Wind resources vary significantly in strength from one location to another over a wide geographical region. The major turbine manufacturers offer a family/series of wind tur- bines to suit the market needs of different wind regimes. The current state of the art in wind farm design however does not provide quantitative guidelines regarding what turbine feature combinations are suitable for different wind regimes, when turbines are operating as a group in an optimized layout. This paper provides a unique exploration of the best tradeoffs between the cost and the capacity factor of wind farms (of specified nameplate capacity), provided by the currently available turbines for different wind classes. To this end, the best performing turbines for different wind resource strengths are identified by minimizing the cost of energy through wind farm layout optimization. Exploration of the “cost - capacity factor” tradeoffs are then performed for the wind resource strengths cor- responding to the wind classes defined in the 7-class system. The best tradeoff turbines are determined by searching for the non-dominated set of turbines out of the pool of best performing turbines of different rated powers. The medium priced turbines are observed to provide the most attractive tradeoffs − 15% more capacity factor than the cheapest tradeoff turbines and only 5% less capacity factor than the most expensive tradeoff turbines. It was found that although the “cost - capacity factor” tradeoff curve expectedly shifted towards higher capacity factors with increasing wind class, the trend of the tradeoff curve remained practically similar. Further analysis showed that the “rated power - rotor diameter” com- bination and the “rotor diameter/hub height” ratios are very important considerations in the current selection and further evolution of turbine designs. We found that larger rotor diameters are not preferred for mid-range turbines with rated powers between 1.5 - 2.5 MW, and “rotor diameter/hub height” ratios greater than 1.1 are not preferred by any of the wind classes.

1. Exploring the “Cost - Capacity Factor” Tradeoffs
Offered by the Best Performing
Commercial Wind Turbines
Souma Chowdhury*, Jie Zhang*, Ali Mehmani#, Achille Messac#, and
Luciano Castillo**
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
# Syracuse University, Department of Mechanical and Aerospace Engineering
** Texas Tech University, Department of Mechanical Engineering
14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
17 - 19 September 2012, Indianapolis, Indiana

2. Key Research Questions
1. What types of commercial turbines perform the best for different wind
regimes?
2. What are the best “cost – capacity factor” tradeoffs offered by these
turbines?
3. How are the best trade-offs related to turbine feature combinations?
2
The Benefit
 Manufacturers: Help develop better product family of turbines
 Wind farm developers: Help gauge overall profitability of wind projects
based on currently available turbines.

3. Regional Variations in a Wind Energy Potential
 The wind pattern/regime varies significantly
over a target market (e.g. onshore USA).
 overall energy available
 variation of wind with time
3
 Turbines with unique feature combinations are necessary to suit the
needs of different wind patterns.
http://www.ge-energy.com/wind

4. Turbine Selection Criteria
Conventional Methods
 Turbines that offer the best trade-off between:
1. Long term energy production capacity for the given resource conditions
2. Survivability in the given site conditions (load bearing capacity)
3. Life-cycle costs
 Other important considerations: Performance history of the specific
turbine-model and of the manufacturer.
 IEC ratings provide information regarding criteria 1 and 2.
Limitations of Conventional Methods:
 Performance of the turbine as a part of an optimized array of turbines
is not considered.
4

5. Presentation Outline
Research Objectives & Introduction
Determining Optimum Turbine Choices
Exploring the Best “Cost – Capacity Factor”
Tradeoffs
5

6. Presentation Outline
Research Objectives & Introduction
Determining Optimum Turbine Choices
Exploring the Best “Cost – Capacity Factor”
Tradeoffs
6

7. Research Objectives
 Determine the best “cost – capacity factor” tradeoffs
offered by commercial turbines for different wind classes.
 Explore how the best tradeoffs are related to the major
turbine features.
Background: This research is based on the comprehensive
framework developed to determine the best performing turbines
for different wind regimes, and quantify their market suitability
using wind map information*.
7* Chowdhury et. Al, AIAA SDM 2012

