1) The document discusses numerical modeling of power losses in large wind farms due to turbine wakes. Large-eddy simulation (LES) coupled with actuator disk models are used to model turbine wakes. 2) Validation studies of the numerical models are needed using data from offshore wind farms, wind tunnels, and field experiments. Remote sensing tools like LIDAR are important for obtaining field measurements. 3) The case study uses LES with an actuator disk model that considers turbine rotation (ADM-R) to simulate turbine wakes in the Horns Rev offshore wind farm and predict overall farm power output with good agreement with observed data.

1. 大型風力發電廠之發電效率分析與預測
吳毓庭 Wu Yu-Ting
國立成功大學工程科學系
Dept. of Engineering Science
National Cheng Kung University
Taken in the EPFL WIRE wind tunnel

2. Horns Rev I offshore wind farm

5. Horns Rev I offshore wind farm
Horns Rev II offshore wind farm
1 km
2 km

6. 1 km
1 km
Nysted offshore wind farm
Lillgrund offshore wind farm

7. One big issue- power deficits
1 km

8. Introduction
 In a large wind farm, the power losses due to turbine wakes are influenced by
[1] Inflow condition: wind direction, wind speed, turbulence intensity, turbulent stress
[2] Wind turbine design: blade geometry, generator efficiency
[3] Wind farm layout: turbine spacing, turbine siting density
 Accurate numerical prediction can provide insight into the characteristics of turbine
wakes and power losses in a large wind farm.
 Challenges include turbulence modeling and turbine parameterization
 LES + actuator-disk models: Jimenez et al (2007, 2008, 2010), Ivanell et al (2009), Calaf et al (2010,
2011), Meyers and Meneveau (2011, 2013)
[1] Turbulence modeling: large-eddy simulation (LES) technique
[2] Turbine parameterizations: actuator-disk/-line/-surface models
Porté-Agel et al (2000), Bou-Zeid et al (2005), Stoll and Porté-Agel (2006), Lu and Porté-Agel (2010, 2013)
Sørensen and Kock (1995), Sørensen and Shen (2002), Shen et al (2009)
8
 Rigorous validation studies for turbine wakes in turbulent boundary layer are needed

9. Rough terrain
(forest)
Less rough
(prairie)
Smooth surface
(sea surface)
Wu and Porté-Agel (2012)

10. Rough terrain
(forest)
Less rough
(prairie)
Smooth surface
(sea surface)
Wu and Porté-Agel (2012)
How far the downstream turbines should be installed

11. Solution
Numerical modelling
Laboratory experiment Field campaign

12. Wind tunnel facility
►28 m × 2.57m × 2 m test section
►25 m/s (90 km/h) maximum velocity
► < 0.1 % free stream turbulence intensity
► 5:1 contraction ratio
► 130 kW fan power
► 16 levels of air temperature control
► 20 m floor temperature control (test section)
►[−10°C ; 120°C] air/floor temperature range
► 450 kW heating and cooling units

13. Wind tunnel facility

17. Wind measurements
Meteorological Masts
Remote-sensing Measurements (e.g., LIDAR, SODAR)
17

18. Meteorological Masts
18

19. 台電離岸式測風塔
19

21. 海氣象觀測塔設備
氣象儀器
儀器
項目
風速計 風向計 大氣壓力計 溫溼度計 雨量計 日輻射儀
廠牌-型號
Thies
4.3351.10.000
Thies
4.3150.10.400
Thies
3.1157.10.000
Driesen+Kern Gmbh
DKRF400
Campbell
TE525MM
Kipp&Zonen
CNR4
規格
範圍 0.3~70 m/s 0~360° 300~1100 mb
-40~+80°C
0~100% RH
4.73 ml/tip
300 to 2800 nm
4.5 to 42 μm
解析度
0.05 m wind
run
0.1° 0.01hPa
0.01°C
0.05%
0.1 mm/tip 0.01 w/m2
精度 < 0.2 m/s 1° ± 0.25 hPa
±0.3°C
±1.8%RH
±1% <1%
安裝於塔架
位置(數量)
EL+95m(2)
EL+50m(1)
EL+30m(1)
EL+10m(1)
EL+95m(1)
EL+50m(1)
EL+30m(1)
EL+10m(1)
EL+95m(1)
EL+10m(1)
EL+95m(1)
EL+10m(1)
EL+10m(1) EL+19m(1)

