Wind Farm Layout Optimization (WFLO) is a typical model-based complex system design process, where the popular use of low-medium fidelity models is one of the primary sources of uncertainties propagating into the esti- mated optimum cost of energy (COE). Therefore, the (currently lacking) understanding of the degree of uncertainty inherited and introduced by different models is absolutely critical (i) for making informed modeling decisions, and (ii) for being cognizant of the reliability of the obtained results. A framework called the Visually-Informed Decision-Making Platform (VIDMAP) was recently introduced to quantify and visualize the inter-model sensi- tivities and the model inherited/induced uncertainties in WFLO. Originally, VIDMAP quantified the uncertainties and sensitivities upstream of the energy production model. This paper advances VIDMAP to provide quantifica- tion/visualization of the uncertainties propagating through the entire optimization process, where optimization is performed to determine the micro-siting of 100 turbines with a minimum COE objective. Specifically, we deter- mine (i) the sensitivity of the minimum COE to the top-level system model (energy production model), (ii) the uncertainty introduced by the heuristic optimization algorithm (PSO), and (iii) the net uncertainty in the minimum COE estimate. In VIDMAP, the eFAST method is used for sensitivity analysis, and the model uncertainties are quantified through a combination of Monte Carlo simulation and probabilistic modeling. Based on the estimated sensitivity and uncertainty measures, a color-coded model-block flowchart is then created using the MATLAB GUI.

1. A Visually-Informed Decision-Making Platform for
Wind Farm Layout Optimization
Souma Chowdhury#, Weiyang Tong*, Ali Mehmani*, and Achille Messac#
# Mississippi State University, Department of Aerospace Engineering
* Syracuse University, Department of Mechanical and Aerospace Engineering
Research supported by the NSF Award: CMMI 1437746
11th World Congress on Structural and Multidisciplinary Optimization
June 7-12, 2015, Sydney, Australia

2. Presentation Outline
 Model-based Wind Farm Design – Challenges
 Motivation & Objectives: 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
2

3. Wind Farm Design
3
Natural resource
System
Environmental
System
Power Generation
System
Power
Transmission
System
Addressing inter & intra-system interactions
• Farm Power Generation
• Annual Energy Production
• Capacity Factor
• Cost of Energy
Wind Farm Layout
Optimization
Framework
Conditions Design Variables
• Turbine Locations
• Type(s) of Turbines
Objectives/Output
Other Design Factors
• Nameplate Capacity
• Land Area per MW inst.
• Land Aspect Ratio
• Land Orientation
• Distribution of Wind
Speed and Direction
• Atmospheric Turbulence
• Wind Shear
• Topography
Wake Effects
A Complex System

4. Model-based Wind Farm Design: Challenges
 Owing to the complexity of the system, and the multitude of variable
factors, model-based systems design (MBSD) is the de facto standard in
wind farm layout optimization (WFLO)*.
 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.
 Understanding and quantifying these uncertainties in the MBSD
process is therefore imperative to designing reliable wind farm
layouts.
4
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010; Chowdhury et al. 2012

5. 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 in the MBSD process.
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.
5

6. Motivating Approaches from Literature
 McManus et al., (2005) constructed a 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 for informed exploitation of different 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).
6

7. VIDMAP: Structure
7
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models & the optimization algorithm
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/algorithms and inter-model
sensitivities in the design process

8. Wind Farm Energy Production Modeling
(from the Unrestricted Wind Farm Layout Optimization
framework)
8

9. Wind Farm Energy Production
9
 Annual Energy Production (AEP) of a farm is given by:
 AEP is numerically expressed as:
 Power Generation (𝑷 𝒇𝒂𝒓𝒎) of a farm:
A complex multi-step function that considers the incoming wind conditions,
wake interactions among turbines (based on their location), wake losses, and
turbines’ power response to their estimated approaching wind speed.
𝑃𝑓𝑎𝑟𝑚 = 𝑓( 𝑈, 𝜃 , 𝑋, 𝑌 , 𝑇)
Probability of
wind condition
Wind farm power
generation
Variable Resource
Messac et al. 2012, Chowdhury et al. 2013, Zhang et al. 2013

