This document presents a bi-level framework for visualizing trade-offs in wind farm design between capacity factor and land use. The lower level uses multi-objective optimization to explore the trade-off for different nameplate capacities. The upper level fits curves to pareto solutions to parametrically represent the trade-off as a function of nameplate capacity. A numerical experiment applies the framework to a case study exploring capacity factor and land area per MW installed. The framework aims to streamline wind farm planning by quantifying key design trade-offs.

1. Multi-objective Wind Farm Design
Exploring the Trade-off between Capacity Factor and Land Use
Weiyang Tong, Souma Chowdhury, Ali Mehmani, and Achille Messac
Syracuse University, Department of Mechanical and Aerospace Engineering
10th World Congress on Structural and Multidisciplinary Optimization
May 19-24, 2013, Orlando, Florida

2. Wind Farm Development
2
 Wind farm development is an extremely complex process that is affected by
several performance objectives (energy production and cost, etc.)
 Most of these factors are strongly coupled in the influence on the performance
objectives
Factors affecting wind
farm performance
Natural factors
(uncontrollable)
Wind shear
Wind speed
& direction
Mean speed Intermittency
Ambient
turbulence …
Design factors
(controllable)
Land
configuration
Land area Farm layout
Turbine
selection
Grid
connection
Energy
storage
…
Early Stage
(up to 3 mon. ~ 3 yr.)
• Wind resource
assessment
• Site selection
• Preliminary feasibility
analysis
Mid Stage
(2 ~ 5 yr.)
• Economics analysis
• Transmission capacity
analysis
• Regulatory framework
• Environmental studies
Late Stage
(up to 25 yr)
• Financing
• Construction
• Operation & Maintenance

3. Research Motivation
3
 Owing to the lack of early stage conceptual design
frameworks, wind farm planning is an undesirably time-
consuming process.
 Transparency and efficiency are compromised in
conventional wind farm planning due to typical
independent decision making of different factors (e.g.,
wind farm layouts are generally designed for prescribed
land area and nameplate capacity)
 Quantitative exploration of the balance between the key
objectives is mostly missing in the state of the art (e.g.,
balance between energy production and land use)

4. Research Objective
4
Develop a Bi-level Wind Farm Trade-off Visualization
framework
Explore the trade-off between the concerned design
objectives: capacity factor – land use
Visualize the trade-off by parametrically translating the
Pareto

5. Outline
5
• Design Objectives
• Wind farm Energy Production (Capacity Factor)
• Land Use (Land Area per MW Installed)
• Bi-level Wind Farm Trade-off Visualization Framework
• Lower-level: Trade-off exploration
• Upper-level: Trade-off visualization
• Numerical Experiment
• Concluding Remarks

6. Wind Farm Energy Production
6
• Wind farm Capacity Factor
𝐶𝐹 =
𝐸𝑛𝑒𝑟𝑔𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑣𝑒𝑟 𝑎 𝑡𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑢𝑡𝑝𝑢𝑡
• Power Generational model in Unrestricted Wind Farm Layout
Optimization (UWFLO) framework
• Quantify the power generation as a function of incoming wind conditions,
farm layout, and turbine features
Denmark's Horns Rev 1 wind farm
The Wake Effect

7. Land Area per MW Installed (LAMI)
7
• Based on the farm layout, the land use is determined by the Smallest Bounding
Rectangle (SBR) enclosing all turbines
• The actual land area is represented as the buffer zone created by making a 2D
distance away from the SBR
• Turbines are not placed on the boundary of a wind farm
• Avoid “zero” area when minimizing the land area

8. Wind Farm Layout Optimization
8
wind farm layout optimization flowchart
Stop criterion
Reach the best performance?
Evaluate design
objective functions
Trade-off between
design objectives
Adjust the
location of
turbines
Prescribed
conditions
Yes
No
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000
optimal layout of 20 turbines optimal layout of 40 turbines
How many turbines should we install?

