UNCERTAINTY The Classical Approach

1. UNCERTAINTYThe Classical Approach ALAN DERRICK SENIOR TECHNICAL MANAGER September 2009

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

3. 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

4. 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.

5. Uncertainty Basics - Definitions and Terminology 2.58SD 99% 1.64SD 90% Dispersion for a given standard uncertainty s Dispersion increases with increasing s

6. Uncertainty Basics – Combined Standard Uncertainty Combined Standard Uncertainty Uncertainty in AEP AEP Correlation Coefficient Sensitivity Coefficients Standard Uncertainty Components

7. Uncertainty Basics - Correlations Negatively Correlated Positively correlated Uncorrelated Fully correlated Uncorrelated/independent Example

8. Uncertainty Basics – Sensitivity Coefficient Evaluated either by partial differentiation or by perturbation of the model inputs e.g. Sensitivity of energy yield to wind speed. Slope evaluated at Vref Ranges from 1.25 to 2.00 typically.

9. Uncertainty Basics - Definitions and Terminology Central Limit Theorem Combined Standard Uncertainty PDF tends to Normal Distribution if: Contributing uncertainty components are independent, random variables. The convergence will occur more rapidly: the larger the number of input distributions the closer to being equal are the individual contributions 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

10. Uncertainty Basic - Definitions and Terminology Central Limit Theorem * = * * = Tending towards normal distribution already

11. Energy Yield Uncertainty Components Overview

12. Wind Speed Uncertainty Sub-Model

13. Energy Yield Uncertainty Components Overview

14. 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.

15. 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

16. Wind Flow Modelling & Met Mast Dependency • Plot error in yield vs. predicted terrain effect 1 Turbine windier than mast 11 turbines predicted to be less windy than mast • Error correlates with the predicted terrain effect. Ref. P. Stuart (RES) BWEA 2008

17. Symmetric Hill Test Case • Consider 9 turbines on a symmetric hill. • Assume a 1.7% change in yield for a 1% change in wind speed. • 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. Ref. P. Stuart (RES) BWEA 2008

18. Multiple Mast Uncertainty Reduction 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

19. SCADA Power Curve SCADA Power Curve T01 T02 3 3 Corrected to Reference Density (1.22 kg/m ) Corrected to Reference Density (1.22 kg/m ) 16/01/02 16/01/02 Date Range:30/06/01 to 21/09/01 Sector: 275 - 360 °N Date Range:30/06/01 to 21/09/01 Sector: 265 - 360 °N 900.0 900.0 800.0 800.0 700.0 700.0 600.0 600.0 500.0 500.0 Measured Measured Density Corrected Power (kW) Density Corrected Power (kW) 400.0 400.0 Warranted Warranted 300.0 300.0 200.0 200.0 100.0 100.0 0.0 0.0 0.0 5.0 10.0 15.0 20.0 25.0 0.0 5.0 10.0 15.0 20.0 25.0 -100.0 -100.0 Wind Speed (m/s) Wind Speed (m/s) D:\Performance\Beenag\SCADA\[BGAll03.xls]NP D:\Performance\Beenag\SCADA\[BGAll03.xls]NP SCADA Power Curve SCADA Power Curve T03 T04 3 3 Corrected to Reference Density (1.22 kg/m ) Corrected to Reference Density (1.22 kg/m ) 16/01/02 16/01/02 Date Range:30/06/01 to 21/09/01 Sector: 252 - 360 °N Date Range:30/06/01 to 30/09/01 Sector: 70 - 271 °N 900.0 900.0 800.0 800.0 700.0 700.0 600.0 600.0 500.0 500.0 Measured Measured Density Corrected Power (kW) Density Corrected Power (kW) 400.0 400.0 Warranted Warranted 300.0 300.0 200.0 200.0 100.0 100.0 0.0 0.0 0.0 5.0 10.0 15.0 20.0 25.0 0.0 5.0 10.0 15.0 20.0 25.0 -100.0 -100.0 Wind Speed (m/s) Wind Speed (m/s) D:\Performance\Beenag\SCADA\[BGAll03.xls]NP D:\Performance\Beenag\SCADA\[BGAll03.xls]NP SCADA Power Curve SCADA Power Curve T05 T06 3 3 Corrected to Reference Density (1.22 kg/m ) Corrected to Reference Density (1.22 kg/m ) 16/01/02 16/01/02 Date Range:30/07/01 to 30/09/01 Sector: 0 - 215 °N Date Range:30/06/01 to 30/09/01 Sector: 95 - 360 °N 900.0 900.0 800.0 800.0 700.0 700.0 600.0 600.0 500.0 500.0 Measured Measured Density Corrected Power (kW) Density Corrected Power (kW) 400.0 400.0 Warranted Warranted 300.0 300.0 200.0 200.0 100.0 100.0 0.0 0.0 0.0 5.0 10.0 15.0 20.0 25.0 0.0 5.0 10.0 15.0 20.0 25.0 -100.0 -100.0 Wind Speed (m/s) Wind Speed (m/s) D:\Performance\Beenag\SCADA\[BGAll03.xls]NP D:\Performance\Beenag\SCADA\[BGAll03.xls]NP 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.

20. Inferring Power Curve Correlations Pre-Construction • 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%

21. Summing Up IS thE method Valid?

22. Weaknesses in Application of GUM to AEP Uncertainty • 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

23. Weaknesses in Application of GUM to AEP Uncertainty • 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.

24. More Evidence..... • Same site, same data package • 4 different, expert consultants

25. Recommendations • 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………….