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The effect of minimum thrust coefficient control strategy on power output and loads ofa wind farm
Meng, Fanzhong; Lio, Alan Wai Hou; Liew, Jaime
Published in:Journal of Physics: Conference Series
Link to article, DOI:10.1088/1742-6596/1452/1/012009
Publication date:2020
Document VersionPublisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):Meng, F., Lio, A. W. H., & Liew, J. (2020). The effect of minimum thrust coefficient control strategy on poweroutput and loads of a wind farm. Journal of Physics: Conference Series, 1452, [012009].https://doi.org/10.1088/1742-6596/1452/1/012009
Journal of Physics: Conference Series
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The effect of minimum thrust coefficient control strategy on power outputand loads of a wind farmTo cite this article: Fanzhong Meng et al 2020 J. Phys.: Conf. Ser. 1452 012009
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NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
IOP Publishing
doi:10.1088/1742-6596/1452/1/012009
1
The effect of minimum thrust coefficient control
strategy on power output and loads of a wind farm
Fanzhong Meng, Alan Wai Hou Lio and Jaime Liew
Department of Wind Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark
E-mail: [email protected]
Abstract. The use of down-regulation control strategies for wind turbines potentiallyoptimises the wind farm performance. One of the promising strategies to minimise the windfarm loads and maximise the energy production is by down-regulating the upstream turbinewith minimum thrust coefficient (Ct). Nonetheless, a majority of minimum Ct control studiesis confined to fatigue load analysis of a single turbine. Therefore, this paper focuses on theinvestigation of the fatigue loads when operating turbines in a wind farm using a minimumCt control strategy, as well as extreme loads and energy production. The control strategy isimplemented in the DTU Wind Energy controller coupled with the aero-elastic code, HAWC2.The Dynamic Wake Meandering model in HAWC2 is used so that the wake deficits generatedfrom the upstream turbines realistically represent the minimum Ct control strategy, as wellas the interactions between wakes. The main contribution of this paper is to investigate thepossible wind farm operating strategy using minimum Ct control that leads to decrease thelifetime fatigue loads and increase the overall energy production of a wind farm due to thepotential extended lifetime of certain wind turbine components.
1. IntroductionAlthough the control of modern variable-speed pitch-regulated wind turbines has achieved a highlevel of maturity in the industry, new control strategies and functionalities are in demand toincrease the efficiency of wind farm operation while adhering to stricter grid code compliance [1]and the demands of the grid operator. In order to satisfy new requirements, such as gridcurtailment, changes should be made in the control strategy from optimizing the performanceof a single wind turbine with respect to power production and load alleviation, to consideringthe loads and overall energy production of a wind farm.
There exists several types of down-regulation strategies (see [2, 3]). To increase the overallenergy production in a wind farm, one of the promising strategies is the minimum thrustcoefficient control [4, 5, 6]. By down-regulating the upstream turbine in the minimum thrustcoefficient operation, the wake deficits from upstream turbine are minimised, thus, resultinga potential increase in the wind farm power output. Nonetheless, the literature in this areatypically focuses on the effect of down regulation control and the dynamic performance of thesingle de-rated wind turbine with respect to fatigue and extreme loads rather than consideringthe effects on a full wind farm due to down-regulation control. For example, the study by Mirzaei[7] investigated the fatigue loads of a single turbine under several down regulation strategies.Similar studies on fatigue loads by additional down-regulation methods were conducted in[2, 3, 4, 5, 6]. In the work of Fleming [8], load analysis and field tests on a single turbine
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Journal of Physics: Conference Series 1452 (2020) 012009
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doi:10.1088/1742-6596/1452/1/012009
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were performed based on torque-based down-regulation strategies. In terms of load analysis ina wind farm setting, a down-regulation study by Galinos [9] investigated the fatigue load fortwo turbines in a row. Clearly, there has been limited research on the effect of down-regulatingwind turbines, which follow minimum thrust coefficient control strategy, on the loads and energyproduction of a wind farm.
Therefore, this paper is to investigate the possible wind farm operating strategy based onminimum Ct control. Furthermore, a further key focus of this paper is to understand that thefatigue and extreme loads and overall energy production of a wind farm under the minimumCt control strategy. Such a wind farm operating strategy could potentially lead to decreasethe lifetime fatigue loads and increase the overall energy production of a wind farm due to thepotential extended lifetime of certain wind turbine components. For this purpose, a dummysmall-scale wind farm consisting three turbines standing in a row is used in the simulation.The analysis is based on high fidelity aero-elastic simulations using the HAWC2 [10] with theDynamic Wake Meandering (DWM) model [11]. The simulations focus on different combinationsof wind classes and down regulation levels using the minimum Ct control strategy. Based onthe simulation results, an useful information of selecting possible wind farm operating strategy,which optimises the wind farm performance, is given. A short description of DWM modeland the minimum Ct control strategy implementation are presented in section 2. The detailedsimulation setup is presented in section 3. In section 4, lifetime fatigue loads, extreme loads andAnnual Energy Production (AEP) are analysed and discussed.
