High-ﬁdelity simulation comparison of wake …pietergebraad/docs/ICOWEShigh...ICOWES2013 Conference 17-19 June 2013, Lyngby High-ﬁdelity simulation comparison of wake mitigation

ICOWES2013 Conference 17-19 June 2013, Lyngby

High-fidelity simulation comparison of wake mitigation controlstrategies 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

1National Renewable Energy Laboratory, Golden CO, USA, [email protected] University of Technology, Delft, The Netherlands, [email protected]

3Boeing Commercial Airplanes, Seattle WA

Abstract

Wind turbines arranged in a wind plant impact each other through their wakes. Wind plantcontrol is an active research field that attempts to improve wind plant performance by mod-ifying 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 toinvestigate the potential of several wake mitigation strategies. The strategies, includingmodification of yaw and tilt angle, as well as repositioning of the downstream turbine, rep-resent a mix of known and novel approaches. The simulation results are compared throughchange relative to a baseline operation in terms of overall power capture and loading on theupstream and downstream turbine.

1 Introduction

Wind turbines influence nearby turbines aerodynamically as they extract energy from and en-hance turbulence in the wind. Recently, wind turbine control systems researchers examinedhow these influences can be accounted for and adjusted such that increased wind power plantefficiency and reduced turbine loads can be obtained. Often in the literature, this is done byadapting the axial induction of individual turbines through pitch and torque control, [1, 2, 3]. Inthese methods, an axial induction factor is found that results in lower individual turbine powerfor an upstream tower, but higher plant power due to increased power capture by downstreamturbines.

An alternative approach to wind plant control focuses instead on redirecting wakes around down-stream turbines. One method of achieving this redirection that has been published in the litera-ture is through intentional yaw misalignment in an upstream turbine. In [4] field-tests are carriedout in a scaled wind plant test field, whereas in [5], computational fluid-dynamics (CFD) simu-lations 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 windplant control using a high-fidelity wind plant simulator, the NREL SOWFA (Simulator forOff/Onshore Wind Farm Applications) tool [6]. SOWFA, described in Section 2, couples a com-putational fluid dynamics (CFD) solver with the aero-elastic turbine simulator FAST [7]. UsingSOWFA, controllers can be compared in terms of their effects on power production and loadingof upstream and downstream turbines. This is an important capability since a controller’s effectson power production must be weighed against its effects on turbine loads.

In addition to evaluating the yaw misalignment method, we also introduce two additional con-cepts. First, we modify the tilt angle of an upstream turbine in order to redirect the wake ver-tically. The second method does not redirect the wake but instead repositions the downstreamturbine (in the case of floating turbines), as proposed in [8]. Additional analysis of the yaw andtilt methods can be found in [9], which analyzes the ability of a single turbine to redirect thewake.

The control methods are evaluated using a simulation of two 5MW turbines, 7 rotor diametersapart, aligned in a turbulent inflow. For each method, the setpoint (yaw misalignment angle, tiltangle or downstream turbine position) is varied, and a 1000 second simulation is run. Addi-tionally, because these techniques might move the downstream turbine from full wake to partialwake, which induces loading [10], we consider the cases where the downstream turbine is andisn’t using independent pitch control (IPC) to mitigate uneven distribution of wind speed acrossthe rotor plane. The results are compared in terms of total power output and key componentloads 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 windplant control, using adaptation of the rotor tilt angle (with [9]), (2) an analysis and comparisonof three methods of wind-plant wake mitigation using a high-fidelity simulator in terms of powerand loading of an upstream and downstream turbine, and (3) an investigation into the use of IPCfor mitigating the effects of partial wake on turbine loads.