10. Wind Farm Layout Optimization
10
• Minimize the Cost of Energy (COE) by optimizing the turbine locations.
• Subject to constraints associated with the land boundaries and the
minimum inter-turbine spacing.
• Optimization is performed by the Mixed-Discrete Particle Swarm
Optimization (MDPSO) algorithm.
Inter-Turbine Spacing

11. VIDMAP: Structure
11
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models & the optimization algorithm
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/algorithms and inter-model
sensitivities in the design process

12. 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)
12

13. 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 AWS (𝜇 = 5.6, 𝜎 = 1.3), reported by Chowdhury et
al., (AIAA SDM 2012) is adopted here to generate the AWS samples.
 For each sample AWS ∈ 3.5,10 , a Rayleigh wind speed distribution is
generated to serve as input to the energy production model (during optimization).
13

14. Design Input Variability
Turbine Features: A sample set of 24 unique 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.
Land Area/MW Installed: The range ( 10 − 50 ha/MW) is
motivated by the reported land footprint of US wind farms 1.
 Assuming a N×N layout of turbines (N=10), with rated power, PR, a sample
land area/MW of AMW, and a fixed land aspect ratio of 7/3, the average turbine
spacing can be perceived as:
𝑑 𝑠 =
1
𝑁 − 1
7
3
𝑁𝑃𝑅 𝐴
1/2
; 𝑑𝑙 =
1
𝑁 − 1
3
7
𝑁𝑃𝑅 𝐴
1/2
141 Denholm et al., Technical Report NREL/TP-6A2-45834, NREL, August 2009.

15. Incorporating Estimated Uncertainty: Energy Production Model
 In order to decouple the variance of the energy production model
(attributed to inherent model assumptions) from that of the independent
parameters, the deviation in its output (𝐸𝑓𝑎𝑟𝑚 ) is represented by a
stochastic parameter (ℇ 𝐸).
 ℇ 𝐸 follows the probability distribution determined via uncertainty
propagation in Chowdhury et al. (Aviation 2014) – with an estimated
variance of 0.0063.
 For every call to the energy production model during optimization, the
return value (estimated function) is given by:
𝑓𝐸 = 𝐸𝑓𝑎𝑟𝑚 1 + ℇ 𝐸
15

16. Uncertainty introduced by PSO Algorithm
 Mixed-Discrete PSO (MDPSO) is stochastic algorithm that involves
random operators, and is initiated with a randomly generated population of
candidate designs.
 As a result, the optimum solution obtained by PSO could vary from one run
of the algorithm to another (all prescribed conditions remaining the same).
 A mixture of 50 samples is created with Average Wind Speed, Land Area
per MW, and Deviation in WF Energy Production.
 WFLO is performed using MDPSO w.r.t. each of the 24 turbine types for
each sample: i.e., 𝟐𝟒 × 𝟓𝟎 optimization cases.
 For each optimization case, MDPSO is run 5 times, and the uncertainty in
the minimum COE estimated by the algorithm is given by:
16

17. VIDMAP: Structure
17
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models & the optimization algorithm
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/algorithms and inter-model
sensitivities in the design process

18. Sensitivity Analysis of Energy Production
 Sensitivity analysis was previously 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.
 The Extended Fourier Amplitude of Sensitivity Test (eFAST)* is
used, which is a variance-based global sensitivity analysis method.
18
Bounds and sampling strategy for inputs parameters for the Sensitivity Analysis
* Saltelli and Bolado 1998

19. VIDMAP: Structure
19
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models & the optimization algorithm
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/algorithms and inter-model
sensitivities in the design process

20. VIDMAP: Illustration
20
 Connectors are colored based on 1st order sensitivity indices.
 Model blocks are colored based on the variance of the model error or
model deviation.
 Total order indices are dominant, indicating highly coupled impact.

21. VIDMAP: Important Observations
21
It is observed that the optimization algorithm is reasonably robust with an estimated variation (in
optimum output) of only 0.12% over the five runs.
The sensitivity of the computed minimum COE to deviations in the energy production model appears
to be small -- small first order index of 0.00118.
The total order index of the deviation in energy production model output is significant (0.87) –
illustrating the coupled influence of different input factors and model assumptions.