2. Modelling and methodology2.1. Dynamic Wake Meandering modelThe Dynamic Wake Meandering model as implemented in HAWC2 calculates the wake deficitfrom Blade Element Momentum (BEM) theory coupled with a 2D axisymmetric boundarylayer approximation of the Navier-Stokes equations [12]. The DWM model utilizes the steady-state minimum thrust operation point(rotor speed and blade pitch angle) of the upstreamturbine to compute the quasi-steady velocity deficit experienced by the downstream turbine.The wake meandering part is based on a fundamental presumption stating that the transportof wakes in the atmospheric boundary layer can be modelled by considering the wakes toact as passive tracers driven by the large-scale turbulence structures [11]. The added waketurbulence is modelled based on a homogeneous Mann turbulence field [13] driven by small-scaleturbulence structures with the cross section covering one rotor diameter. The added turbulenceis approximated by scaling the created homogeneous Mann turbulence field depending on thequasi-steady velocity deficit and the velocity deficit gradient at the considered down streamlocation [14]. Multiple wake sources interact with each other by adjusting the steady-stateoperation point of a wake generation turbine when it is in the wake of another turbine.
In the current implementation of DWM model, the wake sources can operate at differentcombinations of rotor speed and blade pitch angle during down-regulation which have differentimpact on loads. Thus, the generated wakes can be altered to determine the optimal controlsolution for maximizing the overall AEP while minimizing lifetime fatigue loads and extremeloads.
2.2. Down regulation control strategyThe standard control strategy of an individual wind turbine under normal operating conditionsis to maximise the power output below rated wind speed by tracking the optimum tip-speed-ratio, and to track the rated power set point above the rated wind speed. When turbines operatein a wind farm, different control strategies should be considered. For example, down regulationof the upstream turbines such that the generated velocity deficits are minimized, allowing thedownstream turbines to capture more energy while alleviating the fatigue and extreme loads of
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Journal of Physics: Conference Series 1452 (2020) 012009
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both upstream and downstream turbines.One type of down regulation control is the minimum Ct control strategy, which minimizes the
thrust coefficient of a turbine for a given power output. This control strategy, although reducingthe power output of the de-rated turbines, results in an overall increase in power output in thewind farm due to attenuated wake effects. An additional benefit of minimum Ct control is areduction of fatigue loads farm-wide due to a reduction of the wake deficit and added waketurbulence mentioned in [6, 11].
The concept of minimum Ct control strategy is described in the optimisation problem (1).For a given down regulation percentage, ∆P , the following minimization problem is solved tofind the solution of tip-speed-ratio, λ, and pitch angle, β. The power coefficient, Cp, and thrustcoefficient, Ct, of the DTU 10MW reference turbine [15] are illustrated in contour plots asfunctions of λ and β in Figure 1.
-10 -5 0 5 10 15
Pitch angle (deg)
2
4
6
8
10
12
14
16
Tip
sp
ee
d r
atio
(-)
Cp contour
Ct contour
Min Ct
Figure 1: Cp, Ct contours and minimum Ct operational points.
The calculated values of λd and βd that satisfy minimum Ct requirement are plotted inFigure 1 and marked as black circles. The power coefficient, Cp,d, associated with downregulation percentage is tabulated as a function of λd and βd and will be used when calculatingthe generator constant K in Equation 2.
λd, βd = arg minλ,β
Ct(λ, β)
Subject to:
Cp,d(λd, βd) = ∆PCp,max
λmin ≤ λd ≤ λmaxβmin ≤ βd ≤ βmax
(1)
In this work, we utilize the same terminology as defined in literature [16], where the controlregions are referred to as Regions 2, 2.5 and 3. The implementation of this control strategy inRegion 2 is simply re-calculating the generator constant, K, tracking the minimum Ct insteadof the traditional way that tracks the optimal power coefficient Cp,max using the equation
K =1
2ρπR5
(1
Nλd
)3
Cp,d(λd, βd) (2)
where, N is the gearbox ratio, R is the rotor radius, ρ is air density and Cp,d is the powercoefficient value associated with down regulation percentage. In Region 2.5, a PI generatortorque controller with torque limits is implemented. We assume the rated wind speed (Vr) is
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the same as the designed value. Then, the lower limit of generator speed in Region 2.5, Ω2.5, iscalculated as
Ω2.5 =VrλdR
(3)
where, λd is the tip-speed-ratio value as the solution of the minimization problem mentionedbefore. The upper limit generator speed in Region 2.5 during down regulation, which is thede-rated generator speed in Region 3, is defined as Ωr,d = Ω2.5/γ. Here, the γ is an user selectedparameter. In this study, a value of 95% is used for generalizing the minimum Ct control strategyto match the behavior of the DTU Basic Controller when the down-regulation level is at 100%.A linear interpolation factor, σ, is defined as
σ (Ω2.5,Ωr,d; Ω) =
0 Ω < Ω2.5,
Ω−Ω2.5Ωr,d−Ω2.5
Ω2.5 ≤ Ω ≤ Ωr,d,
1 Ω > Ωr,d,
(4)
where, Ω is the current generator speed. Then, the torque limits used by the PI generator torquecontroller in Region 2.5 is expressed as
Qg ∈
[KΩ2,KΩ2] Ω < Ω2.5,
[KΩ22.5, (1− σ)KΩ2 + σQdg,r] Ω2.5 ≤ Ω ≤ Ωr,d,
[Qdg,r, Qdg,r] Ω > Ωr,d,
(5)
where, Qdg,r is the de-rated generator torque.In Region 3, The generator speed and torque set-points are determined by Ωr,d and the de-
rated generator power. The implementation of the switch between Region 2.5 and 3 follows thesame method as described in the report of DTU Wind Energy controller [17].
