Wind farm development is an extremely complex process, most often driven by three im- portant performance criteria: (i) annual energy production, (ii) lifetime costs, and (iii) net impact on surroundings. Generally, planning a commercial scale wind farm takes several years. Undesirable concept-to-installation delays are primarily attributed to the lack of an upfront understanding of how different factors collectively affect the overall performance of a wind farm. More specifically, it is necessary to understand the balance between the socio-economic, engineering, and environmental objectives at an early stage in the design process. This paper proposes a Wind Farm Tradeoff Visualization (WiFToV) framework that aims to develop first-of-its-kind generalized guidelines for the conceptual design of wind farms, especially at early stages of wind farm development. Two major performance objectives are considered in this work: (i) cost of energy (COE) and (ii) land area per MW installed (LAMI). The COE is estimated using the Wind Turbine Design Cost and Scaling Model (WTDCS) and the Annual Energy Production (AEP) model incorporated by the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The LAMI is esti- mated using an optimal-layout based land usage model, which is treated as a post-process of the wind farm layout optimization. A Multi-Objective Mixed-Discrete Particle Swarm Optimization (MO-MDPSO) algorithm is used to perform the bi-objective optimization, which simultaneously optimizes the location and types of turbines. Together with a novel Pareto translation technique, the proposed WiFToV framework allows the exploration of the trade-off between COE and LAMI, and their variations with respect to multiple values of nameplate capacity.

1. Simultaneously Optimizing COE and Land Footprint
of Wind Farms under Different Land Plot Availability
Weiyang Tong*, Souma Chowdhury#, and Achille Messac#
* Syracuse University, Department of Mechanical and Aerospace Engineering
# Mississippi State University, Department of Aerospace Engineering
11th Multi-Disciplinary Design Optimization Conference
AIAA Science and Technology Forum and Exposition
January 5 – 9, 2015 Kissimmee, Florida

2. Major Parties Involved
2
 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 optimal design that
balances the social, economic,
and environmental objectives
Project
Investors
Landowners
Local
Communities
Power
utilities
Local public
authorities
Wind farm developer

3. Landowner Participation
• In commercial wind farms, turbines generally appear in clusters due to
considerations of land plot availability.
• However, closer the turbines in an array, greater are the energy losses due
to wake effects.
• On the other hand, greater land usage increases the net impact on
surroundings (e.g., impact on wildlife), and demands participation of
more landowners.
3
Husum, Germanyhttp://www.sciencebuzz.org/
Thenetimpacton
surroundings
Cost of Energy

4. Research Motivation
4
 Decision making of different factors is impractical and restrictive in
conventional wind farm planning due to typically prescribed conditions:
 Wind farm layouts are generally designed for prescribed land area or farm
boundaries, and prescribed turbine configurations.
 There exist very few instances (in the literature) of exploring how land plot
availability impact wind farm layout planning (e.g., Chen and MacDonald,
2012, 2013).
 Limited literature exists on exploring the trade-offs between COE/energy
production and land footprint (e.g., Tong et al., 2012, 2013).
 Exploration of such multiobjective wind farm layout optimization
scenarios under different land plot availability also demands nonlinear
MO optimizers that are fast, and can deal with constraints, multimodal
functions, and mixed-discrete variables.

5. Research Objective
5
 Investigate the capabilities of a new multi-objective mixed-discrete
PSO to perform bi-objective optimization:
 To simultaneously minimize the cost of energy (COE) and the land
footprint per MW installed of the wind farm.
 Investigate how different land plot availability scenarios impact the
best trade-offs between COE and land footprint, and regulate the
optimal wind farm layout designs.
Cost of Energy ($/kWh)
LandareaperMWinstalled(ha/MW)
0.035 0.04 0.045 0.05
10
20
30
40
50
60
70
80
90
100
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
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7
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7
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7
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7
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7
7
7
7
7
7
7
7
7
7
7
7
7
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000

6. Outline
6
• Multi-Objective Wind Farm Layout Optimization
• Wind Farm Cost and Energy Production Models
• Conventional and Layout-based Land Usage Model
• Multi-Objective Optimization Problem Definition
• Multi-Objective Mixed-Discrete PSO (MO-MDPSO)
 Highly nonlinear
 High dimensional
 Highly constrained
 Non-convex Pareto frontier, and
 Mixture of continuous and discrete design variables
• Wind Farm Optimization under Land Plot Availability
• Concluding Remarks

