The power generation of a wind farm is significantly less than the summation of the power generated by each turbine when operating as a standalone entity. This power reduction can be attributed to the energy loss due to the wake effects − the resulting velocity deficit in the wind downstream of a turbine. In the case of wind farm design, the wake losses are generally quantified using wake models. The effectiveness of wind farm design (seeking to maximize the farm output) therefore depends on the accuracy and the reliability of the wake models. This paper compares the impact of the following four analytical wake models on the wind farm power generation: (i) the Jensen model, (ii) the Larsen model, (iii) the Frandsen model, and (iv) the Ishihara model. The sensitivity of this impact to the Land Area per Turbine (LAT) and the incoming wind speed is also investigated. The wind farm power generation model used in this paper is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) methodology. Single wake case studies show that the velocity deficit and the wake diameter estimated by the different analytical wake models can be significantly different. A maximum difference of 70% was also observed for the wind farm capacity factor values estimated using different wake models.

1. Impact of Different Wake Models on the Estimation
of Wind Farm Power Generation
Weiyang Tong*, Souma Chowdhury#, Jie Zhang#, and Achille Messac*
# Syracuse University, Department of Mechanical and Aerospace Engineering
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
17 - 19 Sep 2012
Indianapolis, Indiana

2. Introduction
2
Factors affecting Wind
Farm Power Generation
Environmental
Conditions
Wind speed
Mean Wind
Speed
Turbulence
Wind
direction
Air density
Farm Design
Turbine
features
Rotor
diameter
Hub height
Rated
capacity
Farm layout
Land
configuration
Wind Farm Power Generation

3. 3
Denmark's Horns Rev 1 wind farm
 Two major impacts:
 Power loss due to the reduction of speed downstream from turbines
 Reduction of turbine lifetime due to increased turbulence-induced structural load
 The power loss due to the wake effects is generally evaluated using wake models
 Computational (CFD-based) wake models
 Analytical wake models
Wake Effects

4. Factors Regulating Wake Effects
Wake
Effects
Wind speed
Topography
Ambient
turbulence
Turbine
features
Land
configuration
• Land area
• Land shape
4

5. Motivation
5
Wind farm power generation is a complex function of the
incoming wind conditions, the farm layout and the turbine
features
• Wake model is used to compute the flow characteristics inside
the farm
The effectiveness of the estimated wind farm power
generation primarily depends on the accuracy of the
wake model in estimating
• Wake speed
• Wake diameter
The sensitivity of the farm power generation to the
wake model predictions also depends on key
parameters
• Incoming wind speed
• Land area per turbine or per MW installed

6. Research Objectives
6
Investigate and compare the impact of different wake models
on the power generated by an array of turbines.
Investigate the sensitivity of this impact to the Land Area per
Turbine (LAT) and the incoming wind speed.

7. Outline
• Standard Wake Models
• Power Generation Modeling
• Comparing Wake Models: Single Wake Test
• Numerical Experiments
• Capacity factor variation with the Land Area per Turbine
• Capacity factor variation with the incoming wind speed
• Concluding Remarks & Future Work
7

8. Wake Models
8
General inputs and outputs of an analytical wake model
Trujillo, 2005
The wake is fully developed as the shear layer reaches the centerline, i.e., a far wake is
considered in this paper.
Incoming wind speed
Rotor diameter
Hub height
Downstream distance
Radial distance
Ambien turbulence
Near Wake
(2D ~ 5D)
Far Wake

9. Layout-based Power Generation Model
UWFLO
framework
Wind Distribution
Model
Power Generation
Model
Wind Farm Cost
Model
Optimization
Methodology
9
We use the Power Generation Model developed in the
Unrestricted Wind Farm Layout Optimization (UWFLO) methodology*
*: Chowdhury et al , 2011

10. Attributes of Major Analytical Wake Models
10
Wake
model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub
height
Turbulence
intensity
Jensen’s √ √ √ √
Frandsen’s √ √ √ √
Larsen’s √ √ √ √ √ √ √
Ishihara’s √ √ √ √ √ √
 A GE 2.5MW-100m/100m turbine is selected for the
single wake test for each wake model.
 The incoming wind over the rotor area is assumed to
be constant and uniformly distributed; the turbulence
intensity is 10% (onshore*).
 Single wake simulation starts from 2D downstream
distance (far wake)
Inputs to each wake model
*: Mittal, 2011
Specifications Values
Rotor diameter 100 m
Hub height 100 m
Cut-in 3 m/s
Cut-out 25 m/s
Rated speed 12.5 m/s
Wake
model
Jensen’s
Frandsen’s
Larsen’s
Ishihara’s
Far wake

11. 11
Wake expansion,
Velocity deficit,
k: Wake decaying constant
s: Normalized downstream distance from the turbine
CT: Thrust coefficient
Wake model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub
height
Turbulence
intensity
Jensen’s √ √ √ √
Frandsen’s √ √ √ √
Larsen’s √ √ √ √ √ √ √
Ishihara’s √ √ √ √ √ √
Single Wake Test: Jensen Model

12. 12
Wake expansion,
Velocity deficit*,
𝛼: Initial wake expansion
𝛽: Wake expansion parameter given by
Deff: Effective rotor diameter
*: “+” applies when a ≤ 0.5; “-” applies when a > 0.5.
Wake model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub
height
Turbulence
intensity
Jensen’s √ √ √ √
Frandsen’s √ √ √ √
Larsen’s √ √ √ √ √ √ √
Ishihara’s √ √ √ √ √ √
Single Wake Test: Frandsen Model

13. 13
Wake expansion,
where constants c1 and x0 are given by,
Velocity deficit,
Wake model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub
height
Turbulence
intensity
Jensen’s √ √ √ √
Frandsen’s √ √ √ √
Larsen’s √ √ √ √ √ √ √
Ishihara’s √ √ √ √ √ √
Single Wake Test: Larsen Model
Wake radius at a relative distance of 9.5D
Ground Effect