3. Simulation setupIn this study, simulations are performed on the DTU 10MW reference turbine [15] using thehigh fidelity aero-elastic simulation code, HAWC2. Three different wind classes, namely IA,IB and IC representing different turbulence intensity values 0.16, 0.14 and 0.12 defined in IECstandard [18], are used in the simulation. The wind speed range is from 4 m/s to 24 m/s in 2m/s increments, and 6 random turbulent seeds are used per wind speed. We select five differentdown regulation levels for the upstream turbine (WT-1), three down regulation levels for thesecond row turbine (WT-2) and two down regulation levels for the third row turbine (WT-3) inthis work. They are combined with all three wind classes. The 20 years lifetime equivalent loadson the blade root, the tower bottom, the yaw bearing and the main shaft bearing are evaluatedfor all turbines assuming that power production period occurs with a probability of 97.5%, andthe wind speed conforms to a Weibull distribution. Wohler exponent values of 3, 4 and 10 arechosen for the bearings (yaw and shaft), the tower and the blade respectively. The absolutevalues of maximum loads on the mentioned components are extracted from the time series toget the extreme loads. The AEPs are evaluated on overall wind farm composed by the threeturbines for different down regulation levels.
3.1. Wind farm setupFor the purpose of this investigation, a simplified wind farm layout with three turbines in arow is formulated. The space distance, which is four rotor diameters (4D) in length, is chosen,which represents a tight wind farm layout similar to the Lillgrund wind farm. The ambient
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Journal of Physics: Conference Series 1452 (2020) 012009
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doi:10.1088/1742-6596/1452/1/012009
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wind direction is set to zero degrees, which means yaw misalignment is not considered in thisstudy. Only one dominating direction in the wind rose is considered in the simulation, whileother directions can be treated in a similar way. WT-1 is down regulated to produce 60%, 70%,80%, 90% and 100% of the available power. WT-2 is down regulated to produce 70%, 80% and100% of the available power. For WT-2 the 90% down regulation level is not simulated in orderto reduce the number of load cases. The results at 90% down regulation level can be obtainedby interpolation based on the simulated de-rating levels. For the turbine in the last row, WT-3,only two different down regulated levels, 80% and 100%, are considered in this work. The 80%de-rating level is kept for checking the fatigue and extreme loads, and the 100% de-rating levelis for giving the reference value of AEP.
4. Results and discussionThe lifetime fatigue loads and extreme loads of each turbine have been normalized with respectto the loads when the turbines are not down-regulated. AEP is normalized by all 3 turbinesoperated normally. For the loads on WT-1, a bar plot is used. Different colors represent differentdown regulation levels in the figure, and the load channel names are plotted on the x-axis. For theloads on WT-2 and WT-3 which are affected by the operational points of the upstream turbines,a color matrix plot is used. The numbers in the colored cells, rounded to have 2 decimal places,represent either the normalized lifetime DELs or extreme loads. The load channel names areshown on the top of each sub-figures.
4.1. Lifetime fatigue loadsFigure 2 shows the 20 years lifetime fatigue loads of the WT-1 operating at wind class IC. Asit is shown, most of the fatigue loads are reduced for different down regulation levels comparedwith normal operation case except for tower bottom fore-aft and side-to-side loads described bychannel name TBFA and TBSS, and the yaw bearing roll moment and main bearing torsionalmoment described by channel name YBRoll and MBTor, which are related to the drive trainloads. The blade root edgewise bending moment is mainly driven by the gravity, therefore, theedgewise fatigue load reduction is smaller compared to the flapwise fatigue load.
A further investigation on the time series and the Fast Fourier Transformed (FFT) signal oftower bottom fore-aft bending moment (see Figure 3) shows that the fatigue load increase atthe tower bottom for fore-aft bending moments is due to higher oscillation when the turbine isde-rated. This is caused by the 3P frequency (0.255 Hz) interaction with the tower fore-aft (0.25Hz) frequency of this DTU 10MW turbine when the turbine is de-rated to 70% with the rotorspeed at 5.1 rpm. Figure 3 shows, at 10 m/s, when the turbine is running without de-rating, the3P frequency is 0.4 Hz. The 3P frequency is reduced to 0.281 Hz and 0.255 Hz when the turbineis de-rated at 90% and 70% respectively. Therefore, when the turbine is de-rated, for example,at 90% and 70%, the tower fore-aft mode is excited and a higher amplitude as it is shown inFigure 3 is observed. Similar resonance phenomena is observed for the tower side-to-side modein Figure 4. Further more, the excited tower side-to-side vibration couples with the drive traintorsional mode and leads to higher drive train torsional oscillation, which is closely related tothe main bearing torsional moment (MBTor) and the yaw bearing roll moment (YBRoll). Thisexplains the fatigue loads increase on channels YBRoll and MBTor.
