This document describes research on developing a consolidated visualization platform for wind farm planning. It involves performing multiple bi-objective optimizations to compare energy production potentials under different land area and turbine capacity combinations. The optimizations aim to maximize capacity factor while minimizing land area usage. The results are displayed in a GUI-based land shape chart to show the optimal land shapes demanded by each combination. The research found that dominant wind directions strongly influence land shapes, which tend to align with dominant directions. Optimal land shapes are highly sensitive to the number of turbines when land area is small, and to land area when turbine capacity is small.

1. A Consolidated Visualization of Wind Farm Energy
Production Potential and Optimal Land Shapes under
Different Land Area and Nameplate Capacity Decisions
Weiyang Tong*, Souma Chowdhury#, and Achille Messac#
* Syracuse University, Department of Mechanical and Aerospace Engineering
# Mississippi State University, Bagley College of Engineering
10th Multi-Disciplinary Design Optimization Conference
AIAA Science and Technology Forum and Exposition
January 13 – 17, 2014 National Harbor, Maryland

2. Early Stage Wind Farm Development
2
Wind
measurement
• Site selection
• Wind resource
assessment
Site selection
• Landowner
negotiation
• Road access
Feasibility
analysis
• Permitting
• Power
transmission
• Economics
analysis
Environmental
assessment
• Noise impact
• Impact on local
wildlife
 A complex process involving multiple objectives (e.g., cost and local impact)
 Demands time-efficient decision-making
 Often Suffers from lacking of transparency and cooperation among the parties involved
Wind farm development at early stage

3. Major Parties Involved
3
 Undesirable concept-to-installation delays are caused by conflicting
decisions from the major parties involved
Wind farm developers
need to address the
concerns of the major
parties involved
Seek the balance between
the social, economic, and
environmental objectives
Project
Investors
Landowners
Local
Communities
Power
utilities
Local public
authoritiesWind farm developer

4. Wind Farm
Developers
Landowners
Project
investors
Local public
authorities
Local
communities
Power
utilities
Research Motivation
4
 Nameplate capacity
 Number of turbines
 Land use
 Land area
 Land shape
 Annual Energy Production
 Capacity factor
 Cost of Energy
 Net Impact on Surroundings
 Noise impact
 Impact on wildlife
 Turbine Survivability
 Turbine type
Many
turbines
Few
turbines
Small land
per turbine
Large land
per turbine
AEP AEP
AEPAEP
CoE CoE
CoECoE
NIS NIS
NISNIS
TS TS
TSTS
Preferred AEP
Preferred NIS

5. Research Objective
5
Develop a Consolidated Visualization platform
for wind farm planning
Compare energy production potentials offered by different
combinations of Nameplate Capacity and Land Area per MW
Installed (LAMI)
Show what exact optimal land shapes are demanded for these
combinations

6. Outline
6
• Layout-based Land Usage
• Multiple bi-objective optimizations
• Consolidated Visualization Platform
• Numerical Experiment
• GUI-based land shape chart
• Concluding Remarks

7. Conventional Wind Farm Layout Optimization
7
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
Farm boundaries
Land area
Land orientation
Number of turbines
𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 = 𝑓(𝑋 𝑚𝑖𝑛, 𝑌 𝑚𝑖𝑛, 𝑋 𝑚𝑎𝑥, 𝑌 𝑚𝑎𝑥)
𝑋 𝑁
∈ [𝑋 𝑚𝑖𝑛, 𝑋 𝑚𝑎𝑥]
𝑌 𝑁
∈ [𝑌 𝑚𝑖𝑛, 𝑌 𝑚𝑎𝑥]
𝑋 𝑚𝑖𝑛 𝑋 𝑚𝑎𝑥
𝑌 𝑚𝑖𝑛
𝑌 𝑚𝑎𝑥
Turbine location vector