22. Concluding Remarks
 We developed a visualization framework (VIDMAP) that allows
exploration of a model-based design process.
 Specifically, for Wind Farm Layout Optimization, we illustrated:
1. “Inter-model” sensitivities and “model – input” sensitivities;
2. Model-induced uncertainties and algorithm uncertainties.
 Important Observations:
 The robustness of the stochastic optimization algorithm – MDPSO
demonstrated a low variation of 0.12% in its optimum objective output.
 High total order sensitivity index of the deviations in the energy production
model; indicating that the uncertainty in the energy production model is
likely to influence decision-making when the following are being considered
in the planning stage of wind farm development.
1. multiple wind farm sites,
2. multiple turbine configuration, and
3. different land plot availability
22

23. Questions
and
Comments
23
Thank you

24. 24
A Design Process can be conceived as a flow of information.
Information
Criticality
Information
Expense
Information
Uncertainty
The Information Flow Perspective to MBSD

25. 25/85
Major Challenges: Wind Farm Modeling
*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)
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*:
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]
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,
Prior
Research
ABL over topography

26. 26/85
Major Challenges: Wind Farm Design
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010
Model Based Systems
Design
Integrative Modeling and
Design of Wind Farms
Energy-Sustainable Smart
Buildings
Reconfigurable Unmanned
Aerial Vehicles (UAV)
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

27. 27
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Jensen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Models w/o
turbulence
Models with
turbulence
Impact of Wake Model Choice: Sensitivity of WF Energy Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Jensen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Fixed incoming wind speed at 7 m/s Fixed incoming wind speed at 11 m/s
Weiyang et al.
IDETC 2013

28. Sensitivity Analysis of Optimized WF Energy Output
(incoming wind speed 10.35m/s – 12.65 m/s)
28
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Ishihara model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Larsen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Frandsen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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

29. Wind Farm Power Generation: Inflow & Shading
29 29
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
 Wake losses are modeled rank-wise:
Turbine-j is in the wake of Turbine-i, if and only if
Cal et al., 2010
Dedicated data More generic
Considers turbines with differing
rotor-diameters and hub-heights
Turbines ranked in order
of encountering wind
Modeling
turbine-wind-turbine
interactions

30. Wind Farm Power Generation: Wake Losses
30
 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
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub height
Turbulence
intensity
Jensen √ √ √ √
Frandsen √ √ √ √
Larsen √ √ √ √ √ √ √
Ishihara √ √ √ √ √ √
 2
2
3
4 1
1
2 4
g b
P
a a
D
k k U
 
 
 
 
Wake model:
At distance s
downstream
Novel dynamically-updated
turbine-adaptive energy loss
(variable induction factor, a)
GE 2.5MW
1
N
farm j
j
P P

 

31. 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 employed different approaches (presented in AIAA
Aviation 2014) to quantify the model-induced uncertainties, e.g.:
 quantify the variance in the output of low-fidelity model choices; or
 Use recorded data from a single site/case to estimate model error.
31
Chowdhury et al., AIAAAviation 2014

32. 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).
32
 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.

33. 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:
𝑈
𝑈 𝑟
=
𝑧
𝑧 𝑟
𝛼
; Log Law:
𝑈
𝑈 𝑟
=
𝑙𝑛 𝑧 𝑧0
𝑙𝑛 𝑧 𝑟 𝑧0
 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:
33

34. 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:
34
1Wharton and Lundquist, Environmental
Research Letters, January 2012

35. 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):
35
Wake speed Wake width
Tong et al.,
ASME IDETC 2013

36. 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.
36
Wake speed Wake width

37. 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
𝑆𝑖 =
𝜎 𝑌 𝑋𝑖
2
𝜎 𝑌
2
 The total-order index estimates the sum of all effects involving the associated
input parameter
𝑆 𝑇 𝑖
= 1 −
𝜎 𝑌 𝑋≠𝑖
2
𝜎 𝑌
2
 We employ the eFAST implementation through the statistical tool, R,
using a sample set of 20,000 data points.
37

38. 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.
38