A Response Surface Based Wind Farm Cost (RS-WFC) model, is developed to evaluate the economics of wind farms. The RS-WFC model is developed using Extended Radial Basis Functions (E-RBF) for onshore wind farms in the U.S.. This model is then used to explore the in uence of di erent design and economic parameters, including number of turbines, rotor diameter and labor cost, on the cost of a wind farm. The RS-WFC model is composed of three parts that estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The accuracy of the cost model is favorably established through comparison with pertinent commercial data. Moreover, the RS-WFC model is integrated with an analytical power generation model of a wind farm. A recently developed Unrestricted Wind Farm Layout Optimization (UWFLO) model is used to determine the power generated by a farm. The ratio of the total annual cost and the energy generated by the wind farm in one year (commonly known as the Cost of Energy, COE) is minimized in this paper. The results show that the COE could decreasesigni cantlythroughlayoutoptimization,toobtainmillionsofannualcostsavings.

1. Economic Evaluation of Wind Farms
Based on
Cost of Energy Optimization
Jie Zhang*, Souma Chowdhury*, Achille Messac# and Luciano Castillo*
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
# Syracuse University, Department of Mechanical and Aerospace Engineering
13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference
September 13-15, 2010
Fort Worth, Texas

2. Outline
• Motivation
• Research Objectives
• Literature Review
• Response Surface Based Wind Farm Cost
(RS-WFC) Model
• Cost of Energy Optimization
• Concluding Remarks and Future Work
2

3. Motivation
 The global installed wind capacity has been growing at an
average rate of 28% per year.
 Wind energy is planed to account for 20% of the U.S. electricity
consumption by 2030.
 Efficient planning and resource management is the key to the
success of an energy project.
 Accurate (flexible to local market changes) cost models of wind
projects would allow investors to better plan their projects.
 Investors can provide valuable insight into the areas that require
further development to improve the overall economics of wind
energy.
3

4. Motivation
International ranking of wind power
Country/Region
Total capacity
end 2009 [MW]
Added capacity
2009 [MW]
Growth rate
2009 [%]
USA 35,159 9,922 39.3
China 26,010 13,800 113.0
Germany 25,777 1,880 7.9
Spain 19,149 2,460 14.7
India 10,925 1,338 14.0
Italy 4,850 1,114 29.8
France 4,521 1,117 32.8
UK 4,092 897 28.1
Portugal 3,535 673 23.5
Denmark 3,497 334 10.6
4
Source: Berkely Lab estimates based on data from BTM Consult and elsewhere
U.S. is lagging behind other countries in wind energy as a percentage of electricity consumption

5. Current
Planned 2030
10 fold increase
Wind Energy
Wind Energy
Motivation
5
• Accurate cost models

6. Research Objectives
Develop an accurate cost model of wind farms
Construct a U.S. cost map for wind farm development
Investigate the optimal cost of a wind farm
6

7. Literature Review
• Existing Cost Models
• Short-cut Model
• Cost Model for the Greek Market
• OWECOP-Prob Cost Model
• JEDI-Wind
• Opti-OWECS Cost Model
• Existing O&M Cost Models
• The Operation & Maintenance Cost Estimator (OMCE)
• Cost of Grid Connection
7

8. Cost models comparison
(a) (b)
(c) (d)
(e) (f)
8

9. Advantages of RS-WFC Model
• Evaluates the Cost of Energy (COE)
• Evaluates the power generation
• Includes life cycle cost
• Considers financial parameters
• Uses appropriate input and output parameters
• Provides analytical expression
9

10. Development of RS-WFC Model
• STEP I: This step formulates the wind farm cost model using
response surface method. The response surface is trained using the
data from the Energy Efficiency and Renewable Energy Program
at the U.S. Department of Energy.
• STEP II: This step incorporates a power generation model
(Unrestricted Wind Farm Layout Optimization (UWFLO)) with
the RS-WFC model.
• STEP III: The COE is evaluated and optimized in this step. COE is
defined as the total annual cost divided by the energy generated by
a wind farm in one year.
10