8. Wind turbine 2D Convex hull
SBR Buffer area
Wind turbine 2D Convex hull
SBR Buffer area
Wind turbine 2D Convex hull
SBR Buffer area
Wind turbine 2D Convex hull
SBR Buffer area
Layout-based Wind Farm Land Usage
8
• The “2D Convex Hull” is applied to
determine the land usage for a given set
of turbines
• The Smallest Bounding Rectangle
(SBR) is fit based on the convex hull
• A buffer zone is added to each side of
the SBR to yield the final land usage
1D
𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 = 𝑓(𝑋 𝑁
, 𝑌 𝑁
)
𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑 = 𝑔(𝑋 𝑁
, 𝑌 𝑁
)

9. Optimal Layout-based Wind Farm Land Usage
9
• An Optimal Layout-based (OL-based) land use
has the following features:
• Farm boundaries are not assumed
• Automatically determined by the layout optimization
• Yield OL-based land area, 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑
∗
• Yield OL-based land shape, 𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑
∗
Step 1: min
𝑋 𝑁,𝑌 𝑁
𝑓 𝑋 𝑁, 𝑌 𝑁 , 𝑔 𝑋 𝑁, 𝑌 𝑁
Step 2: 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑
∗
= 𝑓 𝑋 𝑁
∗
, 𝑌 𝑁
∗
𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑
∗
= 𝑔 𝑋 𝑁
∗
, 𝑌 𝑁
∗
Optimal layout

10. Multiple bi-objective optimizations
10
Land Area per MW Installed
NameplateCapacity
• The development of the consolidated visualization
platform is based on a multiple performance of bi-
objective layout optimizations
• The number of turbines and the maximum
allowed land area are specified for each case
• The objectives are
• Maximizing the wind farm capacity factor
• Minimizing the unit land area
Each bi-objective optimization problem is
solved as multiple constrained single objective
optimization problems
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . .
. . . . . .
Area?
shape?
CF ?
Area?
shape?
CF ?
Area?
shape?
CF ?
Area?
shape?
CF ?
NC1NCm
LAMI1 LAMIn

11. Multiple bi-objective optimizations
11
Stop criterion
Evaluate design
objective functions
Trade-off between
design objectives
Adjust the
location of
turbines
NCi
AMWi
Yes
No
max 𝐶𝐹(𝑉) =
𝐸𝑓𝑎𝑟𝑚
365 × 24 𝑁𝐶
𝑉 = {𝑋1, 𝑋2, ⋯ , 𝑋 𝑁, 𝑌1, 𝑌2, ⋯ , 𝑌𝑁}
subject to
𝑔1 𝑉 ≤ 𝐴 𝑀𝑊𝑖
𝑔2 𝑉 ≤ 2𝐷
Estimated using the power generation model
in UWFLO framework2
𝐸𝑓𝑎𝑟𝑚 = 365 × 24
𝑗=1
𝑁 𝑝
𝑃𝑓𝑎𝑟𝑚 𝑈𝑗, 𝜃𝑗 𝑓(𝑈𝑗, 𝜃𝑗)∆𝑈∆𝜃
Inter-Turbine Spacing
layout-based land
area constraint
Solved by Mixed-Discrete Particle Swarm Optimization1
1: Chowdhury et al., 2013 Struct Multidisc Optim
2: Chowdhury et al., 2012 Renewable Energy

12. Numerical Experiment: Description
• Two design criteria:
• Maximizing the wind farm capacity factor
• Different specified constraints of Land Area per MW Installed (LAMI)
• Identical turbines are used (GE-1.5 xle, rated power 1.5 MW)
• The ambient turbulence over the entire farm site is assumed constant
12
LAMI (ha/MW)
Number
of turbines
40 60 80 100
50 (75 MW)
75 (112.5 MW)
100 (150 MW)

