This is paper presentation from the ASME International Design Engineering Technical Conference (IDETC), 2011 in Washington DC

1. Characterizing the Influence of Land Configuration
on the Optimal Wind Farm Performance
Souma Chowdhury*, Jie Zhang*, Achille Messac#, and Luciano Castillo*
# Syracuse University, Department of Mechanical and Aerospace Engineering
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
ASME 2011 International Design Engineering Technical Conferences (IDETC)
and Computers and Information in Engineering Conference (CIE)
August 28 – 31, 2011
Hyatt Regency
Washington, DC

2. Wind Farm Optimization
 Farm Layout Planning: The power loss in a wind farm due to wake effects
can be substantially regained by optimizing the farm layout.
 Turbine Type Selection: Optimally selecting the turbine-type(s) to be
installed can further improve the performance of the wind farm.
 Planning the Farm Land Configuration: Careful decision making regarding
the orientation and the aspect ratio of the farm land is important to provide
an effective response to the expected wind distribution.
Turbine
Rated Rotor Hub Power
Power Diameter Height Curve
www.wind-watch.org 2

3. Farm Land Configuration
Farm Farm Land: Different Aspect Ratio
Land: Different N-S-E-W Orientation
windsystemsmag.com 3

4. Motivation
 Farm Layout Planning: The net power generated by a wind farm is reduced
by the wake effects, which can be offset by optimizing the farm layout.
 Turbine Type Selection: Optimally selecting the turbine-type(s) to be
installed can further improve the power generation capacity and the economy
of a wind farm.
 Planning the Farm Land Configuration: Careful decision making regarding
the orientation and the aspect ratio of the farm land is important to provide an
effective response to the expected wind distribution.
An effective wind farm layout optimization
method must account for the complex
interactions among these three factors
4

5. Presentation Outline
• Existing Farm Optimization Methods
• Research Objectives
• Characterizing the Role of Land Configuration
• Unrestricted Wind Farm Layout Optimization (UWFLO)
• Application of the Wind Farm Optimization Framework
• Concluding Remarks
5

6. Existing Wind Farm Optimization Methods
Array layout approach Grid based approach
Computationally less expensive. Allows the exploration of different farm
Restricts turbine locating and introduces configurations.
a source of sub-optimality* Results might be undesirably sensitive
to the pre-defined grid size#
Prevailing Challenges
• Simultaneous optimization of the wind turbine selection
• Consideration of the farm land configuration
• Due consideration of the joint variations of wind speed and direction
*Sorenson et al., 2006; Mikkelson et al., 2007; 6
#Grady et al., 2005; Sisbot et al., 2009; Gonzleza et al., 2010

7. Research Objectives
 Model the influence of the farm land configuration (land
aspect ratio and N-S-E-W orientation) on the optimal farm
performance.
 Minimize the Cost of Energy (COE) by simultaneously
optimizing the farm layout and the selection of the type of
turbine to be installed.
 Develop response surfaces to represent the COE and the
farm efficiency of the optimized wind farm as functions
of the land configuration.
7

8. Modeling the Role of Land Configuration in Wind Farm
Optimization
Optimization of farm
layout and turbine
type selection
UWFLO
Land
Configuration 1: Represent the
Generate a set of N Minimum COE minimum farm COE
random combinations as a function of land
of land aspect ratio Land aspect ratio and
and orientation Configuration 2: orientation
Sobol’s Algorithm Minimum COE Adaptive Hybrid
Functions
Land
Configuration N:
Minimum COE
8

9. Adaptive Hybrid Functions (AHF)
 Cross-Validation:
• q-fold strategy
9

10. Wind Farm Optimization Framework
We use the Unrestricted Wind Farm Layout Optimization (UWFLO) framework
UWFLO
Framework
Wind Power
Wind Farm Optimization
Distribution Generation
Cost Model Methodology
Model Model
10

11. Layout based Power Generation Model
 Dynamic co-ordinates are assigned to the
turbines based on the direction of wind.
 Turbine-j is in the influence of the wake
of Turbine-i, if and only if
Avian Energy, UK
 Effectiveapproach allows us to consider turbines with differing rotor-
 This velocity of wind  Power generated by Turbine-j:
approaching Turbine-j:
diameters and hub-heights
11

12. Annual Energy Production and Cost of Energy
Annual Energy Production (AEP) of a farm is given by:
This integral equation can be numerically expressed as:
Cost of Energy (COE) is then given by:
Cost farm
COE
AEP
Kusiak and Zheng, 2010; Vega, 2008 12