This finding suggests that for the turbines designed with narrow rotor speed range, like theDTU 10MW reference turbine, with the range from 6 rpm to 9.6 rpm, the rotor speed exclusionshould be implemented in the down regulation control algorithm to avoid resonance. It alsosuggests that the drive train damping parameters need to be re-tuned in order to damp thedrive train vibration under the down-regulated control. Re-tuning of the drive train dampingparameters for down regulation is out of the range of this investigation.
Similar results have been found for WT-2 when WT-1 is operated at different down regulation
NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
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doi:10.1088/1742-6596/1452/1/012009
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BRFlap
BREdgBRTor
TBFATBSS
TBTorYBTilt
YBRoll
YBYawMBTilt
MBYawMBTor
load channel (-)
0
0.5
1
1.5
2
2.5
Norm
aliz
ed lifetim
e e
quiv
ale
nt lo
ad (
-)
WT-1:60%
WT-1:70%
WT-1:80%
WT-1:90%
WT-1:100%
Figure 2: 20 years normalized damage equivalent loads on WT-1 for wind class IC.
100 200 300 400 500 600 700
Time (s)
-0.5
0
0.5
1
1.5
2
2.5
Tow
er
bottom
fore
-aft m
om
ent (k
Nm
) 105
TBFA:100%
TBFA:70%
TBFA:90%
10-2 10-1 100
Frequency (Hz)
102
103
104
105
FF
T o
f to
wer
bottom
fore
-aft m
om
ent (k
Nm
)TBFA:100%
TBFA:70%
TBFA:90% 0.2550.281
0.4
Figure 3: Time series and FFT of the tower bottom fore-aft bending moment at 10 m/s.
100 200 300 400 500 600 700
Time (s)
-5
0
5
10
Tow
er
bottom
sid
e-s
ide m
om
ent (k
Nm
) 104
TBSS:100%
TBSS:70%
TBSS:90%
10-2 10-1 100
Frequency (Hz)
102
103
104
105
FF
T o
f to
wer
bottom
sid
e-s
ide m
om
ent (k
Nm
)
TBSS:100%
TBFA:70%
TBFA:90%
0.258
0.4
Figure 4: Time series and FFT of the tower bottom side-side bending moment at 10 m/s.
levels. Figure 5 shows the lifetime DELs loads of WT-2 operated at 70%, 80% and 100% of theavailable power indicated in x-axis, in the meantime WT-1 is running at different down regulationlevels indicated in y-axis. The flapwise and torsional fatigue loads on the blades of WT-2 areall reduced with different combination of de-rating levels of WT-1. The same fatigue loadsreduction are found at load channel, namely, TBTor, YBTilt, YBYaw, MBTilt and MBYaw.The edgewise fatigue loads are reduced if the WT-2 is under down regulation but the reductionis smaller than the flapwise and torsional loads due to the loads are mainly driven by the gravityforce. The loads at tower bottom described by TBFA and TBSS, and the loads related to thedrive train described by YBRoll and MBTor are increased when the WT-2 is de-rated.
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Journal of Physics: Conference Series 1452 (2020) 012009
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70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
ating levels BRFlap
0.79
0.79
0.80
0.80
0.81
0.83
0.83
0.84
0.85
0.86
0.94
0.96
0.96
0.98
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
0.99 0.96
0.97
0.99
0.87
0.89
0.92
0.95
1.00
1.01
1.03
1.04
1.00
1.03 1.00
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.76
0.77
0.78
0.80
0.81
0.79
0.80
0.81
0.82
0.84
0.94
0.96
0.96
0.98
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.79
0.81
0.82
0.84
0.87
0.80
0.81
0.83
0.84
0.87
0.92
0.93
0.95
0.97
1.000.8
0.9
1
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
ating levels BREdg
0.95
0.96
0.96
0.96
0.96
0.97
0.97
0.97
0.97
0.97
0.99
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
1.38
1.36
1.39
1.41
1.43
0.93
0.92
0.97
1.00
1.00
1.67
1.69
1.70
1.75
1.68
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
0.87
0.91
0.94
0.86
0.89
0.94
0.76
0.81
0.85
0.921.00
1.07
1.00
1.08 1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
0.79
0.80
0.82
0.84
0.86
0.80
0.81
0.82
0.84
0.87
0.91
0.93
0.95
0.97
1.00 0.8
0.9
1
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
WT
1 d
e-r
ating levels BRTor
0.83
0.84
0.84
0.85
0.85
0.86
0.87
0.86
0.87
0.87
0.97
0.97
0.98
0.99
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.76
0.77
0.78
0.80
0.81
0.78
0.79
0.80
0.82
0.84
0.94
0.95
0.96
0.98
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.77
0.77
0.78
0.80
0.81
0.78
0.79
0.80
0.82
0.84
0.94
0.95
0.96
0.98
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
0.88
0.92
0.96
0.87
0.92
0.96
0.73
0.78
0.83
0.90
1.00
1.03
1.11
1.03
1.120.8
0.9
1
1.1
Figure 5: 20 years normalized DELs on WT-2 for wind class IC.
