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High-fidelity simulation comparison of wake mitigation control
strategies for a two-turbine case
P. Fleming1 , P. Gebraad2 , S. Lee1 , J.W. van Wingerden2 , K. Johnson1 ,
M. Churchfield1 , J. Michalakes1 , P. Spalart3 , P. Moriarty1
1 National
2 Delft
Renewable Energy Laboratory, Golden CO, USA, [email protected]
University of Technology, Delft, The Netherlands, [email protected]
3 Boeing Commercial Airplanes, Seattle WA
Abstract
Wind turbines arranged in a wind plant impact each other through their wakes. Wind plant
control is an active research field that attempts to improve wind plant performance by modifying individual turbine controllers to take into account these turbine-wake interactions.
In this paper, we use high-fidelity simulations of a two-turbine fully-waked scenario to
investigate the potential of several wake mitigation strategies. The strategies, including
modification of yaw and tilt angle, as well as repositioning of the downstream turbine, represent a mix of known and novel approaches. The simulation results are compared through
change relative to a baseline operation in terms of overall power capture and loading on the
upstream and downstream turbine.
1
Introduction
Wind turbines influence nearby turbines aerodynamically as they extract energy from and enhance turbulence in the wind. Recently, wind turbine control systems researchers examined
how these influences can be accounted for and adjusted such that increased wind power plant
efficiency and reduced turbine loads can be obtained. Often in the literature, this is done by
adapting the axial induction of individual turbines through pitch and torque control, [1, 2, 3]. In
these methods, an axial induction factor is found that results in lower individual turbine power
for an upstream tower, but higher plant power due to increased power capture by downstream
turbines.
An alternative approach to wind plant control focuses instead on redirecting wakes around downstream turbines. One method of achieving this redirection that has been published in the literature is through intentional yaw misalignment in an upstream turbine. In [4] field-tests are carried
out in a scaled wind plant test field, whereas in [5], computational fluid-dynamics (CFD) simulations are performed using actuator disk models of a wind turbine.
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In this paper, we describe two-turbine simulation experiments of wake redirection based wind
plant control using a high-fidelity wind plant simulator, the NREL SOWFA (Simulator for
Off/Onshore Wind Farm Applications) tool [6]. SOWFA, described in Section 2, couples a computational fluid dynamics (CFD) solver with the aero-elastic turbine simulator FAST [7]. Using
SOWFA, controllers can be compared in terms of their effects on power production and loading
of upstream and downstream turbines. This is an important capability since a controller’s effects
on power production must be weighed against its effects on turbine loads.
In addition to evaluating the yaw misalignment method, we also introduce two additional concepts. First, we modify the tilt angle of an upstream turbine in order to redirect the wake vertically. The second method does not redirect the wake but instead repositions the downstream
turbine (in the case of floating turbines), as proposed in [8]. Additional analysis of the yaw and
tilt methods can be found in [9], which analyzes the ability of a single turbine to redirect the
wake.
The control methods are evaluated using a simulation of two 5MW turbines, 7 rotor diameters
apart, aligned in a turbulent inflow. For each method, the setpoint (yaw misalignment angle, tilt
angle or downstream turbine position) is varied, and a 1000 second simulation is run. Additionally, because these techniques might move the downstream turbine from full wake to partial
wake, which induces loading [10], we consider the cases where the downstream turbine is and
isn’t using independent pitch control (IPC) to mitigate uneven distribution of wind speed across
the rotor plane. The results are compared in terms of total power output and key component
loads on both the upstream and downstream turbine across all cases.
The contributions of the paper are: (1) the addition of a new method for wake-redirection wind
plant control, using adaptation of the rotor tilt angle (with [9]), (2) an analysis and comparison
of three methods of wind-plant wake mitigation using a high-fidelity simulator in terms of power
and loading of an upstream and downstream turbine, and (3) an investigation into the use of IPC
for mitigating the effects of partial wake on turbine loads.
The remainder of this paper is organized as follows. Section 2 provides an overview of the
simulation tool SOWFA used in this work. Section 3 provides a description of the simulation
scenario in terms of dimension, inflow properties, turbine properties and individual control laws.