13. Problem Definition
Farm Boundaries
Inter-Turbine Spacing
13

14. Case study
• In this paper, we use 10-year wind data for a class 3 site at Baker, ND*.
• The optimization framework is applied to design a commercial scale
25MW wind farm at this site.
*N. Dakota agricultural weather network: http://ndawn.ndsu.nodak.edu/
14

15. Application of the UWFLO Framework
 A set of 100 random combinations of land aspect ratio and orientation is
generated.
 For each sample land configuration, we obtain the minimum COE
 GE 1.5 MW and 2.5 MW turbines were allowed to be selected for this
purpose.
Best Performing Land Configuration
Parameter 1.5 MW Turbines 2.5MW Turbines
Overall Power Generation (MW) 16.56 16.74
Overall Farm Efficiency 0.649 0.669
COE ($/kWh) 0.022 0.021
 For every sample land configuration, the same turbines were selected
during optimization: GE 1.5MW xle and GE 2.5xl 100m/100m.
15

16. Optimized Layouts
Interestingly, both in the case of 1.5MW and 2.5MW turbines, the best farm
performance was given by the same sample land configuration:
Aspect Ratio =2.95 and Orientation =158 (22 W of N)
With 1.5MW turbines With 2.5MW turbines
16

17. Variation of Farm Performance with Land Configuration
 Similar patterns of variation are observed for COE and Farm Efficiency.
 Interestingly, particularly linear combinations of aspect ratio and
orientation seem to provide better farm performances.
COE Farm Efficiency
17

18. Response Surface Redundancy
18

19. Concluding Remarks
 In this paper, the influences of the land aspect ratio (AR) and N-S-E-W
orientation on layout optimization was specifically explored.
 We found that the optimized layout is strongly correlated with the land
configuration. However, optimal turbine selection was found to be fairly
independent of the land configuration.
 Periodically varying linear combinations of land AR and orientation were
found to provide the optimal farm performance.
 Future work should include further investigation of the response of land
configuration variations to differing wind distributions.
19

20. Acknowledgement
• I would like to acknowledge my research adviser
Prof. Achille Messac, and my co-adviser Prof.
Luciano Castillo for their immense help and
support in this research.
• I would also like to thank my friend and colleague
Jie Zhang for his valuable contributions to this
paper.
• Support from the NSF Awards is also
acknowledged.
20

21. Thank you
Questions
and
Comments
21

22. 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.
22

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

24. Wind Distribution Model
In this paper, we use the non-parametric model called the Multivariate and
Multimodal Wind Distribution (MMWD).
• This model is developed using the multivariate Kernel Density Estimation
(KDE) method.
• This model is uniquely capable of representing multimodally distributed
wind data.
• This model can capture the joint variations of wind speed, wind direction
and air density.
• In this paper, we have only used the bivariate version of this model (for
wind speed and direction)
24

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

26. UWFLO Cost Model
• A response surface based cost model is developed using radial basis
functions (RBFs).
• The cost in $/per kW installed is expressed as a function of (i) the
number of turbines (N) in the farm and (ii) the rated power (P) of those
turbines.
• Data is used from the DOE Wind and Hydropower Technologies program
to develop the cost model.
Cost farm
COE
AEP
26

27. Modeling the Land Configuration  Optimum Farm
Performance Relationship
 A set of N random sample land configurations is created using Sobol’s
quasirandom sequence generator.
 For each land configuration, the COE is minimized by optimizing the farm
layout and the selection of the type of turbine.
 A response surface is developed to represent the minimum COE as a
function of the land aspect ratio and land orientation.
 A response surface is developed to represent the farm efficiency of the
optimized design as a function of the land aspect ratio and the land
orientation.
 A new hybrid surrogate model is used for developing the two response
surfaces.
27

28. Turbine Selection Model
• Every turbine is defined in terms of its rotor diameter, hub-height, rated
power, and performance characteristics, and represented by an integer
code (1 – 66).
• The “power generated vs. wind speed” characteristics for GE 1.5 MW xle
turbines (ref. turbine) 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.
U U in
Pn if U in <U Ur
U r U in
P
1 if U out U Ur
Pr
0 if U U out
• However, if power curve information is available for all the turbines
being considered for selection, they can be used directly.
28

29. 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.
www.prairieroots.org
29 *WWEA, 2011 NREL, 2011