The fatigue loads on the WT-3 are more complicated because they are affected by thecombination of the operational points of the two upstream turbines. Therefore, they are shownin two separated plots (Figure 6 and 7) representing the de-rating levels of 80% and 100% onWT-3. The fatigue loads on WT-3 described by BRFlap, BREdg, BRTor, TBTor, YBTilt,YBYaw, MBTilt and MBYaw are all reduced when WT-3 is de-rated at 80% regardless of thede-rating combination of WT-1 and WT-2. The tower bottom side-to-side fatigue loads (TBSS)is largely increased when WT-3 is de-rated at 80% regardless of the de-rating combination ofWT-1 and WT-2 but it is decreased when WT-3 is de-rated at 100% (See Figure 6 and 7) inthe combination of 70% and 80% de-rating on WT-2. Further more, the results indicate thatthere is very little effect of down regulating WT-1 on the fatigue loads on WT-3, which meansthe fatigue loads on WT-3 are dominated by the operational points of WT-2. Similar resultsare also found for wind class IA and IB.
70% 80% 100%
60%
70%
80%
90%
100%
BRFlap
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.82
0.84
0.84
0.84
0.84
0.84
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
0.95
0.95
0.95
0.95
0.95
0.97
0.97
0.97
0.97
0.97
1.03
1.03
1.03
1.03
1.03
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.79
0.79
0.79
0.79
0.79
0.80
0.80
0.80
0.80
0.80
0.83
0.83
0.83
0.83
0.83
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.82
0.82
0.82
0.82
0.82
0.84
0.84
0.84
0.84
0.84
0.88
0.88
0.88
0.88
0.88
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BREdg
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.98
0.98
0.98
0.98
0.98
0.98
0.98
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
1.49
1.49
1.49
1.49
1.51
1.49
1.49
1.49
1.49
1.49
1.52
1.52
1.52
1.52
1.53
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
0.90
0.90
0.90
0.90
0.91
0.94
0.94
0.94
0.94
0.94
1.07
1.07
1.08
1.08
1.08
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
0.82
0.82
0.82
0.82
0.82
0.83
0.83
0.83
0.83
0.83
0.87
0.87
0.87
0.87
0.87
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
BRTor
0.84
0.84
0.84
0.84
0.84
0.85
0.85
0.85
0.85
0.85
0.86
0.86
0.86
0.86
0.86
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.80
0.80
0.80
0.80
0.80
0.81
0.81
0.81
0.81
0.81
0.84
0.84
0.84
0.84
0.84
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.80
0.80
0.80
0.80
0.80
0.81
0.81
0.81
0.81
0.81
0.84
0.84
0.84
0.84
0.84
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
0.90
0.90
0.90
0.91
0.92
0.95
0.95
0.95
0.95
0.95
1.11
1.11
1.11
1.11
1.11
Figure 6: 20 years normalized DELs on WT-3when de-rating at 80%.
70% 80% 100%
60%
70%
80%
90%
100%
BRFlap
0.95
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.96
0.96
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
0.91
0.91
0.91
0.91
0.91
0.93
0.93
0.93
0.93
0.93
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.95
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.96
0.96
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.93
0.93
0.93
0.93
0.93
0.95
0.95
0.95
0.95
0.95
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BREdg
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
0.89
0.89
0.90
0.90
0.90
0.95
0.95
0.96
0.95
0.96
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
0.82
0.82
0.82
0.82
0.83
0.85
0.85
0.85
0.86
0.86
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
0.92
0.92
0.92
0.92
0.93
0.94
0.94
0.94
0.94
0.94
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
BRTor
0.96
0.96
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.98
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.94
0.94
0.94
0.94
0.95
0.96
0.96
0.96
0.96
0.96
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.94
0.94
0.94
0.94
0.95
0.96
0.96
0.96
0.96
0.96
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
0.80
0.80
0.80
0.80
0.81
0.84
0.84
0.84
0.84
0.85
1.00
1.00
1.00
1.00
1.00
Figure 7: 20 years normalized DELs on WT-3when de-rating at 100%.