The remainder of this paper is organized as follows. Section 2 provides an overview of thesimulation tool SOWFA used in this work. Section 3 provides a description of the simulationscenario 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 discussionpoints 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 usinga high-fidelity tool: Simulator for Off/Onshore Wind Farm Applications (SOWFA) [6] whichis 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 ofthe LES framework is based on open-source OpenFOAM libraries [11] which solves the in-

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compressible Navier-Stokes equations augmented with a buoyancy term (based on Boussinesqapproximation) and Coriolis acceleration to simulate atmospheric boundary layers under variousconditions. 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 sec-ond order central differencing scheme. The collocated formulation of the velocity and pressurevariables is decoupled using the Rhie-Chow [12] interpolation method to avoid numerical insta-bility. The time advancement method follows the predictor-corrector pressure-implicit splittingoperation (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-gridscale (SGS) turbulence closure employs the standard Smagorinsky [15] formulation with a con-stant 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 com-puted based on the incoming flow and the airfoil geometry at the actuator points. These forcevectors are projected on to the computational domain space using a three-dimensional Gaussianfilter which, as a collective whole, produce the wake structures similar to those from blade-geometry resolved simulations at significantly reduced computational cost. In SOWFA, theincoming flow velocity data at the actuator points from the flow solver are fed into FAST, fromwhich the computed aerodynamic lift and drag forces and the shifted actuator points (caused bythe blade deflections) are projected on to the momentum equation as a body force term complet-ing the two-way coupling cycle. The structural loading responses induced by the aerodynamicforces are collected as FAST outputs which are later presented in this study. Further details onSOWFA can be found in [17].

With SOWFA, simulations of proposed wind plant control schemes can be analyzed. Becausethe simulation includes high-fidelity modeling of the atmosphere, and the turbine structure, it ispossible 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 wakemitigation (yaw-misalignment based, tilt-misalignment based and repositioning of the down-stream turbine) using SOWFA. To this end, an “open-loop” two-turbine simulation study is per-formed in which the yaw, tilt, and position setpoints are swept and held fixed for separate 1000second simulations with constant wind direction. Later research will develop active closed-loopcontrol strategies for time-varying wind directions.

A scenario was developed to simulate two NREL 5-MW baseline turbines [18] in turbulent in-flow. The turbulent scenario is that of a neutral boundary layer, selected based on a previouslypublished study. [17] The inflow is generated in a precursor atmospheric LES on a domain thatis 3 km by 3 km in the horizontal and 1 km in height. The horizontally-averaged wind speed isdriven 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 turbulentstructures in the surface layer are not ”trapped” by the periodic boundaries, continually cyclingthrough in the same location. In the baseline case, the turbine rotor axis is aligned with the winddirection. The surface temperature flux is set to zero, although a capping inversion initially at750 m above the surface is used both to slow boundary layer growth and because it is a realfeature 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 thedomain are given in fig. 1.

Screenshots from time averaged slices of the flow for the different control strategies is providedin fig. 2. SOWFA requires significant computational power in order to run high-fidelity sim-ulations: using a sample time of 0.02s, the time steps take an average 2.5s to calculate on theSandia/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. Becausewake redirection can move the downstream turbine from full wake to partial wake, inducingloads [10], we compare the use of IPC with the standard collective pitch control by switchingon load-reducing IPC on the downstream turbine for the last 400s of the simulation. The IPCimplementation is based on the design first presented in [20], using the parameters as specifiedin [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-processedas follows. First the 1000s of time domain data for each was broken into segments. The first200s of each run was discarded since the wake was not fully developed. The last 100s werealso discarded due to system problems on the cluster leaving some files incomplete. Finally, theremaining time histories were divided into 200s-600s, in which the downstream turbine is notrunning IPC, and 700s-900s, when it is and the IPC startup transients have vanished. Although itshould be possible to start IPC smoothly, since the transition was not our research focus we rampit 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 thetower load, a combined load is computed from the separate fore-aft and side-side loads using aroot-sum-square combination. This is likewise done to combine the separate My and Mz loads onthe 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 useIPC. For each method, there is a sweep across possibles setpoint (yaw angle, tilt angle or repo-sition 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 denotingpercent change from the baseline case. The remaining rows of the figure indicate percent changein DEL for the components examined.

Starting with yaw-based control, in the best case the method shows an increase in power of4.6%. 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 bearingmoment. The downstream turbine however experiences a rise in blade OOP bending, drivetraintorsion and yaw bearing moment. This change is most likely due to the movement from full topartial wake overlap.

In the tilt case, a maximum power gain of 7.1% is observed. At this peak of power capture, itis seen that for the upstream turbine, the blade and yaw bearing loads have gone up while thedrivetrain and tower loads have declined a small amount. As in the yaw case, the downstreamturbine experiences an increase in blade loads, most likely due to partial-wake overlap. There isalso a decrease in tower loads and increase in yaw bearing loads.

