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Response Surface Based Cost Model 
for Onshore Wind Farms 
Using Extended Radial Basis Functions 
Jie Zhang*, Souma Chowdhury*, Achille Messac# 
Luciano Castillo* and Jose Lebron* 
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering 
# Syracuse University, Department of Mechanical and Aerospace Engineering 
ASME 2010 International Design Engineering Technical Conferences 
(IDETC) and Computers and Information in Engineering Conference (CIE) 
August 15-18, 2010 
Montreal, Quebec, Canada
Outline 
• Motivation 
• Research Objectives 
• Literature Review 
• E-RBF Cost Model 
• Concluding Remarks 
• Future Work 
2
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
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
Current 
Planned 2030 
10 fold increase 
Wind Energy 
Wind Energy 
Motivation 
5 
• Accurate cost models
Research Objectives 
• Develop a cost model of wind farms 
• Analyze the cost of a wind farm 
• Construct a U.S. cost map for wind farm 
development 
6
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
Cost models comparison 
(a) (b) 
(c) (d) 
(e) (f) 
8
9
Advantages of E-RBF Cost Model 
• Includes life cycle cost 
• Considers financial parameters 
• Uses appropriate input and output parameters, and 
• Provides analytical expression 
10
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) 
11 
Local accuracy 
Nonlinear
E-RBF Method 
12 
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:
13 
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.
E-RBF Cost 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) 
14 
Function list of the E-RBF cost 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 E-RBF Cost Model 
Parameter λ c t 
Value 4.75 0.9 2
Installation Cost 
 The installation cost model is developed using data from 40 
different states of the U.S. 
15 
Sample data for developing installation cost model 
State Construction 
labor cost 
($/h) 
Technician 
labor cost 
($/h) 
Management 
labor cost 
($/h) 
Installation 
cost 
($/KW) 
California 20.70 30.97 49.56 2,107 
Colorado 18.32 25.00 40.00 2,043 
Iowa 16.16 22.18 35.28 2,011 
Kansas 16.26 26.77 35.49 2,012 
Minnesota 19.62 26.77 42.83 2,062
Annual O&M Cost 
• Training data: cost of all states in the U.S. (except the state 
of New York) 
Number 
of 
turbines 
Technician 
labor cost 
($/h) 
Management 
labor cost 
($/h) 
O&M 
cost 
($/KW) 
California 
20 19.82 49.56 26.58 
40 19.82 49.56 25.23 
60 19.82 49.56 23.95 
Colorado 
20 16.00 40.00 25.00 
40 16.00 40.00 23.64 
60 16.00 40.00 22.36 
16 
Sample data for developing O&M cost model
Annual O&M Cost VS. The Input Factors 
 The annual O&M cost increases approximately one dollar (per kilowatt installed) for each 
20 wind turbines. 
 When the number of wind turbines increases from 10 to 100, the annual O&M cost 
decreases sharply from $26.67/KW to 21.60/KW, approximately 19.01%. 
 When the number of wind turbines is small (less than 20), the change in the annual O&M 
cost is not clearly evident. 17
Total Annual Cost 
D(m) 49 55 59.2 65 80.5 82 
P0(MW) 0.60 0.85 1.00 1.25 1.50 1.65 
D(m) 84.25 88 92.13 100 101 
P0(MW) 2.00 2.10 2.30 2.50 3.00 
18 
Relation between rotor diameter and rated power
Total Annual Cost VS. The Input Factors 
19 
 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.
20 
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.
State Averaged Cost Map 
21
Conclusion 
• An Extended Radial Basis Function (E-RBF) cost 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. 
• The annual O&M cost roughly increases one dollar (per kilowatt 
installed) for each 20 more wind turbines installed. 
• The change of the total annual cost depends significantly on the number 
and rotor diameters of wind turbines. 
• The preliminary cost map shows wide variation in wind farm cost in the 
U.S.. 
• The resulting cost model can be a useful tool for wind farm planning. 
22
Future Work 
Optimization of cost of energy; 
Optimization of Operation and Maintenance (O&M) 
strategy for offshore wind farms; 
Extensive analysis of the demand and general 
market for critical energy products (turbines). 
23
24 
Selected References 
 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. 
 Kiranoudis, C., Voros, N., and Maroulis, Z., 2001. “Shortcut design of wind farms”. Energy Policy, 29, 
pp. 567–578. 
 Andrawus, J. A., Watson, J., Kishk, M., and Adam, A., 2006. “The selection of a suitable maintenance 
strategy for wind turbines”. Wind Engineering, 30(6), pp. 471–486.
Questions 
and 
Comments 
25 
Thank you