11. 11

12. Response Surface Methods
 Typical response surface methods include:
• Quadratic Response Surface Methodology (QRSM)
• Radial Basis Functions (RBFs)
• Extended Radial Basis Functions (E-RBF)
• Kriging
• Artificial Neural Networks (ANN), and
• Support Vector Regression (SVR)
12
Local accuracy
Nonlinear
Extended Radial Basis Functions (E-RBF) method is adopted to
develop the RS-WFC model in this paper. But the RS-WFC model
also has the flexibility to use other response surface methods.

13. E-RBF Method
13
Extended Radial Basis Functions (E-RBF) is a combination of Radial
Basis Functions (RBFs) and Non-Radial Basis Functions (N-RBFs).
 Radial Basis Functions
The RBFs are expressed in terms of the Euclidean distance,
y (r) = r2 + c2
where c > 0 is a prescribed parameter.
The final approximation function is a linear combination of these basis
functions across all data points.
( )
% =å -
f x sy x x
1
( )
np
i
i
i
=
r = x - xi
One of the most effective forms is the multiquadric function:

14. 14
E-RBF Method
 Non-Radial Basis Functions
N-RBFs are functions of individual coordinates of generic points x
relative to a given data point xi, in each dimension separately
It is composed of three distinct components
( i ) L L ( i ) R R ( i ) ( i )
ij j ij j ij j ij j
f x =a f x +a f x +b f b x
 Extended Radial Basis Function (E-RBF)
The E-RBF approach incorporates both the RBFs and the N-RBFs
np np m
( )
% =å - i +ååéë L L i + R R i + i
ùû
f x sy x x a f x a f x b f b x
( ) ( ) ( ) ( )
i ij j ij j ij j
i i j
= = =
1 1 1
Methods: (i) linear programming, or (ii) pseudo inverse.

15. RS-WFC Model
• Installation cost,
• Annual O&M cost,
• Total annual cost,
in C
O&M C
t C
 The number of coefficients of
the E-RBF cost model,
(3 1) u p n = m+ n
p ( n , Number of data points)
15
Function list of the RS-WFC model
Model Expression No. of
variables
Data
points
No. of
coefficients
Cin = f(CLC,CLT,CLM) 3 40 400
CO&M = f(N,CLT,CLM) 3 500 5,000
Ct = f(N,D) 2 101 707
Parameter Selection for RS-WFC Model
Parameter λ c t
Value 4.75 0.9 2

16. Total Annual Cost VS. The Input Factors
16
 The total annual cost deceases from $131.3/KW
to $126.4/KW (approximately 3.73%) when the
rotor diameter of a wind turbine increases from
50m to 100m.
 The total annual cost decreases slowly when the
rotor diameter is less than 70m.
 The total annual cost begins to decrease sharply
when the rotor diameter changes from 70m to
85m.
 If the rotor diameter continues to increase beyond
85m, the change in the total annual cost is
particularly limited.
The total annual cost based on the rotor
diameter of a wind turbine

17. 17
Total Annual Cost VS. The Input Factors
 The total annual cost decreases from
$131.48/KW to $126.38/KW (approximately
3.88%) while the number of wind turbines
increases from 10 to 100.
 The total annual cost does not change
significantly when the number of wind
turbines increases beyond 60.
The total annual cost based on the number of
wind turbines

18. State Averaged Cost Map
18

19. 19

20. Power Generation Model
• The Unrestricted Wind Farm Layout Optimization
(UWFLO) Power Generation Model
C 20 p: power coefficient curve, a: induction factor curve

21. 21

22. Optimizing Cost of Energy (COE)
• COE is measured by Levelized Production Cost
(LPC)
COE C P N
= ´ ´ ´
AEP
• AEPnet: Net Annual Energy Production
22
0 1000 t
net
365 24 net farm AEP = ´ ´ P

