UNCERTAINTYThe Classical ApproachALAN DERRICKSENIOR TECHNICAL MANAGER

September 2009

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Overview

• Uncertainty Basics• Energy Yield Uncertainty Components• Some Key Components• Discussion on Suitability of Method• Recommendations

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What Measurement?

In the context of Resource Assessment Measurement is interpreted as:

• the process through which a set of Input Quantities is transformed into a single output quantity – The Result.

The Input Quantities include:• Wind speed measurements• Long Term Prediction Process• Terrain and surface roughness model• Wind flow model• Turbine layout• Turbine power curve• Loss Factors

The Result is:• Best Estimate of the Annual Energy Production (AEP)• Standard Uncertainty in AEP

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Uncertainty Basics - What is Uncertainty?

Aim: to evaluate the combined standard uncertainty in energy yield resulting from the individual uncertainty components associated with each of the inputs to the energy yield analysis.

Application: use the above result directly to derive the energy yield with a certain confidence level expressed as a probability: P50, P75, P90, P99, etc.

Problem: identifying, quantifying and combining the individual uncertainty components and distributions in a way that is not over-conservative.

Confidence level: indicates the degree of belief that the true value lies within the specified uncertainty range.

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Uncertainty Basics - Definitions and Terminology

Dispersion for a given standard uncertainty

Dispersion increases with increasing

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1.64SD

90%

2.58SD

99%

Uncertainty Basics – Combined Standard Uncertainty

Combined Standard UncertaintyUncertainty in AEPAEPCorrelation CoefficientSensitivity CoefficientsStandard Uncertainty Components

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Uncertainty Basics - Correlations

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Uncertainty Basics – Sensitivity Coefficient

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Evaluated either by partial differentiation or by perturbation of the model inputs

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20%

40%

60%

80%

100%

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220%

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50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 160%

(v+dv)/v

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e.g. Sensitivity of energy yield to wind speed.

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Ranges from 1.25 to 2.00typically.

Slope evaluated at Vref

Uncertainty Basics - Definitions and Terminology

Central Limit Theorem

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Combined Standard Uncertainty PDF tends to Normal Distribution if:Contributing uncertainty components are independent, random variables.

The convergence will occur more rapidly:i.the larger the number of input distributionsii.the closer to being equal are the individual contributionsiii.the closer to being normal distributions are the individual input distributions .The Result of the Annual Energy Production Uncertainty Evaluation could be expected therefore to exhibit the characteristics of a normal distribution.

May not be a valid assumption if:•a few uncertainty components dominate•model is neither linear nor nearly linear•uncertainty components are not independent

Uncertainty Basic - Definitions and Terminology

Central Limit Theorem

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Tending towards normal distribution already

Energy Yield Uncertainty Components Overview

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Wind Speed Uncertainty Sub-Model

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Energy Yield Uncertainty Components Overview

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Number of Turbines: 81      Hub Height: 80m      Met Masts: 4      

Wind Measurement Height: 50m 80m 80m 80m10 Year Wind Speed

Prediction Uncertainty 3.60% 3.50% 4.30% 4.80%

CombinedCorrelation (Across Turbines)

Component Note on Uncertainty Contribution at each Turbine Across Turbines Distribution Sensitivity Uncertainty[%]

Wind:Nearest Mast Wind Uncertainty or Combination of Masts Correlated Normal 2.15 8.7%

Terrain and Roughness:From Flow Model: Proportional to speed up and distance to mast Correlated Normal 1.00 6.1%

Wake: From Wake Model: Proportional to Wake Loss Correlated Normal 1.00 1.7%

Air Dens.:Assumed ±2 degree C uncertainty in annual average over wind farm lifetime. Correlated Triangular 1.00 0.3%

Loss Factors.:Assumed 2% based on evaluation of production statistics. Correlated Triangular 1.00 0.8%

Power Curve:5%. In this example assumed uncorrelated between turbines. Uncorrelated Normal 1.00 0.6%

Subs Met.: ±1%. Correlated Triangular 1.00 0.4%

Shear Extrapolation to Hub Height:Related to difference between hub and mast heights (varies on this site) Correlated Normal 2.15 1.0%

High Shear:Derived from turbine dimensions and power curve at 2% Correlated Normal 2.15 2.2%

Tree Growth: Proportional to predicted tree growth loss. Correlated Normal 2.15 0.2%Other: None. 0.0%

Combined (Uncorrelated): 11.0%

Uncertainty Model Summary

• Individual uncertainty components can themselves be based on a complex model

• Where standard uncertainty component values are “estimated”, tempting to always round to the nearest “simple” number e.g. 0.5%, 1%, etc.