8. Optimization of farm
layout and turbine
type selection
UWFLO
Overall Framework
8
Generate a set of N
random average wind
speed (AWS) values
Sobol’s Algorithm
AWS-1:
Minimum COE
Optimal Turbine
AWS-2:
Minimum COE
Optimal Turbine
AWS 3:
Minimum COE
Optimal Turbine
Determine the best
cost – capacity factor
tradeoffs from the
best turbines of
different rated-
power classes
Commercial turbine
specifications:
Rated Power, Rotor-
Diameter, Tower
Height, Drive-Train

9. Assumptions
 Load bearing capacity (survivability) of a turbine is not
considered in the optimum turbine selection process.
 A generic normalized power characteristics is used for all
turbines; it is scaled using the rated, cut-in and cut-out speed
of each turbine.
9

10. Presentation Outline
Research Objectives & Introduction
Determining Optimum Turbine Choices
Exploring the Best “Cost – Capacity
Factor” Tradeoffs
10

11. Wind Farm Optimization
 Purpose of wind farm optimization: For a given average wind speed,
determine the turbine choice that provides the minimum Cost of Energy,
when operating as a group in an optimized layout (arrangement).
 From the average wind speed value (s), a distribution of wind speed is
estimated using the 1-parameter Rayleigh distribution.
11
Rayleigh parameter, s

12. Unrestricted Wind Farm Layout Optimization (UWFLO)*
12
UWFLO
Framework
Wind
Distribution
Model
Power
Generation
Model
Wind Farm
Cost Model
Optimization
Methodology
Unique features of UWFLO:
 Avoids limiting restrictions on the layout pattern of the wind farm.
 Uniquely capable of simultaneously optimizing the farm layout and the
selection of the turbine-type(s) to be installed.
 Uses a distribution of wind conditions.
Other Wind Farm Optimization Approaches
• Array Layout approach: Sorenson et al., 2006; Mikkelson et al., 2007;
• Grid-based approach: Grady et al., 2005; Sisbot et al., 2009; Gonzleza et al., 2010
*Chowdhury et al. (Renewable Energy, 2012)

13. Wind Farm Power Generation Model
13
 Turbines are ranked in terms of the order in
which they encounter the incoming wind
 Turbine-j is in the influence of the wake of
Turbine-i, if and only if
 Effective velocity of wind
approaching Turbine-j:
 Power generated by Turbine-j:
Avian Energy, UK
Standard wake velocity deficit models and wake superposition
models are used (Frandsen et al., Katic et al.)

14. Wind Turbine Cost Model
 We use the Wind Turbine Design Cost and Scaling (WTDCS) model by
Fingersh et al. (NREL) to represent the wind farm cost, CFT
CMF: total manufacturing cost; CBS: balance-of-station cost; CLR: levelized replacement cost (LRC)
 All costs components are represented as functions of rated power, rotor
diameter, hub height, and type of drive train.
 Available drive-train types:
1. Three-stage gearbox with high speed generator
2. Direct-drive
14
O&M Costs are not considered, since it was expressed solely as a function of
annual energy production, and is a small fraction of the total cost for onshore
wind farms.
FTC
COE
AEP


15. Problem Definition
15
Land area of the circular farm:
With t = 21, we get an area of 11.7 hectares/MW (NREL’s estimate = 34.5 ± 22.4 hectares/MW)
Inter-Turbine Spacing
Farm Boundaries
Total number of allowed
commercial turbine models
Mixed-integer non-linear programming problem (with highly
multimodal functions and high number of design variables)
Solved by
Mixed-Discrete Particle Swarm Optimization

16. Turbine
Manufacturers
GE
Vestas
Enercon
Siemens
Goldwind
Suzlon
Gamesa
Rated Power
Class
No. of available
Choices
No. installed in
the farm
0.60 3 42
0.80 7 31
0.85 13 29
0.90 3 28
1.25 6 20
1.50 16 17
1.60 5 16
1.80 10 14
2.00 36 13
2.30 14 11
2.60 3 10
2.75 4 9
3.00 11 8
Optimal Turbine Selection: Specifications
 Optimization is performed separately for each rated power class (owing
to differing numbers of design variables involved)
16
131 commercially available turbines
are allowed to be selected
 Optimum turbine selection is performed for a set of 25 random values
of average wind speed (3.5-10.0 m/s)