22. 22

23. LIDAR(光達)
• LIDAR: Light Detection And Ranging
23
3D scanning LIDAR
Galion HALO Photonics WindCube

24. LIDAR(光達)
• HALO Photonics 3D scanning LIDAR
24

25. LIDAR(光達)
• LIDAR: Light Detection And Ranging
25
Profiling LIDAR

26. Light Doppler shift
𝜆 − 𝜆0
𝜆0
=
𝑣
𝑐
𝜆 = Observed wavelength
𝑣 = Emitted velocity of light source
𝑐 = Speed of light
𝜆0= Rest emitted wavelength
Eq:
Observer
Source

27. WindSentinel
 Floating LiDAR device by AXYS
 Buoy System (Vindicator,
Anemometers, Solar Panels,
Turbines, Batteries, etc)
 Vindicator by OADS (Optical Air
Data Systems )

28. WindSentinel
RM YOUNG
Wind Wind Sensor 3.72mZephyr Airdolphin Turbine
SANYO Solar Panels
VectorAnemometer 3.45m
Vector Wind Vane 3.36m
Temperature RH
Vindicator
55m
71m
90m
110m
150m
200m
= deg
R 53.6m
R40.2m
R 29.5m
R 24.1m
R 19.0m
R 14.7m
R
LiDAR
Vindicator has three laser beams shooting simultaneously

29. WindSentinel
𝑈 𝑅1(𝛼1)
𝑈 𝑅2(𝛼2)𝑈 𝑅3(𝛼3)
Buoy
LIDAR
𝑢
𝑣
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3
=
sin 𝛼1 cos 𝛼1 1
sin 𝛼2 cos 𝛼2 1
sin 𝛼3 cos 𝛼3 1
sin 𝛽 0 0
0 sin 𝛽 0
0 0 cos 𝛽
𝑢
𝑣
𝑤
⟹
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3
= 𝐵
𝑢
𝑣
𝑤
⟹ 𝒖 𝒐𝒃𝒔 =
𝑢
𝑣
𝑤
= 𝐵−1
𝑈 𝑅1
𝑈 𝑅2
𝑈 𝑅3

30. WindSentinel
Gyroscope
 Angles: Pitch(𝜃), Roll(𝜙), Yaw(𝜓)
 Angular speeds: Pitch( ሶ𝜃), Roll( ሶ𝜙), Yaw( ሶ𝜓)
𝑼 = 𝑻 𝒖 𝒐𝒃𝒔 + 𝛀 𝒐𝒃𝒔 × 𝑹 + 𝒖 𝒔𝒉𝒊𝒑
Motion correction(compensation) scheme (Edson et al, 1998)
𝑼 = 𝑈, 𝑉, 𝑊 : wind speed vector in the earth’s coordinate
𝑻: transformation matrix for a rotation of the ship coordinate to the earth’s coordinate
𝛀 𝒐𝒃𝒔: angular velocity vector of the ship coordinate system
𝑹: position vector of the wind measurement location with respect to the motion package
𝒖 𝒔𝒉𝒊𝒑: translational velocity vector of the ship with respect to the earth’s coordinate
𝒖 𝒐𝒃𝒔 = 𝒖, 𝒗, 𝒘 : observed wind speed with respect to the ship coordinate

31. Motion correction scheme
𝑼 = 𝑻 𝒖 𝒐𝒃𝒔 + 𝛀 𝒐𝒃𝒔 × 𝑹 + 𝒖 𝒔𝒉𝒊𝒑
𝑻 =
cos 𝝍 sin 𝝍 𝟎
−sin 𝝍 cos 𝝍 𝟎
𝟎 𝟎
𝒀𝒂𝒘
cos 𝜽 𝟎 sin 𝜽
𝟎 𝟎
− sin 𝜽 𝟎 cos 𝜽
𝑷𝒊𝒕𝒄𝒉
𝟎 𝟎
𝟎 cos 𝝓 − sin 𝝓
𝟎 sin 𝝓 cos 𝝓
𝑹𝒐𝒍𝒍
𝒖 𝒐𝒃𝒔 =
𝒖
𝒗
𝒘
𝛀 𝒐𝒃𝒔 =
ሶ𝝓
ሶ𝜽
ሶ𝝍
𝑹 =
𝟎
𝟎
𝒛𝒍𝒊𝒅𝒂𝒓