– The more components and the more detail in the model, the greater the conservatism or over-prediction in the combined standard uncertainty can be.

• Consider if the conservative, fully correlated option is ever appropriate before using to combine uncertainty components.

• Consider if there is any double counting of components, especially in complex models, and eliminate.

• Conservatism should come in the choice of coverage factor “k” and not in the estimate of the standard uncertainty which should be realistic.

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How Universal are these Assumptions?

Based on foregoing example, the largest uncertainty components are typically:

– Wind Speed Prediction– Wind Flow Modelling– Shear Extrapolation– Shear Effect on Power Curve (if in high shear flow)

However result is very sensitive to the following:– Number of Met Masts– Inter Turbine Power Curve Correlations

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Wind Flow Modelling & Met Mast Dependency

• Plot error in yield vs. predicted terrain effect

• Error correlates with the predicted terrain effect.

11 turbines predicted to be less windy than mast

1 Turbine windier than mast

Ref. P. Stuart (RES) BWEA 2008

Symmetric Hill Test Case

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• Consider 9 turbines on a symmetric hill.

• Assume Uncertainty in Yield ≈ Terrain Effect (as on example wind farm).

• Placing the mast at the base of the hill results in 7 turbines being under-predicted.

• Placing the mast at the top of the hill results in 8 turbines being over-predicted.

• Placing mast half way up the hill minimises the error.

• Assume a 1.7% change in yield for a 1% change in wind speed.

Ref. P. Stuart (RES) BWEA 2008

Multiple Mast Uncertainty Reduction

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Combined Wind flow uncertainty versus number of met masts deployed

Very large, complex terrain, forested wind farm

Uncertainty proportional to Flow Correction and Distance to Mast

• Flow correction term does not necessarily decrease if mast to turbine ratio small (81 turbines here).

• However distance term does always decrease if masts sited appropriately

Power Curve (PC) Correlations

• Measured PC’s exhibit certain common features

• probably measurement errors so not relevant to AEP prediction uncertainty

• Likely that turbine performance is also influenced in some correlated way hence PC combined uncertainty increased.

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SCADA Power CurveCorrected to Reference Density (1.22 kg/m

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SCADA Power CurveCorrected to Reference Density (1.22 kg/m

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D:\Performance\Beenag\SCADA\[BGAll03.xls]NP SCADA Power Curve

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SCADA Power CurveCorrected to Reference Density (1.22 kg/m

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D:\Performance\Beenag\SCADA\[BGAll03.xls]NP SCADA Power Curve

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SCADA Power CurveCorrected to Reference Density (1.22 kg/m

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Inferring Power Curve Correlations Pre-Construction

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• CFD can provide clues.• In-Flow angle, Turbulence and Shear• e.g in the 81 turbine example

– Original assumption all uncorrelated Upc = 0.6%

– Assume adjacent turbines correlated in groups, uncorrelated between groups

Upc = 1.9%

– Assume all turbines correlated Upc = 5.0%

IS THE METHOD VALID?Summing Up

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Weaknesses in Application of GUM to AEP Uncertainty

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Weaknesses• Assumption that resultant combined standard uncertainty is

normally distributed• Subjectivity in assessment of many component uncertainty values

and distributions.• Central Limit Theorem Requirements only Approximately Satisfied• Key Models/Methods for Wind Speed Prediction and Wind Flow

Modelling “highly uncertain” and non-linear in complex terrain• Usually only practical to make fully correlated or uncorrelated

assumptions• Some key uncertainty components, influences and/or correlations

may be missing from the model

Weaknesses in Application of GUM to AEP Uncertainty

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Consequences• Combined Standard Uncertainty Distribution may actually deviate

from normal distribution hence wrong coverage factors are being used.

• “Uncertainty” in the uncertainty could be high.• Uncorrected errors or biases may be present in the best estimate

which the GUM assumes should be corrected for (and an uncertainty component in the correction included)

Evidence• comparison of 53 RES windfarm years of

actual production with RES predictions shows: s = 9.7% - close to average of RES

prediction uncertainties• Garrad Hassan study of 535 wind farm years

(right) also shows good agreement of standard deviation

• Both RES and GH studies exhibit small bias.

More Evidence.....

• Same site, same data package• 4 different, expert consultants

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Recommendations

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• Key focus of future work is to further understand and confirm the uncertainty contributions:

Are we overestimating some components but underestimating others and somehow ending up with the correct result?

Where are the biases in the best estimates of AEP coming from?• The extensive production databases now available can help with

this• Simulations can also fill some gaps in our knowledge………….

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