14. 14
Wake expansion,
Velocity deficit,
p is a function related to the turbulence intensity,
Iw is the turbine-generated turbulence intensity,
Wake model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub
height
Turbulence
intensity
Jensen’s √ √ √ √
Frandsen’s √ √ √ √
Larsen’s √ √ √ √ √ √ √
Ishihara’s √ √ √ √ √ √
Single Wake Test: Ishihara Model
k1, k2, and k3 are respectively set to 0.27, 6.0, and 0.004

15. 15
Single Wake Test: Comparing Wake Growth
 Frandsen model and Larsen model predict
greater wake diameters
 Jensen model has a linear expansion
 The difference between wake diameters
predicted by each model can be as large as
3D, and it can be larger as the downstream
distance increases
3D

16. 16
Single Wake Test: Comparing Wake Speed
 Frandsen model predicts the highest
wake speed
 Ishihara model predicts a relatively
low wake speed; however, as the
downstream distance increases, the
wake recovers fast owing to the
consideration of turbine induced
turbulence in this model

17. Numerical Experiments
17
 An array-like wind farm with 9 GE 2.5 MW turbines is considered.
 A fixed aspect ratio of 7/3 is chosen for the investigation; the downstream spacing
is ranged from 5D to 20D, while the lateral spacing is no less than 2D.
 The farm capacity factor is given by
Prj: Rated capacity, Pfarm: Farm output
The Land Area per MW Installed (LAMI) is specified as
Therefore, the Land Area per Turbine (LAT) can be given by
wind
direction

18. Capacity Factor variation with the Land Area per Turbine
18
Incoming wind speed = 4 m/s
Turbine Power Curve
Cut-in speed: 3 m/s
0
0.2
0.4
0.6
0.8
1
1st Row 2nd Row 3rd Row
POWER TREND

19. 19
Incoming wind speed = 8 m/sIncoming wind speed = 12.5 m/s
Capacity Factor variation with the Land Area per Turbine
Rated speed: 12.5 m/s
Turbine Power Curve
0
0.2
0.4
0.6
0.8
1
1st Row 2nd Row 3rd Row
POWER TREND

20. Turbine Power Curve
20
Incoming wind speed = 16 m/sIncoming wind speed = 20 m/sIncoming wind speed = 24 m/s
Capacity Factor variation with the Land Area per Turbine
0
0.2
0.4
0.6
0.8
1
1st Row 2nd Row 3rd Row
POWER TREND

21. 21
Capacity Factor variation with the Incoming Wind Speed
LAT = 15 ha
Single wake test

22. 22
Capacity Factor variation with the Incoming Wind Speed
LAT = 20 ha
Single wake test

23. 23
Capacity Factor variation with the Incoming Wind Speed
LAT = 25 ha
Single wake test

24. Single wake test
24
Capacity Factor variation with the Incoming Wind Speed
LAT = 30 ha

25. Concluding Remarks & Future Work
 The impact of different wake models on the estimation of wind farm power
generation was investigated.
 The sensitivity of using different wake models to the Land Area per Turbine (LAT)
and the incoming wind speed was also investigated.
 A significant difference was observed: in general, Frandsen and Larsen wake models
estimate greater wake diameters, and Frandsen and Jenson wake models estimate
lower wake velocity deficits.
 The maximum difference in the farm capacity factor predicted by different wake
models was as high as 70%.
 Future research can explore the effect of farm-land shape on the wind farm power
generation, when using different wake models.
25

26. Acknowledgement
• I would like to acknowledge my research adviser
Prof. Achille Messac for his immense help and
support in this research.
• I would also like to thank my colleagues Souma
Chowdhury and Jie Zhang for their valuable
contributions to this paper.
• Support from the NSF Awards is also
acknowledged.
26

27. Questions
and
Comments
Thank you

28. 28
Layout-based Power Generation Model
This model quantifies the wind farm power generation as a function of
incoming wind speed, farm layout, and turbine features.
 Transformed co-ordinates are evaluated based on wind direction.
 The turbines are ranked in the increasing order of their x-coordinate.
wind
direction
I II III
x
y
0

29. 29
Layout-based Power Generation Model
 In this power generation model, the induction factor is treated as a
function of the incoming wind speed and turbine features:
U: incoming wind speed; P: power generated, given by the power curve
kg, kb: mechanical and electrical efficiencies, Dj: Rotor Diameter, 𝜌: Air density
 A generalized power curve is used to represent the approximate power
response of a particular turbine
𝑈𝑖𝑛, 𝑈 𝑜𝑢𝑡, and 𝑈𝑟: cut-in speed, cut-out speed, and rated speed
𝑃𝑟: Rated capacity, 𝑃𝑛: Polynomial fit for the generalized power curve*
*: Chowdhury et al , 2011

30. 30
Layout-based Power Generation Model
 Turbine-j is in the influence of the wake of Turbine-i, if and only if
Considers turbines with differing rotor-diameters and hub-heights
 The Katic’s model* is used to account for wake merging and partial wake
overlap
𝑢𝑗: Effective velocity deficit
𝐴 𝑘𝑗: Overlapping area between Turbine-j
and Turbine-k
Partial wake-rotor overlap *: Katic et al , 1987

31. AR = 8/3
31

32. AR = 8/3
32

33. Turbine Power Curve
70%
33
Incoming wind speed = 16 m/sIncoming wind speed = 20 m/sIncoming wind speed = 24 m/s
Capacity Factor variation with the Land Area per Turbine
0
0.2
0.4
0.6
0.8
1
1st Row 2nd Row 3rd Row
POWER TREND