Section 4 presents and analyzes the results of the study. Section 5 provides some discussion
points and considerations for future work. Finally, the conclusions are given in section 6.
2
SOWFA
In this work, a parametric study of the proposed control actuation methods is performed using
a high-fidelity tool: Simulator for Off/Onshore Wind Farm Applications (SOWFA) [6] which
is a large-eddy simulation (LES) framework coupled with NRELs aero-elastic turbine code [7]
for studying wind turbines embedded in the atmospheric boundary layer (ABL). The kernel of
the LES framework is based on open-source OpenFOAM libraries [11] which solves the in2
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compressible Navier-Stokes equations augmented with a buoyancy term (based on Boussinesq
approximation) and Coriolis acceleration to simulate atmospheric boundary layers under various
conditions. The transport of potential temperature is solved in parallel to account for buoyancy.
This set of governing equations are discretized over an unstructured finite volume mesh with second order central differencing scheme. The collocated formulation of the velocity and pressure
variables is decoupled using the Rhie-Chow [12] interpolation method to avoid numerical instability. The time advancement method follows the predictor-corrector pressure-implicit splitting
operation (PISO) of Issa [13] with three sub-step iteration to maintain second order accuracy.
The Moeng model [14] is adapted to estimate the local time-varying shear stress. The sub-grid
scale (SGS) turbulence closure employs the standard Smagorinsky [15] formulation with a constant of 0.135.
The turbine blades are represented by the actuator line (AL) method of Sørenesen and Shen [16],
in which the blades are discritized along the radial line where the lift and drag forces are computed based on the incoming flow and the airfoil geometry at the actuator points. These force
vectors are projected on to the computational domain space using a three-dimensional Gaussian
filter which, as a collective whole, produce the wake structures similar to those from bladegeometry resolved simulations at significantly reduced computational cost. In SOWFA, the
incoming flow velocity data at the actuator points from the flow solver are fed into FAST, from
which the computed aerodynamic lift and drag forces and the shifted actuator points (caused by
the blade deflections) are projected on to the momentum equation as a body force term completing the two-way coupling cycle. The structural loading responses induced by the aerodynamic
forces are collected as FAST outputs which are later presented in this study. Further details on
SOWFA can be found in [17].
With SOWFA, simulations of proposed wind plant control schemes can be analyzed. Because
the simulation includes high-fidelity modeling of the atmosphere, and the turbine structure, it is
possible to study simultaneously a controller’s impact on power and turbine loads.
3
Experimental setup
As described in the introduction, the objective of the paper is to compare three strategies of wake
mitigation (yaw-misalignment based, tilt-misalignment based and repositioning of the downstream turbine) using SOWFA. To this end, an “open-loop” two-turbine simulation study is performed in which the yaw, tilt, and position setpoints are swept and held fixed for separate 1000
second simulations with constant wind direction. Later research will develop active closed-loop
control strategies for time-varying wind directions.
A scenario was developed to simulate two NREL 5-MW baseline turbines [18] in turbulent inflow. The turbulent scenario is that of a neutral boundary layer, selected based on a previously
published study. [17] The inflow is generated in a precursor atmospheric LES on a domain that
is 3 km by 3 km in the horizontal and 1 km in height. The horizontally-averaged wind speed is
driven to 8 m/s at the turbine hub height and is controlled through a time-varying mean driving
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Figure 1: Overview of the experimental setup in the baseline case.
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Figure 2: Example velocity fields for different wake redirection methods, generated by SOWFA.
pressure gradient. The wind comes from the southwest (300◦ ) so that the elongated turbulent
structures in the surface layer are not ”trapped” by the periodic boundaries, continually cycling
through in the same location. In the baseline case, the turbine rotor axis is aligned with the wind
direction. The surface temperature flux is set to zero, although a capping inversion initially at
750 m above the surface is used both to slow boundary layer growth and because it is a real
feature of atmospheric boundary layers. The surface aerodynamic roughness is set to 0.001 m,
which is typically of flow over water. Details on positioning of the turbines and meshing of the
domain are given in fig. 1.