9. Bi-level Wind Farm Visualization Framework
9
wind farm layout optimization flowchart
Stop criterion
Reach the best performance?
Evaluate design
objective functions
Trade-off between
design objectives
Adjust the
location of
turbines
Sample
design
factors
Wind
distribution
Initial
boundary
Yes
No

10. Bi-level Wind Farm Visualization Framework
10
Capital
investment
Nameplate
capacity
Turbine
features

11. Numerical Experiment
• Two design objectives:
• Maximize the wind farm capacity factor
• Minimize the Land Area per MW Installed (LAMI)
• Identical turbines are used (GE-1.5 xle)
• Wind data from a site at North Dakota is used
Upper-level: the trade-off between capacity factor and LAMI is parametrically
represented by Nameplate Capacity
Lower-level: multi-objective wind farm layout optimization is performed as a
constrained single objective optimization using Mixed-Discrete Particle Swarm
Optimization (MDPSO) algorithm*
11*: Chowdhury et al., 2013 Struct Multidisc Optim

12. Lower-level: CF-LAMI Trade-off Exploration
12
 A set of sample nameplate capacities are generated within the 20 MW – 100 MW range
 A square initial region is pre-defined with a size less than 120 hectares per MW installed
 The bi-objective optimization is formulated as
Sample #
Nameplate
Capacity
No. of turbines
1 20 13
2 30 20
3 60 40
4 90 60
5 100 67
max 𝐶𝐹, min 𝐴
subject to
𝑔 𝑉 ≤ 0
𝑉 𝑚𝑖𝑛 ≤ 𝑉 ≤ 𝑉𝑚𝑎𝑥
𝑉 = {𝑋1, 𝑋2, ⋯ , 𝑋 𝑁, 𝑌1, 𝑌2, ⋯ , 𝑌𝑁}

13. Applying the Smallest Bounding Rectangle
enclosing all turbines
max 𝑓(𝑉) =
𝐸𝑓𝑎𝑟𝑚
365 × 24 𝑁𝐶
subject to
𝑔1 𝑉 ≤ 0
𝑔2 𝑉 ≤ 0
𝑉 𝑚𝑖𝑛 ≤ 𝑉 ≤ 𝑉𝑚𝑎𝑥
𝑉 = {𝑋1, 𝑋2, ⋯ , 𝑋 𝑁, 𝑌1, 𝑌2, ⋯ , 𝑌𝑁}
Lower-level: CF-LAMI Trade-off Exploration
 Solved by: Mixed-Discrete Particle Swarm Optimization 13
Estimated using the power generation model
in UWFLO framework
 N is determined by the sample nameplate
capacity
 𝑉𝑚𝑎𝑥 and 𝑉 𝑚𝑖𝑛 are set based on the initial
boundary regulated by the allowable land area
𝐸𝑓𝑎𝑟𝑚 = (365 × 24)
𝑗=1
𝑁 𝑝
𝑃𝑓𝑎𝑟𝑚 𝑝∆𝑈∆𝜃
Inter-Turbine Spacing
Land Area Constraint

14. Lower-level: CF-LAMI Trade-off Exploration
14
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000
optimal layout with land area of 180 ha
optimal layout with land area of 900 ha
optimal layout with land area of 3000 ha
Optimal layouts of 20 turbines with different land area constraints

15. Upper-level: CF-LAMI Trade-off Visualization
15
𝐶𝐹 = 𝑎𝐴 𝑏 + 𝑐
Pareto solutions of 13 turbines
Pareto solutions of 20 turbines
Pareto solutions of 40 turbines
Pareto solutions of 60 turbines
Pareto solutions of 67 turbines
Fitted curve for case of 13 turbines
Fitted curve for case of 20 turbines
Fitted curve for case of 40 turbines
Fitted curve for case of 60 turbines
Fitted curve for case of 67 turbines
22.4ha/MW 22.4ha/MW
US Average Land Use:
34ha/MW