13. Numerical Experiment: Wind Distribution
13
 The Weibull distribution is used for wind speed
 Three characteristic wind patterns are generated with equal wind power density (WPD)
𝑓 𝑥 =
𝑘
𝑐
(
𝑥
𝑐
) 𝑘−1
where
k = 2.022
C=5.247
0
0.05
0.1
0.15
0.2
0 5 10 15
𝑊𝑃𝐷 =
𝑖=1
𝑁 𝑝
1
2
𝜌𝑈𝑖
3
𝑓(𝑈𝑖, 𝜃1)Δ𝑈
=
𝑖=1
𝑁 𝑝
1
2
𝜌𝑈𝑖
3 1
2
𝑓 𝑈𝑖, 𝜃1 +
1
2
𝑓 𝑈𝑖, 𝜃2 Δ𝑈
=
𝑖=1
𝑁 𝑝
1
2
𝜌𝑈𝑖
3 1
2
𝑓 𝑈𝑖, 𝜃1 +
1
2
𝑓 𝑈𝑖, 𝜃3 Δ𝑈
where
Δ𝑈 = 𝑈 𝑚𝑎𝑥 𝑁𝑝
Case 1: single dominant direction
𝜃1 = 30°
Case 2: two opposite dominant directions
𝜃1 = 30°, 𝜃2 = 210°
Case 3: two orthogonal dominant directions
𝜃1 = 30°, 𝜃3 = 120°
m/s

14. 14
Case 1: single dominant direction Case 2: two opposite dominant directions
Case 3: two orthogonal dominant directions
𝜃1 = 30°
𝜃1 = 30°
𝜃3 = 120°
𝜃1 = 30°

15. Numerical Experiment: Parallel Computing
15
. . .
Start
Task n
Core n
Task 2
Core 2
. . .Task 1
Core 1
End
 For each combination, the optimization is run 5 times to compensate the
impact of random parameters
 Totally 180 optimizations are performed using parallel computing on 4
work stations (4/8 cores)

16. Results and Discussion: GUI-based Land Shape Chart
16
Single dominant direction
 Most of land shapes are aligned
with the dominant direction
 The wind farm at the top-left cell
predicted the lowest CF
 The wind farm at the bottom-right
cell predicted the highest CF

17. Results and Discussion: GUI-based Land Shape Chart
17
2
4
1
3

18. Results and Discussion: GUI-based Land Shape Chart
18
Two opposite dominant directions
 The same trend for the predicted CF
is observed
 More closely aligned with the
dominant directions
 Some land shapes in this case are
stretched

19. Results and Discussion: GUI-based Land Shape Chart
19
Two orthogonal dominant directions
 The same trend for the predicted CF
is observed
 Most land plots have a square-like
land shape

20. Land Shape Charts Comparison
20
Two opposite dominant directions Two orthogonal dominant directionsSingle dominant direction

21. Totally 375 optimizations were paralelly performed
Land Shape Charts Comparison
21
Two opposite dominant directions Two orthogonal dominant directionsSingle dominant direction

22. Concluding Remarks
• A Consolidated Visualization platform was developed to show
• Energy production potentials with different combinations of land area and
nameplate capacity
• Optimal land shapes demanded for these combinations
• Three components:
(i) Optimal Layout-based land usage (convex hull and SBR)
(ii) Multiple constrained single objective optimizations
(iii) GUI-based land shape chart
• Dominant directions have a strong impact, and land shapes are
orientated along the dominant directions
• The optimal-based land shape is highly sensitive to the number of
turbines in the case of small allowed LAMI (vice versa) and to the
LAMI in the case of small installed capacity ( few turbines installed)
22

23. Future Work
• Enable the illustration of other important objectives, such as local
impact and Cost of Energy
• Adding one layer of map regarding land plot ownership and landowner
participation
23

24. Acknowledgement
 I would like to acknowledge my research adviser
Prof. Achille Messac, and my co-adviser Dr.
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.
24

25. Questions
and
Comments
25
Thank you

26. Lower-level: CF-LAMI Trade-off Exploration
26
-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

27. Numerical Experiment: Wind Data
27

28. 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)
28

29. Mid-level: Quantification of Trade-offs between Design Objectives
29
• 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

30. 30
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

31. 31
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

32. wind
direction
Numerical Experiments
32
 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

33. 33
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

34. 34
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

35. 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.
35