4.2. Extreme loadsFigure 8 shows the extreme loads of WT-1 operating under different down regulation levels atwind class IC. Most of the extreme loads are reduced considerably for different down regulation
NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
IOP Publishing
doi:10.1088/1742-6596/1452/1/012009
8
levels except for the tower bottom side-to-side bending moment (TBSS), the yaw bearingroll moment (YBRoll) and the main bearing torsional moment (MBTor). The reason for theincreased extreme loads is similar to fatigue loads, which has been explained in the previoussection. One noticeable difference compared to the fatigue loads is that the extreme bendingmoment at the tower bottom in fore-aft direction is not increased. This is because the mean valueof tower bottom fore-aft bending moment during the down-regulated control is reduce largely(see Figure 3), which is able to compensate the high vibration amplitude due to the excited towerfirst fore-aft mode. Another difference is that the extreme yaw bearing roll moment (YBRoll)and the main bearing torsional moment (MBTor) are increased only when down regulating theturbine to produce 80% and 90% of the available power.
BRFlap
BREdgBRTor
TBFATBSS
TBTorYBTilt
YBRoll
YBYawMBTilt
MBYawMBTor
load channel (-)
0
0.5
1
1.5
2
Norm
aliz
ed e
xtr
em
e load (
-) WT-1:60%
WT-1:70%
WT-1:80%
WT-1:90%
WT-1:100%
Figure 8: Normalized extreme loads on WT-1 for wind class IC.
Figure 9 shows the extreme loads of WT-2 operating at 70%, 80% and 100% de-rating levels,in the meantime WT-1 is running at different down regulation levels as it is displayed on y-axis.It shows that all the extreme loads are largely reduced when the WT-2 is operating at 70%and 80% de-rating levels except for Tower bottom side-to-side moment (TBSS), yaw bearingroll moment (YBRoll) and main bearing torsional moment (MBTor). These loads are closelyrelated with drive train vibration which has been discussed in the previous section.
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BRFlap
0.65
0.64
0.65
0.67
0.71
0.74
0.74
0.76
0.77
0.79
0.97
0.97
0.97
0.98
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
0.81
0.83
0.83
0.82
0.83
0.84
0.85
0.84
0.84
0.86
1.01
1.03
1.00
1.03
1.00
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.75
0.74
0.74
0.73
0.77
0.82
0.82
0.83
0.85
0.87
1.00
1.02
1.03
1.02
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.80
0.80
0.80
0.81
0.81
0.76
0.76
0.76
0.78
0.82
0.98
0.99
1.00
1.00
1.000.8
0.9
1
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BREdg
0.92
0.92
0.94
0.95
0.95
0.93
0.95
0.93
0.93
0.92
1.01
1.00
1.04
1.03
1.03
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
1.23
1.23
1.22
1.23
1.22
1.01
0.96
0.95
0.95
1.00
1.50
1.52
1.55
1.59
1.62
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
1.00
1.00
1.00
0.99
0.99
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.00
1.02
1.01
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
0.83
0.83
0.83
0.84
0.84
0.74
0.75
0.77
0.79
0.81
0.96
0.96
0.96
0.97
1.000.8
0.9
1
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BRTor
0.76
0.77
0.79
0.83
0.85
0.92
0.92
0.91
0.88
0.83
0.99
1.00
1.02
1.02
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.89
0.89
0.90
0.89
0.89
0.72
0.74
0.76
0.78
0.80
0.94
0.98
1.00
1.01
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.90
0.90
0.90
0.90
0.90
0.72
0.74
0.76
0.78
0.80
0.95
0.98
1.00
1.01
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
0.99
0.99
0.99
0.99
1.00
1.00
1.00
1.01
1.00
1.00
1.11
1.11
1.12
1.11
1.11 1
1.05
1.1
Figure 9: Normalized extreme loads on WT-2 for wind class IC.
The extreme loads on WT-3 are presented in two separated figures, which are Figure 10and 11. When the WT-3 is operating at 80% de-rating level, all the extreme loads are reduced
NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
IOP Publishing
doi:10.1088/1742-6596/1452/1/012009
9
regardless of the operational condition of the WT-1 and WT-2 except for the extreme loadsrepresented by TBSS, YBRoll and MBTor. Figure 11 shows when the WT-3 is operating at100% de-rating level, only the extreme loads represented by BRFlap, TBTor, YBTilt, YBYawand MBTilt are decreased, the rest of the extreme loads are slightly increased. Similar as thefatigue loads, the extreme loads on WT-3 are dominated by the operational points of WT-2.For wind class IA and IB, similar extreme loads are also found.
