This is a presentation from the Thousand Islands Energy Research Forum, 2011 in Alexandria Bay, NY

1. Exploring and Quantifying the Role of Resource
Uncertainties in Wind Project Planning
Achille Messac#, Souma Chowdhury*, Jie Zhang*, and Luciano Castillo**
# Syracuse University, Department of Mechanical and Aerospace Engineering
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
**Texas Tech University, Department of Mechanical Engineering
1000 Islands Energy Research Forum
Nov 11 – 13, 2011
Alexandria Bay, NY

2. Wind Energy - Overview
 Currently wind contributes 2.5% of the global electricity consumption.
 The growth rate of wind energy has however not been consistent
(WWEA report).
 One of the primary factors affecting its growth is the variability of the
resource itself.
www.prairieroots.org
2

3. Uncertainties in Wind Energy
Long Term
Uncertainties
Physical uncertainties in wind energy may be broadly classified into:
Wind• Long
Environmental Turbine Operational
Term Uncertainties: Introduced by (i) theInterruptions Economic
long term variation of
Conditions Topography
Factors Performance Factors
wind conditions, (ii) turbine design, and (iii) other environmental,
operational and financial factors Turbine Changes in
Terrain/Surface Component
Wind Speed Rain/Snow Component Utility Price
Roughness Depreciation
Breakdown ($/kWh)
• Short Term Uncertainties: Introduced by boundary layer turbulence and
other flow variations that occur in a small time scale (order of minutes) in
Component Power Grid Changes
Wind Direction Storms Vegetation
Replacement Repair O&M Cost
Installation of
Man-made Changes is Govt.
Air Density Additional
Structures Policies
Turbines
Changes in
Interest Rates &
Insurance Rates
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4. Variability of Wind Conditions
 The wind speed, the wind direction, and the air density at a given
site vary significantly over the course of a year.
 The annual distribution of wind conditions also varies from year to
year, although the overall pattern remains somewhat similar.
 The long term variation of wind conditions is generally
represented using probability distribution models.
 These probability distribution models can be developed using
previous years’ recorded wind data at the site.
Zhang et al, 2011 4

5. Uncertainties in Wind Conditions
Uncertainty is introduced by:
 the assumption that, “The expected distribution of wind in the succeeding
years of operation of the wind farm is deterministically equivalent to the
wind distribution estimated from preceding years’ data”.
 Further uncertainties can also be introduced by the assumptions in the
Measure-Correlate-Predict (MCP) method used for long term wind
resource modeling.
[MCP: It is a method implemented to predict the long term wind data/distribution at
the site using short term (1-year) onsite data, and the co-occurring data at nearby
meteorological stations (that also have long term data).]
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6. Presentation Outline
• Research Objectives
• Wind Distribution Modeling
• Uncertainties in the Yearly Wind Distribution
• Modeling the Wind Uncertainties
• Quantifying and Illustrating the Resulting Uncertainties in
the farm AEP and COE.
• Concluding Remarks
AEP: Annual Energy Production; COE: Cost of Energy
6

7. Research Objectives
 Model the yearly (and long term) joint distribution of wind
speed, wind direction, and air density, using recorded site
data.
 Characterize the uncertainty in the yearly distribution of
wind conditions.
 Model the propagation of the wind distribution uncertainty
into the predicted Annual Energy Production (AEP) and
Cost of Energy (COE).
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8. Wind Distribution
8

9. Existing Wind Distribution Models
 Popular wind distribution models include variations of Weibull,
Lognormal, Rayleigh, Beta, inverse-Gaussian and Gamma distributions.
 These models can be broadly classified into:
 univariate and unimodal distributions of wind speed
 bivariate and unimodal distributions of wind speed and wind
direction
 These wind distribution models make limiting assumptions regarding
the correlativity and the modality of the distribution of wind conditions.
9

10. Multivariate and Multimodal Wind Distribution
(MMWD) Model
• MMWD can capture the joint variation of wind speed, wind direction,
and air density.
• MMWD allows representation of multimodally distributed data.
• MMWD is developed using Kernel Density Estimation.
• Case studies:
26NDSU, North Dakota Agricultural Weather Network, online, 2010. 10
27NOAA, National Data Buoy Center, online, 2011.

