SODAR and Extrapolated Tower Wind Shear Profile Comparison in Various Topographic Conditions

March 17, 2009

SODAR and Extrapolated Tower Wind Shear Profile Comparison in Various Topographic Conditions

Elizabeth WallsNiels LaWhite

Second Wind IncEWEC 2009 Marseille

2

Introduction

• SODAR (Sonic Detection and Ranging):– measure wind data by transmitting

acoustic pulses and analyzing the frequency content of the returned signal

• Triton Sonic Wind Profiler:– Low-power, monostatic, phased-array

SODAR commercialized in early 2008

• Several Triton vs. Tower comparisons– Great correlation at anem. height– How do the extrapolated tower shear

profiles compare to the measured Triton data?

– How does the error in extrapolation translate to error in predicted power?

3

Outline

• Site and Data Set Description– 4 sites across the U.S. with varying topography– 2 months of concurrent tower and Triton data

• Triton vs. Tower Data: Validation• Shear Exponent Estimation using Triton Data• Extrapolated Wind Shear Profile Comparison• Theoretical Power Output Comparison

4

Site and Data Set Descriptions

• Cranberry Bog in Massachusetts– Flat site surrounded by trees – 60 m met tower– Data Used for comparison:

• May 15th – July 15th, 2008

• Open Field in Kansas– Flat and open terrain– 60 m met tower– Data Used for comparison:

• Sept. 1st – Nov. 1st, 2008

5

Site and Data Set Descriptions

• Ridgeline in Washington State– Complex, hilly terrain– 50 m met tower– Data Included: August 15th – Oct.

15th, 2008

• Wind Farm in Washington State– Several wind turbines ~300 m

from Triton– 60 m met tower– Data Included: Sept. 1st – Oct.

17th, 2008

6

Triton vs. Tower Data: Filters

• Data Filtering for Correlation Study:– Triton Quality Factor > 90%

• Quality: function of Signal-to-Noise Ratio (SNR) and the number of valid data points over ten-minutes

– Triton Vertical Wind Speed < +/-1.5 m/s– Max Value of Two Anems Used

• Reduces tower shadow effects

• Data Filtering for Average Wind Speed Comparison– Triton Quality Factor > 95%– Triton Vertical Wind Speed < +/-1 m/s– Average Value of Two Anems Used– Ratio of Anems = 0.98 - 1.02– Anem Wind Speed > 2 m/s– Direction Sectors 45º from boom with 30º width

45

30

Anems

Dir. Sectors Included

7

Triton vs. Tower Data: Cranberry Bog, MA

• Data Interval: May 15th to July 15th, 2008

• Triton Operational Uptime = 98.4%Triton vs. Tower Wind Speeds at Cranberry Bog in MA

y = 1.003x - 0.086R = 0.968

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Tower 60 m Wind Speed (Max of Two), m/s

Tri

ton

60

m W

ind

Sp

ee

d, m

/s

• Corr. Coeff. = 0.968• Valid Triton data (High

Q) @ 60 m = 99.5%• % Diff. In Avg. Wind

Speed = -1.1 %

8

Triton vs. Tower Data: Open Field, KS

• Data Interval: Sept. 1st to Nov. 1st, 2008

• Triton Operational Uptime = 99.3%

• Corr. Coeff. = 0.976• Valid Triton data (High

Q) @ 60 m = 94.5%• % Diff. In Avg. Wind

Speed = -0.55 %

Triton vs. Tower Wind Speeds at Field in KS

y = 0.982x + 0.014R = 0.976

02468

10121416182022

0 2 4 6 8 10 12 14 16 18 20 22

Tower 60 m Wind Speed (Max of Two), m/s

Tri

ton

60

m W

ind

Sp

ee

d, m

/s

9

Triton vs. Tower Data: Ridgeline, WA

• Data Interval: Aug. 15th to Oct. 15th, 2008

• Triton Operational Uptime = 94.9%

• Corr. Coeff. = 0.988• Valid Triton data (High

Q) @ 50 m = 91.1%• % Diff. In Avg. Wind

Speed = -7.6 %– Large diff. due to

terrain and distance from tower

Triton vs. Tower Wind Speeds on Ridgeline in WA

y = 0.982x - 0.501R = 0.988

02

468

10

121416

1820

0 2 4 6 8 10 12 14 16 18 20

Tower 50 m Wind Speed (Max of Two), m/s

Tri

ton

50

m W

ind

Sp

ee

d, m

/s

10

Triton vs. Tower Data: Wind Farm, WA

• Data Interval: Sept. 1st to Oct. 17th, 2008

• Triton Operational Uptime = 99.8%

• Corr. Coeff. = 0.966• Valid Triton data (High

Q) @ 60 m = 97.4%• % Diff. In Avg. Wind

Speed = -0.6 %

Triton vs. Tower Wind Speeds in Wind Farm in WA

y = 0.954x - 0.108R = 0.966

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Tower 60 m Wind Speed (Max of Two), m/s