70% 80% 100%
60%
70%
80%
90%
100%
BRFlap
0.66
0.66
0.66
0.66
0.66
0.65
0.65
0.65
0.65
0.65
0.68
0.68
0.68
0.68
0.68
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
0.87
0.88
0.88
0.88
0.88
0.90
0.90
0.90
0.89
0.89
0.94
0.94
0.94
0.94
0.94
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.80
0.80
0.80
0.80
0.80
0.80
0.80
0.81
0.80
0.80
0.80
0.80
0.800.81 0.81
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.72
0.72
0.72
0.72
0.72
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BREdg
0.91
0.94
0.94
0.94
0.94
0.93
0.94
0.94
0.94
0.94
0.94
0.95
0.95
0.95
0.95
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
1.34
1.34
1.34
1.34
1.35
1.35
1.35
1.35
1.35
1.36
1.36
1.36
1.36
1.36
1.36
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.03
1.03
1.03
1.03
1.03
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
0.93
0.93
0.93
0.93
0.94
0.93
0.93
0.93
0.94
0.93
0.93
0.93
0.93
0.940.94
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
BRTor
0.84
0.84
0.84
0.84
0.84
0.83
0.83
0.83
0.83
0.83
0.86
0.86
0.86
0.86
0.86
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.89
0.89
0.89
0.89
0.89
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.87
0.87
0.87
0.87
0.87
0.88
0.88
0.88
0.87
0.87
0.89
0.89
0.89
0.89
0.89
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
1.12
1.12
1.12
1.12
1.12
1.12
1.12
1.12
1.121.12
1.12
1.12
1.12
1.12
1.12
Figure 10: Normalized extreme loads on WT-3when de-rating at 80%.
70% 80% 100%
60%
70%
80%
90%
100%
BRFlap
0.89
0.89
0.89
0.89
0.90
0.93
0.93
0.94
0.94
0.94
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
TBFA
1.01
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.00
1.00
1.05
1.05
1.05
1.05
1.05
70% 80% 100%
60%
70%
80%
90%
100%
YBTilt
0.94
0.94
0.94
0.94
0.94
0.93
0.93
0.93
0.94
0.94
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBTilt
0.95
0.95
0.95
0.95
0.95
0.95
0.95
0.95
0.95
0.95
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls BREdg
1.02
1.02
1.02
1.04
1.05
1.01
1.01
1.01
1.01
1.001.07
1.06
1.06
1.06
1.06
70% 80% 100%
60%
70%
80%
90%
100%
TBSS
1.00
1.00
1.00
1.01
1.00
1.00
1.00
1.00
1.001.02
1.02
1.02
1.02
1.02
1.02
70% 80% 100%
60%
70%
80%
90%
100%
YBRoll
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
60%
70%
80%
90%
100%
MBYaw
1.01
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.001.02
1.02
1.02
1.02
1.02
1.02
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
BRTor
1.03
1.03
1.03
1.03
1.03
1.00
1.00
1.00
1.00
1.00
1.04
1.04
1.04
1.04
1.04
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
TBTor
0.93
0.93
0.93
0.93
0.93
0.95
0.95
0.95
0.95
0.95
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
YBYaw
0.93
0.93
0.93
0.93
0.93
0.95
0.95
0.95
0.95
0.95
1.00
1.00
1.00
1.00
1.00
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
MBTor
1.01
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.001.01
1.01
1.01
1.01
1.01
1.01
Figure 11: Normalized extreme loads on WT-3when de-rating at 100%.
4.3. Wind farm AEPThe normalized AEPs of the wind farm based on different combinations of the operationalstrategies on each turbine are shown in Figure 12. The result shows that the AEPs of wind farmare reduced for all the operational strategies, which indicates, in terms of wind farm AEP, theminimum Ct control strategy for down regulating the turbines in a wind farm gives a lower AEP.On the other hand, it gives lower fatigue and extreme loads on the turbines. Three operational
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
WT
1 d
e-r
atin
g le
ve
ls
WT3: 80%
0.748
0.783
0.816
0.846
0.875
0.778
0.812
0.844
0.873
0.828
0.860
0.889
0.902
0.916
0.941
70% 80% 100%
WT2 de-rating levels
60%
70%
80%
90%
100%
WT3: 100%
0.814
0.849
0.882
0.912
0.942
0.843
0.877
0.909
0.938
0.887
0.919
0.949
0.966
0.975
1.000
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
Figure 12: Normalized AEP of the wind farm for wind class IC.
strategies, namely, CASE1, CASE2 and CASE3 are selected for further investigation based onfatigue loads and AEP discussed in Section 4.1 and 4.3. The Baseline case is defined as all 3turbines are running without down regulation over their lifetime. CASE1, CASE2 and CASE3are described as the following:
• CASE1: WT-1 at 90%, WT-2 at 100% and WT-3 at 100%.
NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
IOP Publishing
doi:10.1088/1742-6596/1452/1/012009
10
• CASE2: WT-1 at 90%, WT-2 at 80% and WT-3 at 100%.
• CASE3: WT-1 at 100%, WT-2 at 80% and WT-3 at 100%.
4.4. Lifetime extension applicationThis investigation focuses on the technical feasibility of lifetime extension on some componentsof wind turbine. Therefore, some assumptions regarding wind farm operation are made for thecalculations without using the real wind farm operation data. Beside this, only fatigue loads areconsidered as the main factor of the lifetime extension.