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COSTMODEL_IDETC_2010_Jie

  • 1. Response Surface Based Cost Model for Onshore Wind Farms Using Extended Radial Basis Functions Jie Zhang*, Souma Chowdhury*, Achille Messac# Luciano Castillo* and Jose Lebron* * Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering # Syracuse University, Department of Mechanical and Aerospace Engineering ASME 2010 International Design Engineering Technical Conferences (IDETC) and Computers and Information in Engineering Conference (CIE) August 15-18, 2010 Montreal, Quebec, Canada
  • 2. Outline • Motivation • Research Objectives • Literature Review • E-RBF Cost Model • Concluding Remarks • 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 a cost model of wind farms • Analyze the cost of a wind farm • Construct a U.S. cost map for wind farm development 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. 9
  • 10. Advantages of E-RBF Cost Model • Includes life cycle cost • Considers financial parameters • Uses appropriate input and output parameters, and • Provides analytical expression 10
  • 11. 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) 11 Local accuracy Nonlinear
  • 12. E-RBF Method 12 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:
  • 13. 13 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.
  • 14. E-RBF Cost 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) 14 Function list of the E-RBF cost 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 E-RBF Cost Model Parameter λ c t Value 4.75 0.9 2
  • 15. Installation Cost  The installation cost model is developed using data from 40 different states of the U.S. 15 Sample data for developing installation cost model State Construction labor cost ($/h) Technician labor cost ($/h) Management labor cost ($/h) Installation cost ($/KW) California 20.70 30.97 49.56 2,107 Colorado 18.32 25.00 40.00 2,043 Iowa 16.16 22.18 35.28 2,011 Kansas 16.26 26.77 35.49 2,012 Minnesota 19.62 26.77 42.83 2,062
  • 16. Annual O&M Cost • Training data: cost of all states in the U.S. (except the state of New York) Number of turbines Technician labor cost ($/h) Management labor cost ($/h) O&M cost ($/KW) California 20 19.82 49.56 26.58 40 19.82 49.56 25.23 60 19.82 49.56 23.95 Colorado 20 16.00 40.00 25.00 40 16.00 40.00 23.64 60 16.00 40.00 22.36 16 Sample data for developing O&M cost model
  • 17. Annual O&M Cost VS. The Input Factors  The annual O&M cost increases approximately one dollar (per kilowatt installed) for each 20 wind turbines.  When the number of wind turbines increases from 10 to 100, the annual O&M cost decreases sharply from $26.67/KW to 21.60/KW, approximately 19.01%.  When the number of wind turbines is small (less than 20), the change in the annual O&M cost is not clearly evident. 17
  • 18. Total Annual Cost D(m) 49 55 59.2 65 80.5 82 P0(MW) 0.60 0.85 1.00 1.25 1.50 1.65 D(m) 84.25 88 92.13 100 101 P0(MW) 2.00 2.10 2.30 2.50 3.00 18 Relation between rotor diameter and rated power
  • 19. Total Annual Cost VS. The Input Factors 19  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.
  • 20. 20 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.
  • 22. Conclusion • An Extended Radial Basis Function (E-RBF) cost 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. • The annual O&M cost roughly increases one dollar (per kilowatt installed) for each 20 more wind turbines installed. • The change of the total annual cost depends significantly on the number and rotor diameters of wind turbines. • The preliminary cost map shows wide variation in wind farm cost in the U.S.. • The resulting cost model can be a useful tool for wind farm planning. 22
  • 23. Future Work Optimization of cost of energy; Optimization of Operation and Maintenance (O&M) strategy for offshore wind farms; Extensive analysis of the demand and general market for critical energy products (turbines). 23
  • 24. 24 Selected References  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.  Kiranoudis, C., Voros, N., and Maroulis, Z., 2001. “Shortcut design of wind farms”. Energy Policy, 29, pp. 567–578.  Andrawus, J. A., Watson, J., Kishk, M., and Adam, A., 2006. “The selection of a suitable maintenance strategy for wind turbines”. Wind Engineering, 30(6), pp. 471–486.
  • 25. Questions and Comments 25 Thank you

Notes de l'éditeur

  1. These are four types of active windows. These are others efforts to decrease the energy lost through windows.
  2. We sought to design a window system that will compensate for all of the heat gained through the glass and maintain a thermal balance. This is our window design that improves upon the current passive window model.
  3. We chose thermoelectric units for our system because they are very small and are solid state.