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Rob Istchenko, P.Eng.
GENIVAR Consultants LP
1
New Trends in Uncertainty Analysis
CanWEA Wind Energy Forum
Toronto, ON, April 14, 2010
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1. Wind Resource Assessment Uncertainty Intro
2. Components
3. Aggregation of Uncertainty
4. Correlated Uncertainty
5. Time-Varying Uncertainty
6. Reality Check…
7. Minimizing Uncertainty
8. Concluding Remarks
Presentation Overview
1
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Resource Assessment Uncertainty Intro
• Uncertainty in energy assessment is inevitable
• Uncertainty affects:
• project feasibility
• financial risk and returns
• Estimates of uncertainty typically used to define probabilities of exceedence for wind power project yields (P50, P70, P95…)
• The goal is to identify, quantify and minimize sources of uncertainty
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Resource Assessment Uncertainty Intro
• Uncertainty frequently defined as “standard uncertainty”
• Can be expressed as a standard deviation assuming a normal distribution
• Some sources report accuracy rather than uncertainty
• Accuracy reflects the maximum error while uncertainty is based on the distribution of errors
Yield
Pro
bab
ility
Estimate
Mean
σ
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Resource Assessment Uncertainty Intro
• Uncertainty frequently defined as “standard uncertainty”
• Can be expressed as a standard deviation assuming a normal distribution
• Some sources report accuracy rather than uncertainty
• Accuracy reflects the maximum error while uncertainty is based on the distribution of errors
• Want to minimize the width and match distribution of estimate with actual (with some understood exceptions)
Yield
Pro
bab
ility
Estimate
Actual
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Contributions to Uncertainty
Wind Speed and Production:
• Anemometer
• Data Quality
• Shear Profile
• Tower Effects
• MCP
• Wind Variability
• Wind Flow Modelling
Losses:
• Power Curve
• Availability
• Wake
• Electrical
• Environmental
• Curtailment
Losses are like uncertainties with a negative bias…
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Aggregation of Uncertainty
1
• Normally distributed uncertainties may be combined by root-sum-squares; however, not all uncertainties are normally distributed…
• Important to identify sources of bias in resource assessment – whether due to met tower placement, sensor performance, availability etc.
86 88 90 92 94 96 98 100
Most Likely = 97Minimum = 88Maximum = 99
Distribution of Annual Average Wind Turbine Availability
Availability
Pro
bab
ility
-6 -4 -2 0 2 4 6
Most Likely = 0
Minimum = -6
Maximum = 10
Distribution of Wind Flow Modelling Uncertainty
Wind Flow Modelling Uncertainty
Pro
bab
ility
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Aggregation of Uncertainty
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• Uncertainties may also be combined using a stochastic random sampling approach (such as Monte Carlo simulation)
• In the stochastic approach, many possible outcomes are randomly sampled for each uncertainty component - flexibility to choose shape of uncertainty distribution: normal, triangular, beta, truncated…
• These outcomes are then combined in order estimate uncertainty in yields
2 4 6 8 10 12 14 -10 -5 0 5 10 -2 -1 0 1 2 3 4 5 6
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Correlated Uncertainty
1
• Generally, uncertainties are assumed to be independent; however, this is not always the case…
• For example, uncertainties in measured wind speeds (anemometer, tower shadow…) impact uncertainty in the shear profile estimate
• Correlations can lead to magnification of uncertainty
• Correlations between uncertainties can be defined as part of a stochastic approach
• Create multiple distributions linked by a specified correlation
Uncertainty Component a
Un
cert
ain
ty C
om
po
nen
t b
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Correlated Uncertainty
1
• Generally, uncertainties are assumed to be independent; however, this is not always the case…
• For example, uncertainties in measured wind speeds (anemometer, tower shadow…) impact uncertainty in the shear profile estimate
• Correlations can lead to magnification of uncertainty
• Correlations between uncertainties can be defined as part of a stochastic approach
• Create multiple distributions linked by a specified correlation
Uncertainty Component bUncertainty Component aP
rob
abili
ty D
ensi
ty
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-10-8-6-4-202468
10
1 4 7 10 13 16 19 22 25 28
Win
d S
pe
ed
% C
han
ge
Years
Wind Speed Uncertainty due to Climate Change
Time-Varying Uncertainty
1
• A stochastic uncertainty assessment also facilitates the incorporation of time-varying uncertainty
• Useful for estimating:
• Impact of losses as a project ages
• Increasing uncertainty in the strength of the wind resource due to changes in the climate
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Reality Check…
1
• In many ways, flexibility of the analysis exceeds our knowledge of the underlying uncertainty distributions… even the uncertainty is uncertain!