According to the Miner’s linear damage hypothesis [19] the total damage as the functionof tn and td after 20 years with combined normal operation and down-regulated operation iscalculated as
Dt(tn, td) =tnTl
+tdTl
(Leq,dLeq,n
)m(6)
where, Dt is the total fatigue damage, Tl is complete lifetime, Leq,n and Leq,d are the lifetimeequivalent loads at normal operation and at down-regulated operation, tn and td are the timeperiods of the turbine running at normal operation and at down-regulated operation, m is thematerial Wohler coefficient. Substituting the values of tn and td, the total fatigue damage canbe calculated. The difference between the reference case and any other case, i, are defined asdamage margin, ∆Dt = Dt,ref − Dt,i, which is used in Equations 7 to calculate the lifetimeextension, Tl,ext.
Tl,ext = ∆DtTl
(Leq,dLeq,n
)−m(7)
In this study the evaluation is performed on the component level of three turbines. we assumetn = 0 and td = 20 years for the down regulated turbines. The normalized lifetime extensionon the main components of three turbines are shown in Figure 13. Among the three selected
BRFlap BREdg BRTor TBFA TBSS TBTor YBTilt YBRoll YBYaw MBTilt MBYaw MBTor AEP
Load channel and AEP
CASE1:WT1
CASE1:WT2
CASE1:WT3
CASE2:WT1
CASE2:WT2
CASE2:WT3
CASE3:WT1
CASE3:WT2
CASE3:WT3
1.092
0.239
0.004
1.092
0.453
0.000
0.439
0.111
0.016
-0.001
0.111
0.314
0.026
0.000
0.319
0.028
1.492
0.082
0.001
1.492
0.293
0.000
2.965
0.275
-0.061
0.212
0.001
-0.061
-0.016
0.345
0.000
-0.096
0.330
-0.591
0.010
-0.001
-0.591
-0.746
0.209
0.000
-0.759
0.196
0.382
0.087
0.001
0.382
1.254
0.182
0.000
1.023
0.175
0.301
0.063
-0.000
0.301
0.782
0.128
0.000
0.658
0.123
-0.118
0.302
0.002
-0.118
0.011
0.598
0.000
-0.198
0.571
0.270
0.067
0.001
0.270
0.833
0.137
0.000
0.687
0.133
0.239
0.093
-0.000
0.239
0.658
0.164
0.000
0.513
0.162
0.248
0.093
-0.000
0.248
0.668
0.195
0.000
0.519
0.192
-0.229
0.383
0.001
-0.229
-0.086
0.685
0.000
-0.296
0.654
0.975
0.975
0.975
0.938
0.938
0.938
0.966
0.966
0.966
4.315
3.474
3.162
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 13: Normalized lifetime extension per load sensor and wind farm AEP for CASE1, CASE2and CASE3.
operational cases, the lifetime of the evaluated load channels are increased except for loadchannels, namely, TBFA, TBSS, YBRoll and MBTor when the turbine is under down regulationcontrol. Consistent result is found from CASE3, in which the WT-2 is down-regulated at 80%while the WT-1 and WT-3 are under normal operation. Although WT-1 is not down-regulated,the extended lifetime of WT-3 is nearly the same as CASE2. This is because the fatigue loadson the WT-3 are dominated by the operational point of WT-2, which has been discussed in
NAWEA WindTech 2019
Journal of Physics: Conference Series 1452 (2020) 012009
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doi:10.1088/1742-6596/1452/1/012009
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Section 4.1. The benefit of CASE3 is that the wind farm AEP is about 2.8% higher thanCASE2. Another noticeable result is found that a larger lifetime extension happens on theblades for all three cases. It shows the effect of the material. For the material with a steep S-Ncurve, a small fatigue load reduction contributes to large a lifetime extension. This investigationis a rough attempt to quantify the contribution of minimum Ct control strategy to the lifetimeextension showing that there is some potential while more specific control parameter tuning isneeded.
5. Conclusions and future workIn this paper, a minimum Ct control strategy for down regulating wind turbines in wind farmis implemented in the basic DTU Wind Energy controller, which couples with the aero-elasticcode, HAWC2. The results show that a minimum Ct control strategy attenuates the wakedeficit generated by upstream turbines, and results in both lower fatigue and extreme loads onmost of the components of both upstream and downstream turbines. Three possible wind farmoperational strategies are investigated and the results indicates that CASE1 and CASE3 canextend the lifetime of the wind turbine main components if the control parameters were finetuned based on the down regulation conditions and the overall energy production of a wind farmcan be increased.
The results also show that the minimum Ct control strategy might result in a sub-optimalperformance or poor robustness (deteriorate the system stability), for example, the possibilityof exciting the tower first fore-aft and side-to-side modes if certain control functionality, such asrotor speed exclusion, is not considered, or the control parameters are not adjusted accordinglybased on the down regulation conditions, which will lead increased fatigue and extreme loads.Therefore, when implementing a down regulation control strategy on the original turbinecontroller, the changes due to down regulation control such as the rotor speed, initial pitchangle and aerodynamic performance need to be investigated in the future work.
AcknowledgementThe authors have received funding from the European Union’s Horizon 2020 research andinnovation programme (TotalControl, grant no. 727680 ).
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