Tilt misalignment shows larger potential power production improvements than yaw when con-

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Figure 3: Summary of results of two tubine simulation. The 3 columns are divided by controlaction. The top row shows the combined power output for each case, compared to the baselinecase on the far left. The remaining rows indicate the percent change in load compared to thebaseline.

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sidering large positive tilt angles. With a positive tilt angle, the rotor would face downwards, andfor conventional upstream turbine designs this would cause the blades to hit the tower. There-fore, a positive tilting mechanism is more suitable to downwind turbines [24]. Both negativeand positive tilt angles will redirect the wake away from the downstream turbine rotor, but thepositive tilting has the advantage that it will redirect the wake towards the ground, allowing highvelocity air from higher altitudes to flow towards the upper part of the downstream rotor, re-sulting in a higher power production of the downstream turbine. Additional details on the wakedisplacements 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 rotorof the downstream turbine is moved more than 25 meters out of the rotor axis of the upstreamturbine (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 po-sition, significant change for the discplacements yielding partial overlap, and then no changeagain when the turbine is moved a full rotor diameter.

Looking at the loads across experiments, the upstream turbine either sees an increase or decreasein blade OOP bending, depending on the angle chosen. Also, for the upstream turbine, yaw andtilt 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 captureof the upstream turbine, and derating can be considered as a load mitigation strategy. For thedownstream turbine, all loads generally increase somewhat, and this is most likely due to mov-ing from full to partial wake overlap.

Fig. 4 performs the same analysis, but now for the case where the downstream turbine is usingIPC to mitigate the effect of partial wake overlap. Note that these results are based on 200s ofsimulation versus 400s in Fig. 3, and are from a different point in the simulation. The resultsare dramatic: the blade loads, tower loads and yaw bearing loads are consistently reduced whencompared to the baseline case (which does not use IPC). The drivetrain loads are the excep-tion, 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 industrialcontrollers that could be used to minimize the changes in drivetrain loads. Overall, the resultsindicates a very strong motivation for the use of IPC, in general, and as a way to eliminate thenegative 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 computa-tional/time constraints, current results are based on simulations of only one inflow case. Futurework will combine results from simulations using multiple wind inputs and better establish therobustness 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 withIPC in all cases except for the baseline. Note that due to system problems, one case is missingbut 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 inorder to be applicable to real wind plants, future work must establish control loops which canaccomplish similar results for changing wind direction conditions.

6 Conclusions

This report shows very good potential for all methods considered. For each case, operatingpoints exist which couple improved power capture with, mostly, reduced loading. It is importantto 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, perhapsthe effects could be considered in the design of future turbines. A second result of the paperis the very good potential of employing IPC to mitigate partial wake effects. This improves thebenefit of the wake redirection or repositioning techniques by reducing the partial-wake-inducedloads on the downstream turbine.

Acknowledgements

The authors are very grateful to Wesley Jones and the NREL High Performance Computing teamfor 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-AC36-08GO28308 with the National Renewable Energy Laboratory and by the NWO Veni Grant no.11930 Reconfigurable floating wind farm.

References

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[3] J.R. Marden, S.D. Ruben, and L.Y. Pao. Surveying game theoretic approaches for windfarm optimization. In Proceedings of the 50th IEEE Conference on Decision and Control,volume 38, pages 584–596, 2012.

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[6] M. Churchfield and S. Lee. NWTC design codes (SOWFA). http://wind.nrel.gov/designcodes/simulators/SOWFA, 2013.

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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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T abl

e1:

Full

resu

ltsta

ble

Cas

ePo

wer

(MW

)O

OP

Ben

ding

(kN

m)

Driv

etra

in(k

Nm

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re-A

ft(k

Nm

)Si

de-S

ide

(kN

m)

Yaw

My

(kN

m)

Yaw

Mz

(kN

m)

T1

T2

Tota

lT

1T

2T

1T

2T

1T

2T

1T

2T

1T

2T

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1.7

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738.

898

2.5

183.

326

9.6

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589.