• Given the same assumptions, results from a stochastic approach to uncertainty propagation agree with simple RSS approach
• A stochastic approach requires more computational power, but that doesn’t make it more difficult to understand or interpret – produces results in an intuitive and flexible format
• The ability to assess non-normally distributed, correlated, and time-varying uncertainty challenges our ability to assess the inputs
• It’s better to estimate rather than ignore known sources of uncertainty
• Performing analyses multiple ways (different reference sites, different wind flow models…) can help to understand sources of uncertainty
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Minimizing Uncertainty
1
• Uncertainty analysis shouldn’t be restricted to a final step in the pre-construction yield assessment process
• Preliminary and interim uncertainty analyses can be very valuable for informing decisions about project spending:
• Tower configuration and locations, remote sensing, wind flow modelling, monitoring duration…
• Consider how probability of exceedence results are going to be used:
• Is the goal to quantify uncertainty in energy production or uncertainty in revenue?
• Account for everything, but don’t double count
• Take advantage of all potential inputs – relevant operational data?
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Minimizing Uncertainty
1
Simplified Example - Sources of Uncertainty
• Somewhat difficult to assess impact in this format
• In a stochastic approach, the correlation of inputs to overall uncertainty can be used to assess individual contributions
Source Standard Uncertainty
Anemometer 0.1 m/s
Shear 0.25 m/s
MCP 1.0% of wind speed
Wind Flow Model 5.0% production
Future Period Variability 1.1% wind speed
Historical Period Variability 1.5% wind speed
Tower Effects 0.5% wind speed
Data Quality 0.1 m/s
Losses 2.7% production
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Minimizing Uncertainty
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Simplified Example – Contribution to Overall Uncertainty
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% 45.0% 50.0%
Losses
Data Quality
Tower Effects
Historical Period Variability
Future Period Variability
Wind Flow Model
MCP
Shear
Anemometer
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Minimizing Uncertainty
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Simplified Example – Revised Contribution to Overall Uncertainty
0.0% 10.0% 20.0% 30.0% 40.0% 50.0%
Losses
Data Quality
Tower Effects
Historical Period Variability
Future Period Variability
Wind Flow Model
MCP
Shear
Anemometer
Reduced Shear and Modelling Uncertainty
Original Uncertainty
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Minimizing Uncertainty
1
• Focus effort on minimizing largest contributors to overall uncertainty
• More information doesn’t necessarily mean that yield estimates will go up – at least not at the P50 level
• However, reduced uncertainty can increase the P90, P95, P99…
• Example: Case 1 has high shear and modelling uncertainty; Case 2 assumes additional on-site monitoring which resulted in lowered yield expectation but also decreased uncertainty
• Despite decreased P50, increased P95 may result in more viable project
• Consider a target DSCR of 1.0x at P95, a 3% increase in expected production is significant
Case 1Probabilities of
Exceedence
(Percentage of Case 1
P50 Net Yield)
Confidence level ( %)
50 70 90 95 99
1-Yr Average Production 100% 91% 78% 72% 61%
10-Yr Average Production 100% 94% 85% 81% 73%
20-Yr Average Production 100% 94% 86% 82% 74%
Case 2: Reduced Yield and UncertaintyProbabilities of
Exceedence
(Percentage of Case 1
P50 Net Yield)
Confidence level ( %)
50 70 90 95 99
1-Yr Average Production 98% 90% 79% 73% 63%
10-Yr Average Production 98% 94% 87% 84% 78%
20-Yr Average Production 98% 94% 88% 85% 80%
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Concluding Remarks
1
• Uncertainty in wind resource assessment is unavoidable
• Tools and techniques are facilitating more comprehensive uncertainty analyses
• Industry’s understanding of wind resource assessment uncertainty is evolving (non-normal, biased, correlated, time-varying…) – expect greater scrutiny
• Positive for the industry because it helps inform/incent good project development practices – reduced uncertainty improves project viability
• Need for continued evaluation and integration of operational experience
• Probability of exceedence results are valuable, but so is the process –include this at intermediate stages in development process
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