This document describes a visually-informed decision-making platform (VIDMAP) for model-based design of wind farms. It aims to quantify and illustrate the criticality of information exchanged between different models in the wind farm layout optimization process. The platform consists of three main components: (1) uncertainty quantification to quantify variability in inputs and uncertainties introduced by upstream models, (2) sensitivity analysis to analyze sensitivity of downstream models, and (3) information visualization to visualize uncertainties and inter-model sensitivities. Sensitivity analysis is performed to quantify the sensitivity of an energy production model to first-level inputs and errors in upstream models like wind distribution, shear, turbine power response, and wake models.

1. A Visually-Informed Decision-Making Platform for
Model-based Design of Wind Farms
Souma Chowdhury#, Ali Mehmani*, Weiyang Tong*, and Achille Messac#
* Syracuse University, Department of Mechanical and Aerospace Engineering
# Mississippi State University, Bagley College of Engineering
Research supported by the NSF Award: CMMI 1437746
The AIAA Aviation and Aeronautics Forum and Exposition
June 16 – 20, 2014 Atlanta, Georgia

2. Wind Farm Design
Addressing inter & intra-system interactions
2
Natural resource
System
Environmental
System
Power Generation
System
Power
Transmission
System
Conditions Design Variables
• Farm Layout
• Type(s) of Turbines
Wind Farm Design
Objectives/Output
• Farm Power Generation
• Annual Energy Production
• Capacity Factor
• Cost of Energy
Other Design Factors
• Nameplate Capacity
• Land Area per MW inst.
• Distribution of Wind
Speed and Direction
• Atmospheric Turbulence
• Wind Shear
• Topography
Wake Effects
A Complex System

3. Model-based Wind Farm Design: Challenges
 Owing to the complexity of the system, and the multitude of factors,
model-based systems design is the de facto standard in wind farm design.
 Uncertainties are inherent in various forms in this MBSD process, e.g.:
 Resource uncertainties: The wind resource is naturally uncertain, and the lack of a clear
understanding/knowledge of the ABL leads to further uncertainties.
 Model inadequacies: High-fidelity analysis of wind farm flow is extremely expensive
(30 CPU-hr/simulation), leading to the use of lower-fidelity models in the design process.
 Unrealistic assumptions: The impact of various natural and design factors is highly
coupled and their interactions are often not duly accounted for.
 Existing wind farm layout optimization (WFLO) methods* generally only
consider certain aspects of resource variations.
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010; Chowdhury et al. 2012
3

4. 4
Fixed incoming wind speed at 7 m/s Fixed incoming wind speed at 11 m/s
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Sensitivity Analysis of Array-like Farm Output
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Jensen model
first-order index total-order index
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Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Models w/o turbulence
Models with turbulence
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turbulence
Land area/MW
installed
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first-order index total-order index
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Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Weiyang et al.
IDETC 2013

5. Sensitivity Analysis of Optimized Farm Output
(Region II: incoming wind speed 10.35m/s – 12.65 m/s)
5
1
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Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Ishihara model
first-order index total-order index
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Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Larsen model
first-order index total-order index
0
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Frandsen model
first-order index total-order index
0
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Jensen model
first-order index total-order index
Weiyang et al.
IDETC 2013

6. Visually-Informed Decision-Making Platform
(VIDMAP)
Overall Concept
Considering WFLO frameworks to be comprised of a series of interconnected
models, we will take an information flow perspective to WFLO to aid informed
(hence more reliable) decision-making.
Specific Objectives
1. To quantify and illustrate the criticality of information exchanged between
different models (i.e., inter-model sensitivities) in the WFLO process.
2. To quantify the model-induced uncertainties in the WFLO process.
6

7. Presentation Outline
 Information Flow Perspective to Model-based Systems Design (MBSD)
 Visually Informed Decision-Making Platform (VIDMAP)
 Wind Farm Energy Production Modeling
 Quantifying Input Variability and Model-induced Uncertainties
 Sensitivity Analysis of Energy Production Model
 Graphical Illustration of VIDMAP
 Concluding Remarks
7