Screenshots from time averaged slices of the flow for the different control strategies is provided
in fig. 2. SOWFA requires significant computational power in order to run high-fidelity simulations: using a sample time of 0.02s, the time steps take an average 2.5s to calculate on the
Sandia/NREL Red Mesa supercomputer [19] using distributed computation with 256 processors.
This yields an execution time of 34.4h for each simulation.
In each case, the turbines use the baseline controller defined in [18]) independently. Because
wake redirection can move the downstream turbine from full wake to partial wake, inducing
loads [10], we compare the use of IPC with the standard collective pitch control by switching
on load-reducing IPC on the downstream turbine for the last 400s of the simulation. The IPC
implementation is based on the design first presented in [20], using the parameters as specified
in [21], with some adaptations to be able to use the load-reducing IPC in below-rated conditions.
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A supervisory wind plant controller [22] collects the data from the individual turbines.
4
Results and Analysis
Following completion of the runs, the data was collected from each case and post-processed
as follows. First the 1000s of time domain data for each was broken into segments. The first
200s of each run was discarded since the wake was not fully developed. The last 100s were
also discarded due to system problems on the cluster leaving some files incomplete. Finally, the
remaining time histories were divided into 200s-600s, in which the downstream turbine is not
running IPC, and 700s-900s, when it is and the IPC startup transients have vanished. Although it
should be possible to start IPC smoothly, since the transition was not our research focus we ramp
it on rather abuptly. In the baseline case, IPC is never enabled, to provide a basis for comparison.
From these two blocks of time (200-600s and 700-900s), several metrics are computed. First,
the average power is computed for each turbine. Next, loads are computed for blade out-of-plane
(OOP) bending, drivetrain torsion, tower bending and yaw bearing moment. In the case of the
tower load, a combined load is computed from the separate fore-aft and side-side loads using a
root-sum-square combination. This is likewise done to combine the separate My and Mz loads on
the yaw bearing. Individual loads are provided in the appendix. For each of these load signals,
a damage equivalent load (DEL) is computed. The DEL is a standard metric of fatigue damage
(see [23]). These results are summarized in figs. 3 and 4.
Fig. 3 shows the comparison of methods in the case where the downstream turbine does not use
IPC. For each method, there is a sweep across possibles setpoint (yaw angle, tilt angle or reposition of downstream turbine position). The top row shows the total power output of each case,
with the horizontal line indicating the baseline level and the numbers above each bar denoting
percent change from the baseline case. The remaining rows of the figure indicate percent change
in DEL for the components examined.
Starting with yaw-based control, in the best case the method shows an increase in power of
4.6%. Additionally, the simulation shows that for the upstream turbine with misaligned yaw,
significant load reduction is observed for blade OOP bending, tower bending and yaw bearing
moment. The downstream turbine however experiences a rise in blade OOP bending, drivetrain
torsion and yaw bearing moment. This change is most likely due to the movement from full to
partial wake overlap.
In the tilt case, a maximum power gain of 7.1% is observed. At this peak of power capture, it
is seen that for the upstream turbine, the blade and yaw bearing loads have gone up while the
drivetrain and tower loads have declined a small amount. As in the yaw case, the downstream
turbine experiences an increase in blade loads, most likely due to partial-wake overlap. There is
also a decrease in tower loads and increase in yaw bearing loads.
Tilt misalignment shows larger potential power production improvements than yaw when con6
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Figure 3: Summary of results of two tubine simulation. The 3 columns are divided by control
action. The top row shows the combined power output for each case, compared to the baseline
case on the far left. The remaining rows indicate the percent change in load compared to the
baseline.
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sidering large positive tilt angles. With a positive tilt angle, the rotor would face downwards, and
for conventional upstream turbine designs this would cause the blades to hit the tower. Therefore, a positive tilting mechanism is more suitable to downwind turbines [24]. Both negative
and positive tilt angles will redirect the wake away from the downstream turbine rotor, but the
positive tilting has the advantage that it will redirect the wake towards the ground, allowing high
velocity air from higher altitudes to flow towards the upper part of the downstream rotor, resulting in a higher power production of the downstream turbine. Additional details on the wake
displacements that can be achieved using yawing or tilting can be found in [9].