23. Wind Farm Optimization Problem Formulation
Optimization Problem Constraints
Minimum clearance
Ensure the location of wind
turbines within the fixed size
23

24. Case Study
Wind farm parameters Wind conditions
Parameter Value
Number of wind turbines 25
Type of wind turbines ENERCON
E-82
Length of the wind farm 1,200m
Breadth of the wind farm 800m
Rated power (P0) 2MW
Rotor diameter (D) 82m
Hub height (H) 85m
Cut-in wind speed 2m/s
Cut-out wind speed 28m/s
Rated wind speed 13m/s
Parameter Value
Average wind speed 8.35m/s
Wind direction 00 with positive
x-axis
Air density 1.2kg/m3
24

25. 25
Estimated i Estimated pnodwucetri ocno effafcictoiern ctu cruvrev, ea, Cp

26. Convergence history
• COE decreases
approximately by 5.41%
• Annual cost savings for
the wind farm is
approximately 5.3%,
$342,151
26

27. Convergence history
• The power generated
increases approximately
by 5.23%
27

28. Conclusion
• A Response Surface Based Wind Farm Cost (RS-WFC) model was
developed, which can estimate: (i) the installation cost, (ii) the annual
O&M cost, and (iii) the total annual cost of a wind farm.
• A power generation model was incorporated into the RS-WFC model.
• The Cost of Energy (COE) was minimized to improve the overall
economics of wind energy project.
• The preliminary cost map shows wide variation in wind farm cost in
the U.S..
• The resulting cost model could be a useful tool for wind farm
planning.
28

29. Future Work
Optimization of Operation and Maintenance (O&M)
strategy for offshore wind farms;
Pattern classification based market demand analysis
methodology: investigate the demand pattern and
identify markets niches for offshore wind turbines.
29

30. 30
Selected References
 Zhang, J., Chowdhury, S., Messac, A., Castillo, L., and Lebron, J., “Response Surface Based Cost
Model for Onshore Wind Farms Using Extended Radial Basis Functions”. ASME 2010 International
Design Engineering Technical Conferences.
 Chowdhury, S., Messac, A., Zhang, J., Castillo, L., and Lebron, J., “Optimizing the Unrestricted
Placement of Turbines of Differing Rotor Diameters in a Wind Farm for Maximum Power Generation”.
ASME 2010 International Design Engineering Technical Conferences (IDETC).
 Mullur, A. A., and Messac, A., 2005. “Extended radial basis functions: More flexible and effective
metamodeling”. AIAA Journal, 43(6), pp. 1306–1315.
 Mullur, A. A., and Messac, A., 2006. “Metamodeling using extended radial basis functions: a
comparative approach”. Engineering with Computers, 21(3), pp. 203–217.
 Goldberg, M., 2009. Jobs and Economic Development Impact (JEDI) Model. National Renewable
Energy Laboratory, Golden, Colorado, US, October.
 Sisbot, S., Turgut, O., Tunc, M., and Camdali, U., 2009. “Optimal positioning of wind turbines on
gokceada using multi-objective genetic algorithm”. Wind Energy.
 Pallabazzer, R., 2004. “Effect of site wind properties on wind-electric conversion costs”. Wind
Engineering, 28(6), pp. 679–694.
 Jin, R., Chen, W., and Simpson, T., 2001. “Comparative studies of metamodelling techniques under
multiple modelling criteria”. Structural and Multidisciplinary Optimization, 23(1), pp. 1–13.
 Lindenberg, S., 2008. “20% wind energy by 2030: Increasing wind energy contribution to u.s.
electricity supply”. Tech. Rep. DOE/GO-102008-2567, U.S. Department of Energy: Energy Efficiency
& Renewable Energy, July.
 Cockerill, T. T., Harrison, R., Kuhn, M., and Bussel, G. V., 1998. “Opti-owecs final report vol. 3:
Comparison of cost of offshore wind energy at European sites”. Tech. Rep. IW-98142R, Institute for
Wind Energy, Delft University of Technology, August.

31. Questions
and
Comments
31
Thank you