7. Outline
7
• Multi-Objective Wind Farm Layout Optimization
• Wind Farm Cost and Energy Production Models
• Conventional and Layout-based Land Usage Model
• Multi-Objective Optimization Problem Definition
• Multi-Objective Mixed-Discrete PSO (MO-MDPSO)
 Highly nonlinear
 High dimensional
 Highly constrained
 Non-convex Pareto frontier, and
 Mixture of continuous and discrete design variables
• Wind Farm Optimization under Land Plot Availability
• Concluding Remarks

8. 𝐶𝑂𝐸 =
𝐼𝐶𝐶 × 𝐹𝐶𝑅 + 𝐿𝑅𝐶
𝐴𝐸𝑃
+ 𝐿𝐿𝐶 + 𝑂&𝑀
where
ICC – Initial Capital Cost
LRC – Levelized Replacement Cost
LLC – Land Lease Cost
O&M – Operation & Maintenance Cost
FCR – Fixed Charge Rate
AEP – Annual Energy Production
Wind Farm Cost of Energy
8
𝐸𝑓𝑎𝑟𝑚 = 365 × 24
𝑗=1
𝑁 𝑝
𝑃𝑓𝑎𝑟𝑚 𝑈𝑗, 𝜃𝑗 𝑓(𝑈𝑗, 𝜃𝑗)∆𝑈∆𝜃
1: Fingersh et al., 2006 NREL Tech. Report
2: Chowdhury et al., 2012 Renewable Energy
Estimated using the Wind Turbine Design
Cost and Scaling Model1
 Rotor:
Blades
Hub
Pitch mechanisms, etc;
 Drive train nacelle
Gearbox
generator, etc;
 Control, safety system, and monitoring
 Tower
 Balance of station
Foundation
Transportation
Assembly and installation, etc
Energy production model offered by UWFLO2:

9. 9
Energy Production Model in UWFLO
 This model quantifies the power generation of an array of turbines as a
function of the incoming wind conditions, turbine features, and the
locations of turbines
 It allows a variable induction factor:
U: incoming wind speed; P: power generated, given by the power curve
kg, kb: mechanical and electrical efficiencies, Dj: Rotor Diameter, 𝜌: Air density
 The Katic’s model is used to account for wake merging and partial wake
overlap
𝑢𝑗: Effective velocity deficit
𝐴 𝑘𝑗: Overlapping area bt.Turbine-j and Turbine-k

10. Conventional Wind Farm Layout Optimization
10
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

11. 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
11
• A given layout (siting of an array of
turbines) is obtained.
• 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
)

12. Optimal Layout-based Wind Farm Land Usage
12
• 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

13. Evaluate
Performance
Objectives
Cost of
Energy
Land
Footprint
MO-MDPSO
Multi-Objective Wind Farm Optimization Framework
13
1. Turbine Locations
2. Turbine Config.
Trade-off bt. objectives
Optimal designs:
o Location of turbines
o Selection of turbine types
o Site orientation
𝑚𝑖𝑛 {𝐶𝑂𝐸 𝑉 , 𝐴 𝑀𝑊 𝑉 }
𝑉 = 𝑥1, 𝑥2, ⋯ , 𝑥 𝑁, 𝑦1, 𝑦2, ⋯ , 𝑦 𝑁, 𝑇
𝑇 = {1,2, ⋯ , 16}
subject to
𝑔1 𝑉
𝑔2 𝑉 ≤ 2𝐷
Inter-Turbine Spacing
Binary-decision
landowner participation
Highly nonlinear
and multimodal
Mixed-Integer Variables
Nonlinear constraints

14. Outline
14
• Multi-Objective Wind Farm Layout Optimization
• Wind Farm Cost and Energy Production Models
• Conventional and Layout-based Land Usage Model
• Multi-Objective Optimization Problem Definition
• Multi-Objective Mixed-Discrete PSO (MO-MDPSO)
 Highly nonlinear
 High dimensional
 Highly constrained
 Non-convex Pareto frontier, and
 Mixture of continuous and discrete design variables
• Wind Farm Optimization under Land Plot Availability
• Concluding Remarks