Repositioning of (floating) turbines produces the most substantial gains in power if the rotor
of the downstream turbine is moved more than 25 meters out of the rotor axis of the upstream
turbine (up to 41% improvement when the downstream turbine is moved a full rotor diameter).
Observing the loads for the downstream turbine, there is little change for small changes in position, significant change for the discplacements yielding partial overlap, and then no change
again when the turbine is moved a full rotor diameter.
Looking at the loads across experiments, the upstream turbine either sees an increase or decrease
in blade OOP bending, depending on the angle chosen. Also, for the upstream turbine, yaw and
tilt angle adjustments either decrease or minimally increase the drivetrain, tower and yaw load.
A possible explanation for this effect is that these methods generally reduce the power capture
of the upstream turbine, and derating can be considered as a load mitigation strategy. For the
downstream turbine, all loads generally increase somewhat, and this is most likely due to moving from full to partial wake overlap.
Fig. 4 performs the same analysis, but now for the case where the downstream turbine is using
IPC to mitigate the effect of partial wake overlap. Note that these results are based on 200s of
simulation versus 400s in Fig. 3, and are from a different point in the simulation. The results
are dramatic: the blade loads, tower loads and yaw bearing loads are consistently reduced when
compared to the baseline case (which does not use IPC). The drivetrain loads are the exception, but the lack of a clear pattern indicates that perhaps this is a somewhat stochastic load.
Missing from the current controller is a drivetrain damper, a very common element in industrial
controllers that could be used to minimize the changes in drivetrain loads. Overall, the results
indicates a very strong motivation for the use of IPC, in general, and as a way to eliminate the
negative impacts of using wake-mitigation strategies.
The appendix provides the full results listed in absolute values (not relative to baseline).
5
Discussion
It is important to acknowledge the shortcomings of this current work. First, due to computational/time constraints, current results are based on simulations of only one inflow case. Future
work will combine results from simulations using multiple wind inputs and better establish the
robustness of these results. Additionally, the experiments are not of a closed-loop control, but
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Figure 4: Comparison of data as in fig. 3, however with the downstream turbine operating with
IPC in all cases except for the baseline. Note that due to system problems, one case is missing
but will be present in final version.
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of settings that take advantage of a stationary wind direction. This is a good first step, but in
order to be applicable to real wind plants, future work must establish control loops which can
accomplish similar results for changing wind direction conditions.
6
Conclusions
This report shows very good potential for all methods considered. For each case, operating
points exist which couple improved power capture with, mostly, reduced loading. It is important
to point out though that presently, the technology only exists to implement yaw misalignment.
However, given that tilt and repositioning are capable of yielding more power capture, perhaps
the effects could be considered in the design of future turbines. A second result of the paper
is the very good potential of employing IPC to mitigate partial wake effects. This improves the
benefit of the wake redirection or repositioning techniques by reducing the partial-wake-induced
loads on the downstream turbine.
Acknowledgements
The authors are very grateful to Wesley Jones and the NREL High Performance Computing team
for their crucial help and support in completing this simulation study.
This work was supported by the U.S. Department of Energy under Contract No. DE-AC3608GO28308 with the National Renewable Energy Laboratory and by the NWO Veni Grant no.
11930 Reconfigurable floating wind farm.
References
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Wind, 2012.
[2] K.E. Johnson and G. Fritsch. Assessment of extremum seeking control for wind farm
energy production. Wind Engineering, 36(6):701–716, 2012.
[3] J.R. Marden, S.D. Ruben, and L.Y. Pao. Surveying game theoretic approaches for wind
farm optimization. In Proceedings of the 50th IEEE Conference on Decision and Control,
volume 38, pages 584–596, 2012.