17. Performance of the Optimally Selected Turbines
 Beyond average wind speeds of 7
m/s, the decrease in the COEmin is
marginal
 For high average wind speeds,
there is less than 25% difference
in the COEmin accomplished by
the best performing turbines of
different rated-power classes
17

18. Presentation Outline
Research Objectives & Introduction
Determining Optimum Turbine Choices
Exploring the Best “Cost – Capacity
Factor” Tradeoffs
18

19. The Best “Cost – Capacity Factor” Tradeoffs
 Out of the pool of best performing turbines (of different rated power
class) for different wind regimes, we select the best tradeoff choices.
 To this end non-dominated solution searching is used with respect to the
cost/kW installed of and the capacity factor yielded by the turbines.
 For ease of exploration, we consider the best tradeoffs corresponding to
the 7 average wind speed values closest to the 7 wind classes [NREL*].
19*Renewable Resource Data Center, NREL

20. “Cost – Capacity Factor” Tradeoffs for Different Wind
Classes
 With increasing wind class, the
tradeoff curve shifts towards higher
capacity factors.
 For an increase of $13/kW installed
in average annual cost, the increase
in farm capacity factor is
approximately 20% for each wind
class.
 The initial cost increase of $7/kW
installed allows a significantly
higher increase in capacity factor
(14-15%); thereafter, the capacity
factor increases only 5% for the
next $6/kW cost increase –
medium-priced turbines thus offer
more attractive tradeoffs.
20

21. Turbine Features Offering the Best Tradeoffs
 Some of the taller turbines are less expensive and yield lower capacity
factors compared to turbines with shorter towers but similar rotor sizes
(mid-size rotors of approx. D=70 m) – Turbine 3 vs. Turbine 4
21
Wind Classes 1-2

22. Turbine Features Offering the Best Tradeoffs
22
Wind Classes 3-4
 Some of the taller turbines are less expensive and yield lower capacity
factors compared to turbines with shorter towers but similar rotor sizes
(mid-size rotors of approx. D=70 m) – Turbine 2 vs. Turbine 5

23. Turbine Features Offering the Best Tradeoffs
23
Wind Classes 5-6
 Some of the taller turbines are less expensive and yield lower capacity
factors compared to turbines with shorter towers but similar rotor sizes
(mid-size rotors of approx. D=70 m) – Turbine 3 vs. Turbine 4.
 Shorter turbines are preferred for higher wind classes.

24. Some of the Taller Turbines are Cheaper and Providing
Lower Capacity Factors!!!
 Taller tower are generally
associated with greater costs.
 However, in this case, the taller
towers also correspond to higher
rated powers (2.5 vs. 1.5 MW).
 The cost reduction for higher
rated powers outweighs the cost
appreciation associated with
taller towers.
24
For Rotor Diameter = 70m
3
4

25. Turbine Feature Analysis: D and Pr
 For mid-range turbines (1.5-
2.7MW), larger rotors are not
preferred.
 Higher costs and greater
wake effects most probably
make larger rotor diameters
less desirable, especially for
mid-range turbines.
 The best tradeoff turbines
cost $50/kW or less.
25
Circles : Best tradeoff turbines; Triangles : Other dominated turbines

26. Turbine Feature Analysis: D and H
 Towers heights below 65m are
not preferred for any wind
class.
 The desirable D/H ratios are
below 1.1, whereas D/H ratios
of up to 1.5 are currently
available.
 Hence, the pursuit of larger
rotors should also seek a
necessary balance between
rotor diameter and hub height.
26
Circles : Best tradeoff turbines; Triangles : Other dominated turbines