11. Kernel Density Estimation
Univariate Kernel Density Estimation
Multivariate Kernel Density Estimation
Optimal Bandwidth Matrix Selection
MISE: Minimum Integrated Squared Error 11

12. Wind Distribution Results
Onshore Offshore
Wind data is observed to be multimodal
12

13. Comparison of Distribution Accuracies
 To compare the distributions, we use coefficient of determination, (R2) that
is a measure of the agreement between an estimated distribution and the
recorded data.
 Higher the value of R2, better the distribution
13

14. Uncertainties in the Yearly Wind
Distribution
14

15. Year-to-Year Variations (Onshore Site)
Estimated Wind May not be the right Predicted Long Term
Distribution way to account for
Deterministic assumption Variation of Wind
(preceding years’ data) wind variations (succeeding years)
Zhang et al., 2011 15

16. Wind Distribution in Annual Power Generation
Wind Probability Distribution
• Annual Energy Production of a farm is given by:
• This integral equation can be numerically expressed as:
Kusiak and Zheng, 2010; Vega, 2008 16

17. Characterizing the Uncertainties
In this paper, two different models have been proposed.
 Parametric Wind Uncertainty (PWU) Model: We consider the
parameters of the wind distribution model to be stochastic - e.g. the k and
c parameters in the Weibull distribution.
 Non-Parametric Wind Uncertainty (NPWU) Model : We consider the
predicted yearly probability of a wind condition itself to be stochastic.
17

18. Parametric Wind Uncertainty (PWU) Model
 The uncertainty in the parameters of the wind distribution model is
represented by their variance (in this paper).
 For a mp-parameter wind distribution model, the corresponding
uncertainties in the predicted yearly probabilities of the sample wind
conditions can be expressed in terms of a covariance matrix p as
 qk: kth parameter; q: Covariance of the distribution parameters;
 pi: frequency of the ith sample wind condition;
18

19. PWU Model (continued…)
 The uncertainty propagating into the AEP is modeled as a function of the
uncertainty in the wind distribution.
 Subsequently, the uncertainty in the COE can be expressed as
where
Lindberg, 1999 19

20. NPWU Model: Formulation
 The probability of a given wind condition was observed to vary in orders
of magnitude from year to year.
 To model this variability, a multivariate normal distribution of the
logarithms of the predicted yearly wind probabilities is used.
 The uncertainty in the predicted yearly wind probabilities is then given
by
 The uncertainty in the AEP and the COE can be determined as in PWU.
20

21. Illustration of the Estimated Uncertainty
Uncertainty in the univariate distribution of wind speed: Using NPWU
model without cross-covariance terms
 For a major portion of the wind distributions, there is approximately 10%
uncertainty.
21

22. Illustration of the Estimated Uncertainty
Uncertainty in the bivariate distribution of wind speed and direction, using
NPWU model without cross-covariance terms
Uncertainty in Yearly Wind Distribution Wind Distribution
Offshore
Onshore
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23. Uncertainty in the Farm Performance
• We consider a wind farm comprising 25 GE 1.5MW xle turbines at the
onshore site.
• Uncertainty is evaluated for the optimized farm layout, adopted from a
recent publication*.
• The AEP of the optimized wind farm was reported to be 4.4% higher
than that of a reference wind farm having a 5x5 array layout.
• The relative uncertainties in the AEP and in the COE, estimated
using the NPUW model without cross-covariance, are each
approximately 4%.
*Chowdhury et al. 2011 23

24. Concluding Remarks
 This research developed a distribution model that represents the joint
variation of wind speed, wind direction, and air density.
 However, the predicted annual distribution of wind conditions themselves
varied significantly from year to year.
 A novel methodology to characterize these yearly wind distribution
uncertainties was therefore developed.
 Uncertainty propagation models were developed to quantify the resulting
uncertainties in the farm AEP and COE.
 The relative uncertainty in the predicted yearly wind distribution was found
to be as high as 10% (approx.) for the sites considered.
 The uncertainty in the AEP and COE of an optimized farm layout was
found to be as high as 4% of their nominal values.
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25. Future Research
• Future research would investigate the impact of the wind resource
uncertainties on farm layout planning.
• Future research should also investigate the interaction of “the
uncertainties occurring due to year-to-year variations” with “the
uncertainties introduced by the MCP method”.
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26. Thank you
Questions
and
Comments
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27. 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.
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28. Prediction of 5-year wind distribution
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29. UWFLO Power Generation Model
 Turbines locations are defined by a
Cartesian coordinate system
 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
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30. 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.:
Frandsen et al., 2006; Katic et al.,1986 30