[4] J.W. Wagenaar, L.A.H. Machielse, and J.G. Schepers. Controlling wind in ECN’s scaled
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[5] Á. Jiménez, A. Crespo, and E. Migoya. Application of a LES technique to characterize the
wake deflection of a wind turbine in yaw. Wind energy, 13(6):559–572, 2010.
[6] M. Churchfield and S. Lee. NWTC design codes (SOWFA). http://wind.nrel.
gov/designcodes/simulators/SOWFA, 2013.
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[7] J. Jonkman.
NWTC Design Codes (FAST).
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[8] J.W. van Wingerden. Reconfigurable floating wind turbines, VENI project no. 11930,
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SOWFA. In Proceedings of ICOWES, 2013.
[10] Z. Yang, Y. Li, and Y.E. Seem. Improved individual pitch control for wind farm turbine
load reduction via wake modeling. In Proceedings of AIAA, 2011.
[11] OpenFOAM, the open source CFD toolbox. http://www.openfoam.com/, 2013.
[12] C.M. Rhie and W.L. Chow. Numerical study of the turbulent flow past an airfoil with
trailing edge separation. AIAA Journal, 21:1525–1532, 2012.
[13] R.I. Issa. Solution of the implicitly discretised fluid flow equations by operator-splitting.
Journal of computational physics, 62(1):40–65, 1986.
[14] C.H. Moeng. A large-eddy simulation model for the study of planetary boundary layer
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[15] J. Smagorinsky. General circulation experiments with the primitive equations. Monthly
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[16] J.N. Sørensen and W.Z. Shen. Numerical modeling of wind turbine wakes. Journal of
Fluids Engineering, 124(2):393–399, 2002.
[17] M.J. Churchfield, S. Lee, J. Michalakes, and P.J. Moriarty. A numerical study of the effects
of atmospheric and wake turbulence on wind turbine dynamics. Journal of Turbulence,
13(14):1–32, 2012.
[18] J. Jonkman, S. Butterfield, W. Musial, and G. Scott. Definition of a 5-MW reference wind
turbine for offshore system development. Technical report, NREL/TP-500-38060, 2009.
[19] NREL’s high-performance computing capabilities.
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[20] E.A. Bossanyi. Controller for 5MW reference turbine. Technical report, Garrad Hassan
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[23] M. Buhl Jr. MCrunch theory manual for version 1.00.
[24] Andrew Scholbrock. Private conversation.
Appendix
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Baseline
T1 yaw = -35◦
T1 yaw = -30◦
T1 yaw = -25◦
T1 yaw = -20◦
T1 yaw = -20◦
T1 yaw = -10◦