8. The Information Flow Perspective to MBSD
8
A Design Process can be conceived as a flow of information.
Information
Criticality
Information
Expense
Information
Uncertainty

9. Motivating Approaches from Literature
 McManus et al., (2005) construct component behavior model to capture faulty
behavior (for design verification and validation in complex systems design).
 Allaire et al., (2012) developed a quantitative metric for measuring system
complexity based on information theory.
 Otto et al., (2013) elaborated on what challenges mechanical complex design
faces to reach the level of design automation in the embedded systems domain.
 Allaire et al., (2013) developed a multifidelity approach for complex systems
design and analysis to exploit optimally of all available models.
 Mehmani at al., (2013, 2014) developed a new approach to quantify the
uncertainty in surrogate models – for effective model selection and multi-fidelity
optimization.
 Visualization has been used in the context of multi-attribute/multi-objective
decision-making (Chiu and Bloebaum, 2009-2010), as well as in the context of
value–driven design Bertoni et al. (2013-2014).
9

10. VIDMAP: Structure
10
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process

11. Wind Farm Energy Production Modeling
11

12. Wind Farm Energy Production
Wind farm power
generation
12
 Annual Energy Production (AEP) of a farm is given by:
 AEP is numerically expressed as:
 Capacity Factor:
Probability of
wind condition

13. Wind Farm Power Generation: Inflow & Shading
13 13
The complex flow in a wind farm is due to turbine-wind interactions.
A multi-step model is developed to estimate the farm power generation.
 Rotor averaged velocity derived from the wind shear profile
Dedicated data More generic
Cal et al., 2010
 Wake losses are modeled rank-wise:
Turbine-j is in the wake of Turbine-i, if and only if
Considers turbines with differing
rotor-diameters and hub-heights
Turbines ranked in order
of encountering wind
Modeling
turbine-wind-turbine
interactions

14. Wind Farm Power Generation: Wake Losses
 
 
 
14
 Effective velocity of wind approaching Turbine-j:*
 Accounts for wake merging & partial wake-rotor overlap
 The power generated by turbine-j:
 Power generated
by wind farm:
Wake model
 
P P
Incoming
wind speed
Downstream
spacing
Radial
spacing
GE 2.5MW
Induction
factor
Rotor
Diameter
  2
 
Hub height
P
Turbulence
intensity
Jensen √ √ √ √
Frandsen √ √ √ √
Larsen √ √ √ √ √ √ √
Ishihara √ √ √ √ √ √
2
3
4 1
1
2 4 g b
a a
D
k k  U
Wake model:
At distance s
downstream
Novel dynamically-updated
turbine-adaptive energy loss
(variable induction factor, a)
1
N
farm j
j


15. VIDMAP: Structure
15
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process

16. First-Level Inputs
 The natural or commercial distributions of the first-level
inputs are determined, in order to generate samples for:
 Quantifying the uncertainty in the upstream models
 Performing the sensitivity analysis
 Natural Inputs:
1. Wind Resource – Average Wind Speed (Rayleigh distribution)
 Design Inputs:
2. Turbine Array Layout – Land Area/MW installed (7/3 aspect ratio)
3. Turbine Type – Turbine Features (major manufacturers)
16

17. Design Input Variability
Turbine Features: A sample set of 130 turbines from major
manufacturers, ranging from 0.6MW to 3.0MW, was created.
 Each turbine is defined in terms of its rotor diameter, hub height, rated power,
cut-in/cut-out/rated speed, and drivetrain type.
 LHS is used to prepare the integer-coded sample set of turbine features.
Land Area/MW Installed: The range is motivated by the reported
land footprint of US wind farms 1 (34.5 ± 22.4 ha/MW).
 LHS is used to generate the sample set of land area/MW installed.
 Assuming a N×N layout of turbines (N=10), with rated power, PR, for each
sample land area/MW of AMW, the turbine spacing is given by:
푑푠 =
1
푁 − 1
7
3 푁푃푅퐴
1/2
; 푑푙 =
1
푁 − 1
3
7 푁푃푅퐴
1/2
1 Denholm et al., Technical Report NREL/TP-6A2-45834, NREL, August 2009. 17