425

29.5

5595

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83.6

1856

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21.6

1829

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1ya

w=

-35◦

1.2

1.2

2.4

913.

311

33.9

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7.8

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472.

919

64.4

4244

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5.0

1519

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3.8

1535

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1ya

w=

-30◦

1.3

1.1

2.4

905.

811

52.5

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632

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07.3

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39.2

925.

214

84.6

949.

817

98.7

T1

yaw

=-2

5◦1.

41.

02.

588

6.7

1124

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1.0

309.

255

04.9

1180

3.0

1264

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29.3

988.

318

12.6

982.

317

00.9

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yaw

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0◦1.

50.

92.

587

3.2

1081

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2.5

331.

354

46.8

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0.8

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92.8

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15.1

1005

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40.4

T1

yaw

=-2

0◦0.

92.

584

8.4

1026

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1.5

291.

953

23.0

1202

4.4

1411

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68.5

1036

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66.6

1041

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43.5

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yaw

=-1

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70.

82.

579

8.9

981.

118

8.5

281.

652

21.8

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38.6

1062

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42.1

1079

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73.8

T1

yaw

=-5

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82.

578

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92.6

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1107

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71.1

T1

yaw

=5◦

1.7

0.9

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810

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181.

529

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929

27.8

7635

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50.7

1733

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34.4

1676

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w=

10◦

1.7

1.0

2.6

678.

610

44.4

181.

630

1.9

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934

35.5

5038

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39.3

1503

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20.4

1698

.2T

1ya

w=

15◦

1.6

1.0

2.6

649.

311

05.9

180.

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2.7

5146

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553.

136

79.8

4731

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13.6

1641

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21.8

1551

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1ya

w=

20◦

1.5

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2.7

642.

111

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762.

341

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w=

25◦

1.4

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811

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75.7

928.

815

09.7

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71.4

T1

yaw

=30

◦1.

31.

32.

760

7.6

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7.7

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243

27.6

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5120

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63.7

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716

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980.

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21.3

T1

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660

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1080

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93.0

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947.

217

56.4

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559

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149

65.4

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3.8

5989

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22.0

852.

214

70.8

899.

217

01.3

T1

tilt=

-15◦

1.6

0.9

2.5

620.

290

8.4

197.

324

4.5

5380

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32.7

2908

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57.4

1085

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48.4

1078

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29.6

T1

tilt=

-12◦

1.6

0.9

2.5

645.

591

6.5

195.

923

3.6

5404

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291.

227

02.8

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63.0

1644

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89.3

1815

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1til

t=-9

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70.

92.

565

7.5

967.

019

0.1

232.

956

49.4

1146

7.2

2523

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28.9

1076

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61.2

1108

.117

89.5

T1

tilt=

-6◦

1.7

0.9

2.5

695.

497

0.6

193.

925

1.5

5454

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910.

224

46.4

5733

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82.2

1944

.811

30.6

1845

.2T

1til

t=-3

◦1.

70.

82.

572

2.1

979.

918

6.4

252.

754

53.2

1310

0.4

2508

.461

15.3

1078

.118

04.4

1136

.417

01.6

T1

tilt=

3◦1.

70.

92.

676

0.9

1032

.617

8.1

286.

852

78.6

1202

1.9

2450

.758

34.5

1074

.417

66.1

1094

.618

14.5

T1

tilt=

6◦1.

70.

92.

678

3.4

1043

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4.1

294.

252

37.4

1249

2.4

2665

.462

88.1

1060

.815

71.3

1082

.516

67.6

T1

tilt=

9◦1.

70.

92.

680

3.6

1137

.317

5.7

328.

452

23.9

1235

0.6

2588

.960

18.5

1019

.617

04.2

1035

.516

55.4

T1

tilt=

12◦

1.6

1.0

2.6

806.

612

03.6

176.

033

9.3

5187

.512

808.

024

80.8

5902

.099

3.1

1540

.510

00.2

1695

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t=15

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781

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1489

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2.6

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t=21

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51.

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782

2.3

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9.5

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t=27

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783

1.3

1297

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21.4

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03.5

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1.9

1533

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6.3

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t=30

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31.

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781

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1270

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303.

751

49.2

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69.6

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t=33

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52.

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151

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1485

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05.4

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