27. Concluding Remarks
 This paper explores what types of turbines provide the best tradeoffs between
cost and energy production capacity for various wind regimes.
 In general, the medium priced turbines provided the most attractive tradeoffs
− they offered 15% more capacity factor than the cheapest tradeoff turbines
and only 5% less capacity factor than the most expensive turbines.
 “Rotor diameter/hub height” (D/H) ratios greater than 1.1 were not preferred
by any of the wind regimes.
 Larger rotor diameters are not preferred for higher rated turbines (with rated
powers between 1.5 - 2.7 MW).
27

28. Future Work
 Consider other important aspects of turbine selection - e.g. load bearing
capacity of the turbine.
28

29. Acknowledgement
• I would like to acknowledge my previous research
adviser Prof. Achille Messac, and my co-adviser
Prof. Luciano Castillo for their immense help and
support in this research.
• Support from the NSF Awards is also
acknowledged.
29

30. Questions
and
Comments
30
Thank you

31. Broad Research Question
How to quantify:
 The demand potential of different wind turbines to aid
turbine manufacturers?
 The performance potential (COE) of a given geographical
region to aid wind energy investors?
31
COE: Cost of Energy produced by the farm

32. Research Strategy
Wind
Regimes
Properties
of available
commercial
turbines
1. Best performing turbines
and their performance
2. Cost – Capacity Factor
tradeoffs offered by the best
performing turbine-feature
combinations
32
A complex combination of
advanced models

33. 33
Annual average wind speed (AWS) is a measure of the resource strength/potential

34. Wind Map Information
 Wind map is digitized using image processing tools
 Total area under different average wind speeds (AWS) is estimated with
an interval of 0.5 m/s
 A normal distribution is fitted to represent the geographical distribution
of average wind speeds (AWS) over contiguous USA
34
  5.6 m/s
s  1.3 m/s

35. Optimal Turbine Selection: Results
 The best performing turbines among all rated power classes (best of the
best) are of direct-drive type.
 For AWS > 6.5 m/s, 2.3 MW turbines performed the best
 For AWS < 6.5 m/s, 3.0 MW turbines performed the best
35

36. The Best COE Accomplished for any Given Wind Regime
u36
Wind Farm
Optimization
UWFLO
Optimize Turbine
Choice - 1
Optimize Layout - 1
Optimize Turbine
Choice - 2
Optimize Layout - 2
Optimize Turbine
Choice - n
Optimize Layout - n
Average wind
speed - 1
Average wind
speed - 2
Average wind
speed - n
Minimum
Cost of Energy
(COE) - 1
Minimum
Cost of Energy
(COE) - 2
Minimum
Cost of Energy
(COE) - n
Regression Model

37. Regression Model: COEmin = f (average wind speed)
 An inverse polynomial regression (multiplicative surrogate) is performed to
represent the minimum COE accomplished by the best performing turbine
(of each class) as a function of AWS, s.
where c1 > 0 and c2 < 0
37
Direct-drive
NOT available
Accurate Fits obtained:
R2 > 0.96
-1.4 > c2 > -2.2

38. Performance of the Optimally Selected Turbines
 Beyond average wind speeds of 7 m/s,
the decrease in the COEmin is marginal
 For high average wind speeds, there is
less than 25% difference in the COEmin
accomplished by the best performing
turbines of different rated-power
classes
38
 The capacity factor of the optimized
farm is observed to follow roughly a
linear variation with average wind
speed (wind distribution and wake
effects)
 The minimized COE is expected to vary
as a inverse polynomial function of the
AWS

39. Turbine Suitability for a Target Market
 The selection likelihood of turbine feature combinations governed by:
1. How often different feature combinations were selected during the 13x25
wind farm optimizations?
2. What level of performance (in terms of COE) was offered by the best
performing turbines (from each rated-power class)?
3. The probability of occurrence of each of the 25 sample average wind speeds
over the US onshore market.
 A metric called the Performance-based Expected Market Suitability
(PEMS) is developed to represent the likely market success of turbines.
 PEMS is expressed in total Gigawatts of likely installation of that turbine
in the concerned market.
39