18. Wind Resource Input Variability
 The distribution of wind resource is defined in terms of the distribution of
average wind speed (AWS), derived from the US wind map.
 A normal distribution of the average wind speed, reported by Chowdhury
et al., (AIAA SDM 2012) is adopted here to generate the AWS samples.
 For each sample AWS, we generate a Rayleigh wind speed distribution –
to serve as an input to energy production model.
18

19. Quantifying Model Uncertainty
 High-fidelity estimates of the outputs of the upstream (or
constituent) models are not readily available, due to
 lack of data (e.g., vertical wind profile, decade-long met-tower data);
 Lack of access to data (e.g., proprietary turbine power data); or
 lack of understanding of the physical systems involved (e.g., ABL).
 Hence, we have employed different approaches to quantify
the model-induced uncertainties, such as:
 quantify the variance in the output of low-fidelity model choices; or
 Use recorded data from a single site/case to estimate model error.
19

20. Uncertainty in Wind Distribution Model
 Model error is given by the difference between the Rayleigh wind
distribution estimated using 1-year data and the scaled histogram of the
actual recorded wind conditions over the subsequent 10 years (a ND site).
20
 The output of the wind distribution model,
for given conditions (U i), is the set of wind
speed probabilities:
 The errors in the estimated wind speed
probabilities are treated as linearly
dependent random variables.
 Distribution of the normalized errors gives
the uncertainty in the wind distribution
model.

21. Uncertainty in Wind Shear Model
 Wind shear in ABL scarcely follows the power law or log law, which are
typically used in modeling and design.
Power Law:
푈
푈푟
=
푧
푧푟
훼
; Log Law:
푈
푈푟
=
푙푛 푧 푧0
푙푛 푧푟 푧0
 Dedicated wind shear data is often lacking in practical wind energy
projects. LIDAR and SODAR are likely solutions (not yet widely used).
 Uncertainty is quantified in terms of the distribution of the deviations
between different implementations of the two models, which rely on local
surface roughness assumptions (e.g., smooth ground – foot high grass).
 Output of wind shear model (hub-height wind speed):
 The deviation is estimated as:
21

22. Uncertainty in Turbine Power Response Model
 The power response of turbines often deviate from that given by the
manufacturer-reported power curves (e.g., due to atm. stability issues).
 Since access to actual turbine power response data is limited, we use
reported data from literature1 to quantify the deviations, and define
uncertainty as the distribution of these deviations.
 Output of turbine power response model:
22
1Wharton and Lundquist, Environmental
Research Letters, January 2012

23. Uncertainty in Wake Model
 Generally, analytical wake models are used in wind farm layout design.
 Access to actual field data is limited, and high-fidelity wake models are
too expensive (e.g., 30 CPU-hrs) to conduct Monte Carlo simulations.
 Hence, we quantify the uncertainty in the wake model as the deviations in
the estimates made by the four popular analytical wake models.
 Two model outputs (wake speed and wake width):
Wake speed Wake width
Tong et al.,
23
ASME IDETC 2013

24. Uncertainty in the Wake Model
 The deviations in the wake model outputs are given by
 Frandsen model is used as the scaling reference.
 A 10% ambient turbulence intensity is assumed.
24
Wake speed Wake width

25. VIDMAP: Structure
25
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process

26. Sensitivity Analysis of Energy Production
 Sensitivity analysis is performed to quantify the sensitivity of the
energy production model for a 100-turbine wind farm with respect to:
1. the independent first-level inputs; and
2. the deviations/errors in the upstream models.
 To perform sensitivity analysis, the sample set was prepared from:
26
Independent first-level inputs
Normalized errors/deviations in upstream models

