a systematic method for quantifying flow model uncertainty in wind resource assessment

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A SYSTEMATIC METHOD FOR QUANTIFYING FLOW MODEL UNCERTAINTY IN WIND RESOURCE ASSESSMENTALEX CLERC, PETER STUART AND MIKE ANDERSON

16 APRIL 2012

CONTENTS

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• Background and motivation

• Dataset and derivation of method

• Example calculation

ENERGY YIELD – MAJOR COMPONENTS

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EXAMPLE ENERGY YIELD

4Taken from “EWEA Comparison of Resource and Energy Yield Assessment Procedures” presented during EWEA Wind Resource Assessment Technology Workshop, Brussels, 11 May 2011

5Taken from “EWEA Comparison of Resource and Energy Yield Assessment Procedures” presented during EWEA Wind Resource Assessment Technology Workshop, Brussels, 11 May 2011

COMBINED STANDARD UNCERTAINTY

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Combined Standard UncertaintyAnnual Energy Production (AEP)Uncertainty in AEP due to flow modelNumber of flow predictions in Energy YieldSensitivity of AEP to flow predictions (wind speed) Standard uncertainty of flow predictionsCorrelation of flow prediction errors,

N

i

N

jjijijic uucc

E

EU

1 1,

22

cU

EE

ji,

iciu

11

N

DATASET AND METHOD

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• Dataset: mast pairs from Europe and North America, wind speed ratios calculated by 30° sector

• Speed-ups taken from a flow model very similar to WAsP

• The observed speed-up errors are used to study:

– uncertainty of a speed-up prediction for a particular wind direction (u)

– correlation of errors (ρ)

557 mast pairs

EFFECT OF DISTANCE ON SPEED-UP ERROR

8Log scale

1/D 1 LDMTeλ = 10%, L1 = 1km

EFFECT OF SPEED-UP ON SPEED-UP ERROR

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A = 0.5, S is the speed-up

EFFECT OF DIRECTION ON CORRELATION

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EFFECT OF DISTANCE ON CORRELATION

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2

11 /2/2 LDLD

D

MMTT ee

DTT is distance between turbinesDMM is distance between masts

SUMMARY

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• Uncertainty (u) depends on:– distance from mast to turbine– speed-up predicted by the model

• Correlation of errors (ρ) depends on:– wind direction– distance from turbine to turbine– distance from mast to mast if applicable

• Sensitivity (c) mainly depends on the shape of the wind distribution and power curve

N

i

N

jjijijic uucc

E

EU

1 1,

22

EXAMPLE CALCULATION

13Taken from “EWEA Comparison of Resource and Energy Yield Assessment Procedures” presented during EWEA Wind Resource Assessment Technology Workshop, Brussels, 11 May 2011

EXAMPLE CALCULATION

14Modified from “EWEA Comparison of Resource and Energy Yield Assessment Procedures” presented during EWEA Wind Resource Assessment Technology Workshop, Brussels, 11 May 2011

With one mast flow model uncertainty is 3.14%

original mast

optimal second mast

3.14% with one mast2.00% with two masts

With two masts flow model uncertainty is 2.00%

CONCLUSIONS

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• The presented flow model uncertainty method is systematic and evidence-based

• Easy to use and applicable to linear models such as WAsP and MS3DJH

• Many possible applications– Optimisation of mast deployment– Optimisation of mast weight scheme– Quantify benefits of masts in financial terms

• Open-source software “DeltaWindFlow” available from RES website

– http://www.res-group.com/resources/download-area.aspx

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