15. 1
2
3
4
5
1
2
3
4 5
f1
f2
0 0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
2
2.5
3
Infeasible
R
egion
Actual Boundary
Local
Pareto set
Multi-Objective Mixed-Discrete PSO
Position update:
𝒙𝑖 𝑡 + 1 = 𝒙𝑖 𝑡 + 𝒗𝑖 𝑡 + 1
Velocity update:
𝒗𝑖 𝑡 + 1 = 𝑤𝒗𝑖 𝑡 + 𝑟1 𝐶1 𝑷𝑖
𝑙
(𝑡) − 𝒙𝑖 + 𝑟2 𝐶2 𝑷𝑖
𝑔
(𝑡) − 𝒙𝑖 + 𝑟3 𝛾 𝑐,𝑖 𝒗𝑖(𝑡)
15
𝑷𝑖
𝑙
– local leader of particle-i, which is
selected from the local Pareto set
𝑷𝑖
𝑔
– global leader of particle-i that is
determined by a stochastic process
Crowding Distance – to manage the
size of local/global Pareto set
Multiple global leaders
Inertia Local search Global search
Applied w.r.t.
each particle’s
global leader
Current particle Stored particle
Highly
constrained
High
dimensional
Non-convex
Pareto frontier
Highly
nonlinear
Mixed types of
variables

16. Hypercube enclosing
72 candidate solutions
X1
X2
0 1 2 3
0
1
2
3
Particles
Global leaders
Multiple λ-Fractional Domains
16
• 7 global leaders are observed
• Ideally, each fractional
domain should enclose 10
particles
• Particles located in the
overlapping regions are
uniformly re-allocated
between domains
• This method uniquely exploits
diversity preservation to both
prevent particle stagnation
and accomplish a desirable
distribution of Pareto
solutions.
13
10
14
𝜆 = 0.25
Design Variable Space

17. Outline
17
• Multi-Objective Wind Farm Layout Optimization
• Wind Farm Cost and Energy Production Models
• Conventional and Layout-based Land Usage Model
• Multi-Objective Optimization Problem Definition
• Multi-Objective Mixed-Discrete PSO (MO-MDPSO)
 Highly nonlinear
 High dimensional
 Highly constrained
 Non-convex Pareto frontier, and
 Mixture of continuous and discrete design variables
• Wind Farm Optimization under Land Plot Availability
• Concluding Remarks

18. Case Study Setup: Assumptions and Prescriptions
Assumptions:
• A wind distribution (based on 10yr measured data) is used
• 16 square land plots are considered
• Identical turbines are used with 16 candidate turbine types
• Landowner participation is assumed to be Binary (deterministic)
18
User-defined parameters in MO-MDPSO
Parameter
Mixed-discrete
constrained problems
𝑤 0.5
𝐶1 1.5
𝐶𝑐0 1.5
𝛾 𝑐0 2.0
𝛾 𝑚𝑖𝑛 1e-5
𝛾 𝑑0 1.0
𝜆 0.1
Local set size 10
Global set size Up to 100
Population size 1000
Particle Velocity
parameters
Diversity
parameters
Multi-objective
Search
parameters

19. Three Case Studies: Based on Land Plot Availability
19
Parameter Case Study I Case Study II Case Study III
Number of turbines 50 50 50
Plots allowed to be used All 16 plots 8 specified plots
No more than any
6 plots
No. of design variables 101 101 101
Max. Function Evaluations 250,000 250,000 250,000
Case I Case II Case III

20. 8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
88
8
8
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8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
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12
12
12 12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Case Study I: All 16 Land Plots
20
𝑔1 𝑉 = min
max(𝑥 − 𝑋 𝑚𝑖𝑛, 0)+max(𝑋 𝑚𝑎𝑥 − 𝑥, 0),
max 𝑦 − 𝑌 𝑚𝑖𝑛, 0 +max(𝑌 𝑚𝑎𝑥 − 𝑦, 0)
Cost of Energy ($/kWh)
LandareaperMWinstalled(ha/MW)
0.035 0.04 0.045 0.05
10
20
30
40
50
60
70
80
90
100
COE – LAMI Tradeoff
Major turbine features
Land plot availability constraint
Optimal wind farm layout:
Max. Land, Min. COE
Min. Land, Max. COE