T1 yaw = -5◦
T1 yaw = 5◦
T1 yaw = 10◦
T1 yaw = 15◦
T1 yaw = 20◦
T1 yaw = 25◦
T1 yaw = 30◦
T1 yaw = 35◦
T1 yaw = 40◦
T1 tilt = -15◦
T1 tilt = -12◦
T1 tilt = -9◦
T1 tilt = -6◦
T1 tilt = -3◦
T1 tilt = 3◦
T1 tilt = 6◦
T1 tilt = 9◦
T1 tilt = 12◦
T1 tilt = 15◦
T1 tilt = 18◦
T1 tilt = 21◦
T1 tilt = 24◦
T1 tilt = 27◦
T1 tilt = 30◦
T1 tilt = 33◦
T1 tilt = 36◦
T1 moved -130m
T1 moved -100m
T1 moved -50m
T1 moved -25m
T1 moved -10m
T1 moved -5m
T1 moved -2m
T1 moved 2m
T1 moved 5m
T1 moved 10m
T1 moved 25m
T1 moved 50m
T1 moved 100m
T1 moved 130m
Case
Power (MW)
T1
T2
Total
1.7
0.8
2.6
1.2
1.2
2.4
1.3
1.1
2.4
1.4
1.0
2.5
1.5
0.9
2.5
0.9
2.5
848.4
1.7
0.8
2.5
1.7
0.8
2.5
1.7
0.9
2.6
1.7
1.0
2.6
1.6
1.0
2.6
1.5
1.1
2.7
1.4
1.2
2.7
1.3
1.3
2.7
1.2
1.4
2.6
1.0
1.5
2.5
1.6
0.9
2.5
1.6
0.9
2.5
1.7
0.9
2.5
1.7
0.9
2.5
1.7
0.8
2.5
1.7
0.9
2.6
1.7
0.9
2.6
1.7
0.9
2.6
1.6
1.0
2.6
1.6
1.0
2.7
1.6
1.1
2.7
1.5
1.2
2.7
1.5
1.2
2.7
1.4
1.3
2.7
1.3
1.4
2.7
1.3
1.5
2.7
1.2
1.6
2.7
1.7
1.7
3.4
1.7
1.5
3.2
1.7
1.0
2.7
1.7
0.9
2.6
1.7
0.8
2.5
1.7
0.8
2.5
1.7
0.8
2.6
1.7
0.9
2.6
1.7
0.9
2.6
1.7
0.9
2.6
1.7
1.0
2.7
1.7
1.2
2.9
1.7
1.7
3.4
1.7
1.9
3.6
OOP Bending (kNm)
T1
T2
738.8
982.5
913.3
1133.9
905.8
1152.5
886.7
1124.8
873.2
1081.6
1026.4
171.5
798.9
981.1
781.1
1018.0
705.8
1042.1
678.6
1044.4
649.3
1105.9
642.1
1123.2
628.8
1136.9
607.6
1104.5
609.6
1080.7
598.9
1059.7
620.2
908.4
645.5
916.5
657.5
967.0
695.4
970.6
722.1
979.9
760.9
1032.6
783.4
1043.4
803.6
1137.3
806.6
1203.6
817.8
1226.3
827.2
1292.1
822.3
1265.1
838.8
1282.3
831.3
1297.2
812.2
1270.2
811.3
1222.6
785.1
1212.3
738.0
1001.9
739.5
1125.1
739.1
1092.4
740.6
1002.0
738.2
994.1
737.8
991.0
738.2
982.3
738.2
986.5
737.5
984.8
737.4
994.9
737.4
1052.3
739.3
1178.6
740.1
1047.6
739.6
868.8
Fore-Aft (kNm)
T1
T2
5382.3
11589.4
5247.1
10472.9
5412.3
9407.3
5504.9
11803.0
5446.8
14530.8
12024.4
1411.8
5221.8
11252.3
5192.6
15435.1
5425.9
13374.9
5360.1
11023.9
5146.6
11553.1
4677.1
11762.3
5020.8
9839.3
4327.6
11043.2
4097.8
10525.8
4965.4
10523.8
5380.7
9632.7
5404.2
11291.2
5649.4
11467.2
5454.0
10910.2
5453.2
13100.4
5278.6
12021.9
5237.4
12492.4
5223.9
12350.6
5187.5
12808.0
5311.1
12819.7
5597.0
11633.0
5383.3
13218.3
5224.5
10089.3
5121.4
9331.2
5149.2
9415.0
5121.8
9900.1
5105.4
9205.0
5406.1
8475.2
5404.8
10555.4
5410.4
11368.8
5365.5
12031.7
5415.7
11915.1
5391.1
11908.1
5385.8
11446.8
5392.9
11507.7
5401.8
11354.7
5381.3
12062.1
5392.2
12869.2
5367.7
10923.0
5377.1
7353.5
5409.2
6724.1
Side-Side (kNm)
T1
T2
2529.5
5595.1
1964.4
4244.0
1347.3
5139.2
1264.3
5529.3
1465.8
6492.8
5568.5
1036.9
1758.0
5338.6