27. Sensitivity Analysis Method
 We use the Extended Fourier Amplitude of Sensitivity Test (eFAST),
which is a variance-based global sensitivity analysis method
 Based on Fourier analysis, the first-order index is defined as the ratio of the
conditional variance due to each input parameter to the variance of the model
output
푆푖 =
2
휎푌 푋푖
2
휎푌
 The total-order index estimates the sum of all effects involving the associated
input parameter
푆푇푖 = 1 −
2
휎푌 푋≠푖
2
휎푌
 We employ the eFAST implementation through the statistical tool, R,
using a sample set of 20,000 data points.
27

28. VIDMAP: Structure
28
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process

29. VIDMAP: Illustration
 Connectors are colored based on 1st order sensitivity indices.
 Total order indices are dominant, indicating highly coupled impact.
 Model blocks are colored based on the variance of the model error or
29
model deviation.

30. VIDMAP: Important Observations
Among the independent inputs, turbine features have the strongest impact.
The turbine power response model and the wake width estimation model are
observed to have the strongest impact among model.
These two models are also associated with the highest degrees of uncertainty.
30

31. Concluding Remarks
 We developed a visualization framework (VIDMAP) for informed
model-based design of wind farms.
 Specifically, we quantified and presented a MBSD visualization for:
1. Inter-model sensitivities and model-input sensitivities;
2. Model-induced uncertainties.
 The VIDMAP obtained is found to be uniquely helpful in pointing out:
 Which models/inputs in the WFLO process have stronger impact on the
energy production estimates – turbine features, turbine power response
model, and wake model.
 Which models have higher degrees of uncertainty - turbine power response
model, and wake width estimation model.
31

32. Future Directions
 Develop and implement a more standardized quantification of model
uncertainty, e.g., in comparison to measured data.
 Develop informed decision-making rules/strategies that directly utilize
VIDMAP – towards faster and more reliable wind farm design.
32

33. Questions
and
Comments
33
Thank you

34. Major Challenges: Wind Farm Modeling
The state of the art (2009) in modeling wind farm energy
production (for design purposes) does not capture the coupled
impact of the key natural/design factors at affordable
computational costs*:
Prior
Research
1. Turbines with differing features (size/power characteristics) are not considered;
2. Variability of induction factor or energy loss fraction/turbine is not considered;
3. Coupled variation of wind speed, wind direction, and turbulence intensity not captured
4. High-fidelity wake models are computational prohibitive: current LES models [NREL SOFWA, 2012]
ABL over topography
34/85
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et
al.
Model Based Systems
Design
Integrative Modeling and
Design of Wind Farms
Energy-Sustainable Smart
Buildings
Reconfigurable Unmanned
Aerial Vehicles (UAV)
would need 600 million CPU-hours for optimizing a 25-turbine farm
5. Current WF energy output models do not account for spatial variations of the boundary layer over the
site (e.g., due to vegetation cover or topographic variations)
Different turbine
sizes available
CT and energy
loss varies
IPCC, 2011; Chowdhury et al., 2013; ETH LEC,

35. Major Challenges: Wind Farm Design
The state of art in wind farm layout design makes
limiting assumptions*:
1. Selection and siting of turbines are not simultaneously optimized.
2. The flexibility of installing non-identical turbines on a site is generally lacking.
3. The extent of the site to be used (land area and shape) and the total nameplate capacity
are prescribed prior to farm layout design (not quantitatively decided) .
4. Existing methods do not allow exploration of the important trade-offs among the
engineering, socio-economic, & environmental objectives of wind farm development.
5. Existing methods generally pursue decision-making at a single scale of wind power
generation technology (e.g., blade-scale or turbine-scale or farm-scale) – propagation
of performance uncertainties and the impact of design-decisions across scales remain
unexplored. Prior Research
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010
35/85
Model Based Systems
Design
Integrative Modeling and
Design of Wind Farms
Energy-Sustainable Smart
Buildings
Reconfigurable Unmanned
Aerial Vehicles (UAV)