21. Cost of Energy ($/kWh)
LandareaperMWinstalled(ha/MW)
0.035 0.04 0.045 0.05
10
20
30
40
50
60
70
80
90
100
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Case Study II: 8 Specified Land Plots
21
𝑔1 𝑉 =
𝑖=1
𝑁
𝑝
∀𝑝∈𝑃
min
max(𝑥 − 𝑋 𝑚𝑖𝑛
𝑝
, 𝑋 𝑚𝑎𝑥
𝑝
− 𝑥, 0)
+max(𝑦 − 𝑌 𝑚𝑖𝑛
𝑝
, 𝑌 𝑚𝑎𝑥
𝑝
− 𝑦, 0)
where 𝑃={3, 4, 6, 7, 9, 10, 11, 13}
COE – LAMI Tradeoff
Major turbine features
Land plot availability constraint
Optimal wind farm layout:
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
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7
7
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7
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7
7
7
7
7
7
7
7
7
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
Max. Land, Min. COE
Min. Land, Max. COE

22. Cost of Energy ($/kWh)
LandareaperMWinstalled(ha/MW)
0.035 0.04 0.045 0.05
10
20
30
40
50
60
70
80
90
100
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Case Study III: No More than 6 Land Plots
22
COE – LAMI Tradeoff
Major turbine features
Land plot availability constraint
Optimal wind farm layout:
𝑔1 𝑉 = 𝑖=1
𝑁
1
16
𝑢(𝑥, 𝑦) ≤ 6, and
𝑢 𝑥, 𝑦 =
1, 𝑖𝑓 𝑋 𝑚𝑖𝑛
𝑝
≤ 𝑥 ≤ 𝑋 𝑚𝑎𝑥
𝑝
𝑎𝑛𝑑 𝑌 𝑚𝑖𝑛
𝑝
≤ 𝑦 ≤ 𝑌 𝑚𝑎𝑥
𝑝
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
8
8
8
8
8
8
8
8
8
8
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8 8
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8
8
8
8
8
8
8
8
8
8
8
8
8
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
16
16
16
16
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16
16
16
16
16
16
16
16
16
16
16
16
16
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
Max. Land, Min. COE
Min. Land,
Max. COE

23. WFLO Cases with Non-Identical Turbines
23
1
9
8
16
4
7
1
12
3
6
6
6
8
12
2
1
8
16 16
16
7
8
7
8
2
8
9
16
8
8
10
1
8
1
9
16
2
4
13
6
8
3
8
13
5
10
16
16
2
2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
1
9
12
5
14
7
3
10
11
4
8
15
6
13
9
2
13
5
1
9
3
11
15
7
8
16
12
4
10
2
6
14 7
15
11
4
9
2
5
13
14
6
3
10
5
12
16
8
11
3
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
Cost of Energy ($/kWh)
LandareaperMWinstalled(ha/MW)
0.035 0.04 0.045 0.05
10
20
30
40
50
60
70
80
90
100
Case I
Case II
Case III
1
12
9
16
16
13
2
12
9
11
6
16
5
11
11
5
16
5
1
16
3
7
16
8
15
16
16
5
16
1
16
16
9
13
16
7
5
7
12
5
16
16
8
13
15
16
16
10
16
6
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
1
8
9
8
14
6
2
8
9
1
7
16
6
9
8
1
16
9
1
3
3
9
16
9
8
16
8
4
8
1
13
16
8
16
11
6
8
3
8
16
14
8
3
8
3
7
16
9
7
8
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
1
16
11
8
16
8
1
8
12
2
8
16
8
16
8
3
16
3
1
8
1
8
16
5
8
16
5
8
9
1
9
16
8
16
7
2
9
3
8
16
11
5
2
16
1
15
16
9
8
4
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
1
16
9
9
15
8
1
8
16
2
7
16
8
16
8
2
16
1
1
7
1
9
16
16
9
16
12
1
9
1
3
16
16
16
6
2
5
4
3
16
16
16
2
16
1
16
16
9
9
13
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
X (m)
Y(m)
-4000 -2000 0 2000 4000
-4000
-2000
0
2000
4000
Rated Power (W)
2.4E+06
2.2E+06
2E+06
1.8E+06
1.6E+06
1.4E+06
1.2E+06
1E+06
800000
• Each turbine can take any of the
16 configurations.
• No. of variables = 150
• Max function calls = 250 × 1500
• As before Case I results are
not fully converged.
• Beyond a certain land
footprint per MW, additional
land area provides marginal
benefit