2145.4
7366.2
2927.8
7635.2
3435.5
5038.3
3679.8
4731.9
4174.0
5284.8
4720.7
5275.7
5120.2
5663.7
5183.9
5293.0
5989.8
5422.0
2908.4
4557.4
2702.8
4660.6
2523.8
5328.9
2446.4
5733.0
2508.4
6115.3
2450.7
5834.5
2665.4
6288.1
2588.9
6018.5
2480.8
5902.0
2506.9
5002.5
2688.8
4992.8
3143.5
4837.8
3315.6
5340.7
3703.5
4665.5
3569.6
4779.3
3587.1
4478.2
4157.1
3859.6
2511.4
3763.8
2517.2
5037.3
2543.7
5308.0
2557.7
6262.6
2497.1
5360.0
2510.4
5735.2
2507.6
5476.8
2508.5
5971.5
2506.4
5387.4
2522.2
5266.4
2460.7
5944.7
2540.4
5033.1
2508.2
4404.4
2523.9
3333.5
Table 1: Full results table
Drivetrain (kNm)
T1
T2
183.3
269.6
159.5
347.8
164.6
327.6
181.0
309.2
182.5
331.3
291.9
5323.0
188.5
281.6
178.9
254.8
181.5
291.3
181.6
301.9
180.0
282.7
180.9
302.3
177.4
344.2
167.7
381.2
160.7
355.2
150.7
366.1
197.3
244.5
195.9
233.6
190.1
232.9
193.9
251.5
186.4
252.7
178.1
286.8
174.1
294.2
175.7
328.4
176.0
339.3
180.0
332.3
172.7
279.6
188.1
292.3
185.4
267.1
181.0
287.3
170.0
303.7
157.7
269.1
145.9
255.9
182.7
303.6
180.0
425.5
181.4
397.9
183.0
306.8
183.2
265.3
182.0
282.9
182.0
278.8
182.7
277.1
181.8
294.0
182.1
294.0
182.0
308.8
181.5
324.9
181.2
328.9
182.4
308.5
Yaw My
T1
1083.6
915.0
925.2
988.3
1021.6
1666.6
1062.4
1072.9
1050.7
1039.3
1013.6
973.7
928.8
888.7
858.6
852.2
1085.8
1063.0
1076.3
1082.2
1078.1
1074.4
1060.8
1019.6
993.1
975.4
953.8
931.0
913.6
871.9
859.9
846.3
812.0
1082.3
1080.8
1082.9
1081.3
1080.8
1081.7
1081.1
1081.9
1081.1
1079.2
1081.0
1081.0
1079.5
1080.8
(kNm)
T2
1856.9
1519.2
1484.6
1812.6
1715.1
1041.4
1642.1
1639.4
1733.7
1503.3
1641.8
1533.6
1509.7
1608.3
1396.3
1470.8
1548.4
1644.4
1761.2
1944.8
1804.4
1766.1
1571.3
1704.2
1540.5
1466.2
1489.2
1443.2
1466.6
1533.3
1443.1
1485.5
1519.0
1550.1
1561.8
1673.3
1658.9
1757.8
1819.6
1820.1
1695.8
1649.8
1596.7
1554.0
1493.3
1399.7
1147.4
Yaw Mz
T1
1121.6
913.8
949.8
982.3
1005.2
2043.5
1079.8
1107.4
1134.4
1120.4
1121.8
1095.9
1046.0
980.6
947.2
899.2
1078.6
1089.3
1108.1
1130.6
1136.4
1094.6
1082.5
1035.5
1000.2
966.0
922.6
895.0
859.5
826.3
778.9
755.0
704.6
1114.0
1116.0
1115.8
1117.7
1122.1
1123.2
1122.9
1123.0
1124.3
1122.0
1110.8
1117.6
1115.4
1117.7
1873.8
1871.1
1676.2
1698.2
1551.5
1675.3
1771.4
1721.3
1756.4
1701.3
1829.6
1815.6
1789.5
1845.2
1701.6
1814.5
1667.6
1655.4
1695.6
1630.0
1841.3
1829.0
1731.2
1847.7
1840.8
1928.3
1782.3
1571.5
1496.6
2195.6
1958.4
1865.8
1873.8
1875.7
1926.9
1893.5
1841.0
1728.5
1652.9
1515.1
1386.9
(kNm)
T2
1829.2
1535.1
1798.7
1700.9
1840.4
ICOWES2013 Conference
17-19 June 2013, Lyngby
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