32. Large-eddy simulation framework
𝜕෤𝑢𝑖
𝜕𝑥𝑖
= 0
𝜕෤𝑢𝑖
𝜕𝑡
+ ෤𝑢𝑗
𝜕෤𝑢𝑖
𝜕𝑥𝑗
−
𝜕෤𝑢𝑗
𝜕𝑥𝑖
= −
𝜕 ෤𝑝∗
𝜕𝑥𝑖
−
𝜕𝜏𝑖𝑗
𝜕𝑥𝑖
+ 𝜈
𝜕2 ෤𝑢𝑖
𝜕𝑥𝑗
2 −
𝑓𝑖
𝜌
+ 𝛿𝑖1 𝐹𝑝
: air kinematic viscosity
: modified pressure
: resolved (filtered) velocity
: a filter scale (Δ)~
෤𝑢𝑖
෤𝑝∗
𝜈
: subgrid-scale (SGS) stress
: turbine-induced body forces
: constant pressure gradient𝐹𝑝
𝜏𝑖𝑗
𝑓i

33. Lagrangian scale-dependent dynamic model
𝜏𝑖𝑗 − 1
3
𝛿 𝑖𝑗 𝜏 𝑘𝑘
= −2 Δ2 𝐶𝑆
2
Δ ሚ𝑆 ሚ𝑆ij
𝐶𝑆
2
Δ =
𝐿𝑖𝑗 𝑀𝑖𝑗 𝐿
𝑀𝑖𝑗 𝑀𝑖𝑗 𝐿
=
𝑄𝑖𝑗 𝑁𝑖𝑗 𝐿
𝑁𝑖𝑗 𝑁𝑖𝑗 𝐿
■ Traditional Smagorinsky model
̶ Smagorinsky coefficient
→ dynamically compute based on the flow information
Refs: Porté-Agel et al (2000); Stoll and Porté-Agel (2006)
z/dz/d
x/d
x/d
𝐶𝑆
𝐶𝑆
Wu and Porté-Agel (2011)
Wu and Porté-Agel (2013)
33

34. Ω
• Blade element theory
Δr
c : chord length
Blade Element
Vrel : relative velocity
Vx
: velocity at the rotor
Ω : angular velocity
α : angle of attack
γ : twist angle
projection
Total (shaft) Torque: 𝑄 = σ 𝐹𝜃 ∙ 𝑟
Rotor Power: 𝑃𝑅 = 𝑄 ∙ Ω
Power Output: 𝑃𝑂 = 𝑃𝑅 ∙ 𝜂
Ω r-V θ =Ω r(1+a’)
L
D
Fx
Fθ θ
α
φ
γ
F
Vx = u(1-a)~
x
r
θ
x
c
Δr
Actuator-disk model with rotation (ADM-R)
34

35. ADM-NR ADM-R
Uniform distribution of thrust
No considering rotation effect
Integrating thrust force over time
Non-uniform distribution of thrust
Considering rotation effect
Integrating the forces over time
Actuator-disk model without rotation Actuator-disk model with rotation
Jimenez et al (2007; 2008)
Calaf et al (2010; 2011)
Wu & Porté-Agel (2011, 2013)
Sørensen & Kock (1995)
Kasmi & Masson (2008)
Wu & Porté-Agel (2011, 2013)
Blade element theory1D momentum theory
Actuator-disk models (ADM)
ADM-R cannot predict Ω and P
Dynamic procedure:
[1] Calculate 𝑉𝑥 and 𝑉𝜃;
[2] Guess an initial value for Ω 𝑜
;
[3] Calculate the shaft torque Q
using the ADM-R;
[4] Calculate the new Ω 𝑛
based on
the torque-speed relationship;
[5] Calculate 𝜖 𝑡𝑜𝑙 = 1 − ΤΩ 𝑜
Ω 𝑛
;
[6] Replace Ω 𝑜
with Ω 𝑛
[7] Return to [3] until 𝜖 𝑡𝑜𝑙 < 0.01;
[8] Compute the forces and power
Ω r-V θ =Ω r(1+a’)
L
D
Fx
Fθ θ
α
φ
γ
F
Vx = u(1-a)~
x
r
θ
x
c
Δr
ADM-NR requires 𝑪 𝑻 and 𝑪 𝒑 35