24. Outline
24
• Multi-Objective Wind Farm Layout Optimization
• Wind Farm Cost and Energy Production Models
• Conventional and Layout-based Land Usage Model
• Multi-Objective Optimization Problem Definition
• Multi-Objective Mixed-Discrete PSO (MO-MDPSO)
 Highly nonlinear
 High dimensional
 Highly constrained
 Non-convex Pareto frontier, and
 Mixture of continuous and discrete design variables
• Wind Farm Optimization under Land Plot Availability
• Concluding Remarks

25. Concluding Remarks
 A Multi-Objective Wind Farm Layout Optimization framework was developed:
1. UWFLO Energy Production Model and Layout-based Land Usage Model
2. WTDCS/NREL Cost Model
3. A new Multi-Objective Mixed-Discrete PSO algorithm
 This framework provides optimal turbine locations, turbine types, and the
land plots to be used for turbine installation.
 Three different land plot availability scenarios were explored, while minimizing
COE and land-footprint per MW installed. Findings include:
1. Under frugal land usage, the most productive land plots are automatically selected.
2. Layout pattern for “max COE/min land” solutions remained similar across specified, limited,
and unlimited land plot availabilities scenarios.
3. Most desirable results were obtained under limited land plot availability, where – for a 66%
increase in land footprint (15 to 25 Ha/MW), a 15% reduction in COE is obtained.
25

26. Future Work
• Further fine-tune the optimizer to accomplish greater convergence.
• Consider a probabilistic model of landowner participation and a benefit
model for landowners.
• Develop a strategy to assign a utility value to each land plot, based on
their potential productivity for given wind conditions.
26

27. Acknowledgement
 I would like to thank the co-authors Prof. Achille
Messac and Weiyang Tong.
 Support from the NSF Awards (CMMI-1437746) is
also acknowledged.
27

28. Questions
and
Comments
28
Thank you

29. Comparison of Performance Indicators
24
Performance of Accuracy
Performance of Diversity
ZDT 4
0
1
2
3
ZDT 3
0
0.01
0.02
0.03
0.04
0.05
ZDT 1
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
ZDT 2
0
0.0002
0.0004
0.0006
0.0008
0.001
ZDT 6
0
0.1
0.2
0.3
0.4MO-
MDPSO
NSGA2
MO-
MDPSO NSGA2
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
ZDT 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ZDT 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ZDT 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ZDT 4
0
5
10
ZDT 6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
MO-
MDPSO
NSGA2
The lower the better

30. 30
• The MINLP problem
adopted from Dimkou
and Papalexandri*
No. of design variables 6
No. of discrete variables 3 (binary)
Function evaluations 10,000
Population size 100
Elite size of NSGA-II 78
Elite size of MO-MDPSO 100
*: Dimkou and Papalexandri (1998)
Mixed-Discrete Constrained Test Problem 1
f1
f2
-60 -50 -40 -30 -20 -10 0
-20
0
20
40
60
80
100
Pareto solution by NSGA-II
Pareto solution by MO-MDPSO

31. 31
• The design of disc brake
problem adopted from
Osyczka and Kundu*
No. of design variables 4
No. of discrete variables 1 (integer)
Function evaluations 10,000
Population size 100
Elite size of NSGA-II 87
Elite size of MO-MDPSO 100
*: Osyczka and Kundu (1998)
Mixed-Discrete Constrained Test Problem 2

32. Optimal layout-based land usage
32
-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

33. 33
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

34. Wind Farm Cost of Energy
34
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