31. The Solution
 Economic and timeline constraints limit the feasibility of
recording detailed onsite wind data over a longer time period.
 Uncertainties in wind predictions thus remain unavoidable.
 Therefore, if these uncertainties can at least be accurately
quantified, a more credible farm resource assessment and a
reliable farm performance projection/economic evaluation can
be made.
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32. Motivation
 One of the key factors restraining the development of wind energy is
the ill-predictability of the actual power that will be generated.
 The power generated by a wind farm is a variable quantity that is a
function of a series of highly uncertain parameters.
 A majority of these uncertainties are not well understood.
 Careful modeling of these uncertainties, together with their
propagation into the overall system, will allow for
1. More credible wind resource assessment, and
2. Development of wind farms that have a reliable performance.
32

33. Year-to-Year Variations (Offshore Site)
Estimated Wind May not be the right Predicted Long Term
Distribution way to account for
Deterministic assumption Variation of Wind
(preceding years’ data) wind variations (succeeding years)
Zhang et al., 2011 33

34. Jacobian of Popular Univariate Wind Distribution
Models
34

35. Non-Parametric Wind Uncertainty (PWU) Model :
Concept
Stochastic models of the wind distribution probabilities
5
Estimated probability of wind distribution, log(p(Ui, i))
 The variability in the predicted yearly probabilities MMWD is directly
3 10-yr pi
2000 MMWD
1
represented by a stochastic model. 2001 MMWD
2002 MMWD
-1 2003 MMWD
 Let us-3consider an example of the following five sample wind conditions 2004 MMWD
2005 MMWD
2006 MMWD
-5 2007 MMWD
2008 MMWD
-7 2009 MMWD
sample-1 DPSWC
-9 sample-2 DPSWC
sample-3 DPSWC
-11 Sample # Wind Speed (m/s) Wind Direction (deg) Air Density (kg/m3)
sample-4 DPSWC
sample-5 DPSWC
-13 1 6.50 180 1.245
-15
2 9.75 90 1.323
3 3.25 270 1.168
-17
1 2 3 4 5 6
4 4.88 Sample number, i 135 1.284
5 11.38 315 1.129
DPSWC: Distribution of the yearly probability of the sample wind condition
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36. NPWU Model: Alternative
 The number of wind condition samples used (np) is significantly higher
than the number of years for which wind data is available.
 The estimation of the probability pp thus requires fitting a high
dimensional data with a significantly small number of data points.
 Alternatively, we can neglect the cross-covariance terms, thereby
assuming the sample wind conditions to be independent random variables.
 The uncertainty in the AEP is then given by:
ith diagonal element of the cov matrix
Lindberg, 1999 36

37. Comparing the Two Uncertainty Models
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38. Uncertainty in the WPD: Validation
 The uncertainty in the annual WPD can also be readily evaluated by its
standard deviation over the ten years.
WPD
Uncertainty in the predicted WPD
Reasonably accurate Underestimation Overestimation
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39. Wind Distribution in Wind Power Density
Wind Probability Distribution
• WPD of a potential site is given by:
• Using Monte Carlo integration, this integral equation can be numerically
expressed as:
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40. Concluding Remarks
 The parametric model provides a reasonably accurate estimation of the
uncertainty in the WPD.
 Further advancement of the non-parametric model is necessary in order to
provide accurate uncertainty quantification.
 Significant uncertainties were also observed in the AEP and the COE of a
wind farm with an optimized layout.
 Therefore, an exploration of the trade-offs between optimal and reliable
wind farm design is crucial in wind project planning.
 Future research should also investigate the interaction of “the uncertainties
occurring due to year-to-year variations” with “the uncertainties
introduced by the MCP method”.
40