.
Future work should include an extension of the analysis to other types of
turbines with different aerodynamics and elastic characteristics to further
assess their impact on the changes in both ultimate and fatigue loads. These
additional findings will support the development of future standards for the
design and certification of wind turbines that operate under programmatic yaw
misalignments for increased plant performance. For example, techniques to
calculate acceptable ranges for yaw offsets as a function of operating wind
speeds could be provided to minimize impact on the structural design. It can
also be expected that site-specific loads, obtained by using the actual site
conditions and plant layout, will need to be verified against the design
loads and perhaps even component test loads, during the site suitability
assessment and for project certification.
Data are available upon request.
Fatigue load comparisons
Figures in Appendix portray comparisons between
predicted (FAST) and measured (field) DELs as a function of yaw offsets for
mean hub-height wind speeds of 10 and 14 m s-1. DELs are normalized by
the mean measured value at 0∘ yaw offset. The error bars represent
±1 standard deviations.
Comparison between predicted (FAST) and measured (field) FBM DELs.
Comparison between predicted (FAST) and measured (field) EBM DELs.
Comparison between predicted (FAST) and measured (field) RBM DELs.
The largest component among eight load-rose sectors was selected for each yaw
offset.
Comparison between predicted (FAST) and measured (field) LSSTq
DELs.
Comparison between predicted (FAST) and measured (field) TTBM DELs.
The largest component among eight load-rose sectors was selected for each yaw
offset.
Comparison between predicted (FAST) and measured (field) TTTq DELs.
Comparison between predicted (FAST) and measured (field) TBBM DELs.
The largest component among eight sectors was selected for each yaw offset.
The authors declare that they have no conflict of
interest.
This article is part of the special issue “Wind Energy Science
Conference 2017”. It is a result of the Wind Energy Science Conference 2017,
Lyngby, Copenhagen, Denmark, 26–29 June 2017.
Acknowledgements
Valuable suggestions for improving this paper came from Paul Veers and
Jeroen van Dam. This work was supported by the U.S. Department of Energy
under contract no. DE-AC36-08GO28308 with the National Renewable Energy
Laboratory. Funding for the work was provided by the DOE Office of Energy
Efficiency and Renewable Energy, Wind Energy Technologies Office.
Edited by: Gerard J. W. van
Bussel Reviewed by: Dominique Philipp Held and one anonymous
referee
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