40. Performance-based Expected Market Suitability (PEMS)
40
* A total wind power potential value of 10,459 GW at 80 m height for the contiguous
USA (excluding Hawaii and Alaska), as estimated by NREL is used in this paper.
Probability of occurrence of the
jth sample average wind speed
Total wind power potential
of USA in GW*
COE obtained by ith turbine for the
jth sample average wind speed

41. Market Suitability: Rotor Diameter & Rated Power Combinations
 Expectedly, “higher rated powers and larger rotor diameters” are the most
favored among available commercial variants.
41

42. Market Suitability: Hub Height & Rated Power Combinations
 “Higher rated-power turbines with higher tower heights” are far less
favored by the US onshore conditions than some (not all) of the “small-
medium rated power turbines with higher hub heights” (e.g. 0.8 MW and
1.5 MW)
42

43. Market Suitability: Hub Height & Rotor Diameter Combinations
 “Turbines with larger rotor diameter and medium sized tower heights”
(approx. 100 m) are the most popular, which again indicates that relatively
higher tower heights are not favored for the larger turbines.
 The use of shear profiles other than log law and power law should provide
further insights in this direction.
43

44. Optimized Layout
44
An optimally selected 2.0 MW turbine
 Rotor Diameter: 90 m
 Tower Height: 100 m

45. Turbine Characterization Model
45
• Every turbine is defined in terms of its rotor diameter, hub-height, rated
power, and performance characteristics, and represented by an integer
code (1 – 131).
• The “power generated vs. wind speed” characteristics for GE 1.5 MW xle
turbines is used to fit a normalized power curve Pn().
• The normalized power curve is scaled back using the rated power and
the rated, cut-in and cut-out velocities given for each turbine.
• However, if power curve information is available for all the turbines
being considered for selection, they can be used directly.
if <
1 if
0 if
in
n in r
r in
out r
r
out
U U
P U U U
U U
P
U U U
P
U U
  
  
 

  
 




46. Wake Model
46
 We implement Frandsen’s velocity deficit model
Wake growth Wake velocity
a – topography dependent wake-spreading constant
 Wake merging: Modeled using wake-superposition principle
developed by Katic et al.:
Frandsen et al., 2006; Katic et al.,1986

47. Annual Energy Production
• Annual Energy Production of a farm is given by:
• This integral equation can be numerically expressed as:
• A careful consideration of the trade-offs between numerical errors and
computational expense is important to determine the sample size Np.
47
Wind Probability Distribution
Kusiak and Zheng, 2010; Vega, 2008
Wind Farm Power Generation

48. Features of the Best Performing Turbines
 Smaller rotor diameters and lower tower heights of the 0.90 MW turbines
restricts the amount of power these turbines can extract from the wind.
 For resources with higher average wind speeds, relatively lower tower
heights are preferred.
48

49. Wind Energy - Overview
 Currently wind contributes 2.5% of the global electricity consumption.*
 The 2010 growth rate of wind energy has been the slowest since
2004.*
 Large areas of untapped wind potential exist worldwide and in the US.
 Among the factors that affect the growth of wind energy, the state-of-
the-art in wind farm design technologies plays a prominent role.
49
www.prairieroots.org
NREL, 2011*WWEA, 2011

50. 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.
50

51. The Best COE Accomplished for any Given Wind Regime
51
Wind Farm
Optimization
UWFLO
Optimize Turbine
Choice - 1
Optimize Layout - 1
Optimize Turbine
Choice - 2
Optimize Layout - 2
Optimize Turbine
Choice - n
Optimize Layout - n
Average wind
speed - 1
Average wind
speed - 2
Average wind
speed - n
Minimum
Cost of Energy
(COE) - 1
Minimum
Cost of Energy
(COE) - 2
Minimum
Cost of Energy
(COE) - n
Regression Model

52. Presentation Outline
• Research Objectives
• Characterizing Wind Map Information
• Exploring “Turbine - Wind Regime” Compatibilities
– Turbine Characterization Model and Cost Model
– Wind Farm Optimization
• Optimal Turbine Choices and their Performance
– Results and Discussion
– Turbine Suitability for the US Onshore Market
• Concluding Remarks
52