36. Model validation
Horns Rev offshore wind farm
(Wu and Porte-Agel, 2015)
A model wind farm in ABL wind tunnel (Wu and Porte-Agel, 2013)

37. U [m s-1]
LES+ADM-R
37
Grid number: 𝟔𝟒𝟎 × 𝟔𝟒𝟎 × 𝟐𝟖
CPU cores: 256 cores
Computational time: 24 hours
Simulation time: 80 mins
LES of turbine wakes in the Horns Rev offshore wind farm

38. Model validation: farm power prediction
Horns Rev offshore wind farm
 Wind farm area : 20 [km2]
 80 Vestas V80 2MW wind turbines
 Total wind farm output: 160 MW
 Cut-in wind speed: 4 [m s-1]
 Cut-out wind speed: 25 [m s-1]
 Constant CT for wind speed < 10 [m s-1]
 Rotor diameter (d) = 80 [m]
 Turbine hub height (HHUB) = 70 [m]
 Three masts around the farm
5 8 11 14 17 20
0
0.5
1
1.5
2
Power[MW]
Wind Speed [ms-1
]
5 8 11 14 17 20
0
0.25
0.5
0.75
1
ThrustCoefficient
Measured Power
Manufacturers CT
(Hansen et al, 2012)
From: Fredy Rodriguez @ http://vimeo.com/28745771
38

39. U [m s-1]
Yaw misalignment is ignored in the sorting of the observed power data, which can cause an overestimation on the
power output of downstream turbines in a narrow full wake condition (e.g. 270o±1o).
Lines: simulated power
Symbols: measured power
Power prediction for different wind sectors

40. Time-averaged streamwise velocity

41. Streamwise turbulence intensity

43. Case Circles 1st circle 2nd circle 3rd circle 4th circle
Turbines Radius Turbines Radius Turbines Radius Turbines Radius
Case 1 1 80 31.23 d
Case 2 2 60 31.23 d 20 10.41 d
Case 3 3 44 31.23 d 28 18.74 d 8 6.25 d
Case 4 4 36 31.23 d 24 21.86 d 16 13.43d 4 4.37 d
Wind farm Horns Rev I Case 1 Case 2 Case 3 Case 4
Efficiency (%) 82.4 78.6 79.6 81.5 81.3

44. Simulations of large wind farms
44
𝐿 𝑥 = 24,000 𝑚 = 300 𝑑
𝐿 𝑦 = 1,200 𝑚 = 15 𝑑
𝐿 𝑧 = 996.8 𝑚 = 12.5 𝑑
120 wind turbines are sited in the simulations
𝑁𝑥 = 1,200
𝑁 𝑦 = 192
𝑁𝑧 = 160

45. Inflow condition
45
A constant pressure gradient is specified up to 800 m to drive the boundary-layer flow
Surface characteristics: 𝑢∗ = 0.488 𝑚/𝑠 and 𝑧0 = 0.05 𝑚
Wind speed at hub: 9.3 𝑚/𝑠

46. Turbine model
46
 Vestas V80 2MW
 Rotor diameter:80 m
 Constant CT for wind speed < 10 [m s-1]
Ref: Wu & Porté-Agel (2015),
Renewable energy

47. Simulated power output
47
0.50
0.55
0.60
0.65
0.70
0.75
0.80
WF1 WF2 WF3 WF4 WF5 WF6 WF7 WF8
Average Power (1-10) Average Power (11-20) Average Power (21-30) Average Power (1-30)

49. Averaged streamwise velocity
49

51. Published: Wu et al, Renewable Energy, 2019

52. Lu & Porté-Agel (2011)
Thanks for your attention
Q&A