16. Concluding Remarks
• A Bi-level Wind Farm Trade-off Visualization framework was proposed for
conceptual design of wind farms.
• The CF-LAMI trade-off was parametrically represented as a function of
nameplate capacity.
• This proposed framework can streamline the wind farm development process,
especially for large-scale wind farm projects, and help wind farm developers to
make efficient and effective decisions.
• Future work
• Use both turbine features (turbine rated power) and nameplate capacity to
parameterize the trade-off curve
• Explore the trade-off, such as Capacity Factor vs. Net Impact on
Surroundings
16

17. Acknowledgement
 I would like to acknowledge my research adviser
Prof. Achille Messac, and my co-adviser Prof.
Souma Chowdhury for their immense help and
support in this research.
 I would also like to thank my friend and colleague
Ali Mehmani for his valuable contributions to this
paper.
 Support from the NSF Awards is also
acknowledged.
17

18. Questions
and
Comments
18
Thank you

19. CF Response Surface Obtained
 Even if turbines are allowed the same land area per MW installed, a
greater number of turbines (higher nameplate capacity) would lead to
greater wake losses, leading to lower energy production.
 A contour plot of the function can provide the “LAMI vs. nameplate
capacity” cutoff curve that corresponds to the threshold CF.
LandAreaperMWinstalled(m2/MW)
Nameplate Capacity (MW)
19

20. Mid-level: Quantification of Trade-offs between Design Objectives
20
• The wind distribution is unique
• A group of Pareto curves can be obtained from the multi-objective wind farm
layout optimization at the bottom-level
• Based on observation, use an appropriate form of function to fit all the Pareto
curves, for example, a form of power function with 3 coefficients
• Once the global design factors are specified, a trade-off curve between two
objectives can be generated
𝑜𝑏𝑗2
𝑛
= 𝑎(𝑝1, 𝑝2, ⋯ , 𝑝 𝐾)𝑜𝑏𝑗1
𝑛 𝑏(𝑝1,𝑝2,⋯,𝑝 𝑁)
+ 𝑐(𝑝1, 𝑝2, ⋯ , 𝑝 𝐾)
where 𝑛 = 1,2, ⋯ , 𝑁 representing 𝑁 sets of samples of global design factors; and 𝐾 is the total
number of global design factors accounted for

21. 21
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

22. 22
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

23. wind
direction
Numerical Experiments
23
 An array-like wind farm with 9 GE 2.5 MW – 100m turbines is considered.
 A fixed aspect ratio is selected; the streamwise 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

24. 24
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

25. 25
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 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

26. Mixed-Discrete Particle Swarm Optimization (PSO)
 This algorithm has the ability to
deal with both discrete and
continuous design variables, and
 The mixed-discrete PSO presents
an explicit diversity preservation
capability to prevent premature
stagnation of particles.
 PSO can appropriately address the
non-linearity and the multi-
modality of the wind farm model.
26

27. Lower-level: multi-objective wind farm layout optimization
27
 A set of sample nameplate capacity factors is generated
within the 20 MW – 100 MW range
 A square initial region is pre-defined, f which size is
less than 110 hectares per MW installed
 The bi-objective optimization was solved as a
Constrained single objective optimization
Sample #
Nameplate
Capacity
No. of
turbines
1 20 13
2 30 20
3 60 40
4 90 60
5 100 67
max 𝑓(𝑉) =
𝐸𝑓𝑎𝑟𝑚
365 × 24 𝑁𝐶
subject to
𝑔1 𝑉 ≤ 0
𝑔2 𝑉 ≤ 0
𝑉 𝑚𝑖𝑛 ≤ 𝑉 ≤ 𝑉𝑚𝑎𝑥
𝑉 = {𝑋1, 𝑋2, ⋯ , 𝑋 𝑁, 𝑌1, 𝑌2, ⋯ , 𝑌𝑁}

28. 28