Tri

ton

60

m W

ind

Sp

ee

d, m

/s

11

Shear Exponent Estimation using Triton

Data• Power Law Profile:

RZ

Z

z

z

U

U

R

Finding Alpha

y = 0.2664x + 0.7255

0.1

1.0

10.0

0.1 1 10

ln(z/zr)

ln(U

/Ur)

• Use Triton Data from 40 m to 120 m

• Plot ln(U/Ur) vs ln(z/zr)

• Slope of best-fit = Power Law Exponent, Alpha

Average Wind Speed Profile

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Measured byTriton

Average Wind Speed Profile

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Measured by Triton

Power Law Profile,Alpha = 0.26

12

Shear Exponent Estimation using Triton

Data, cont’d• Alpha

found for each Triton data set:

Triton Wind Speed ProfileField in KS

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Triton Alpha = 0.266

Triton Wind Speed ProfileRidgeline in WA

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Wind Speed, m/s

He

igh

t, m

Triton Alpha = 0.061

Triton Wind Speed ProfileCranberry Bog in MA

0

20

40

60

80

100

120

140

0 2 4 6 8

Wind Speed, m/s

He

igh

t, m

Triton Alpha = 0.392

Triton Average Wind Speed ProfileWind Farm in WA

0

20

40

60

80

100

120

140

0 2 4 6 8 10

Wind Speed, m/s

Hei

gh

t, m

Triton Alpha = 0.176

13

Extrapolated Wind Speed ProfileField in KS

0

20

40

60

80

100

120

140

160

4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Extrapolated Wind Shear Profile Comparison

• For each data set, found:– Triton Alpha (using data from 40 to 120 m)– Tower Alpha (using data from 2 heights)

• Tower data extrapolated using both Triton and Tower Alphas

Extrapolated Wind Speed ProfileField in KS

0

20

40

60

80

100

120

140

160

4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.165

Extrapolated Wind Speed ProfileField in KS

0

20

40

60

80

100

120

140

160

4 6 8 10 12

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.165

Triton Alpha = 0.266

Extrapolated Wind Speed ProfileCranberry Bog in MA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Extrapolated Wind Speed ProfileCranberry Bog in MA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.443

Extrapolated Wind Speed ProfileCranberry Bog in MA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.443

Triton Alpha = 0.392

14

Extrapolated Wind Shear Profile Comparion, cont’d

• Wind speed profile extrapolations from other two sites:

Extrapolated Wind Speed ProfileRidgeline in WA

0

20

40

60

80

100

120

140

160

4 5 6 7 8 9 10

Wind Speed, m/s

He

igh

t, m

Extrapolated Wind Speed ProfileRidgeline in WA

0

20

40

60

80

100

120

140

160

4 5 6 7 8 9 10

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.044

Extrapolated Wind Speed ProfileRidgeline in WA

0

20

40

60

80

100

120

140

160

4 5 6 7 8 9 10

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.044

Triton Alpha = 0.061

Extrapolated Wind Speed ProfileWind Farm in WA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Extrapolated Wind Speed ProfileWind Farm in WA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.148

Extrapolated Wind Speed ProfileWind Farm in WA

0

20

40

60

80

100

120

140

160

2 3 4 5 6 7 8

Wind Speed, m/s

He

igh

t, m

Tower Alpha = 0.148

Triton Alpha = 0.176

15

Theoretical Power and Equivalent Wind Speed

• How do varying wind shear profiles translate into theoretical power available in wind?

32

2

1URCP P

dhAUA

U eq 1

• Power Produced:

• Equivalent Hub Height Wind Speed:

16

Theoretical Power Output Comparison

• Assuming ideal turbine operation: Cp = 16/27 and 100% efficiency

• % Difference = 100

AlphaTritononBased

AlphaTritononBasedAlphaToweronBased

Power

PowerPower

Open Field in KS

Ridgeline in WA

Cranberry Bog in MA

Wind Farm in WA

-11.0% -2.8% 6.0% -3.2%

• With hub height = 80 m and rotor radius = 40 m, % difference in predicted power:

17

Power as function of Rotor Radius and Hub Height

• Error increases with both rotor radius and hub height• +ve % diff. : Tower data leads to overprediction• -ve % diff. : Tower data leads to underprediction

% Difference in Predicted Power as function of Rotor Radius

-14%-12%-10%

-8%-6%-4%-2%0%2%4%6%8%

0 20 40 60 80Rotor Radius, m

% D

iff.

in

Po

we

r

Field Ridge Bog Wind Farm

Hub Height = 80 m

% Difference in Predicted Power as function of Hub Height

-20%

-15%

-10%

-5%

0%

5%

10%

15%

0 20 40 60 80 100 120Hub Height, m

% D

iff.

in

Po

we

r

Field Ridge Bog Wind Farm

Radius = 40 m

• With hub height of 100 m and a radius of 40 m, the percent difference ranged from -16.4% to 9.3%

Range of Uncertainty

18

Summary

• Analyzed two months of concurrent Triton and tower data from 4 different sites across the U.S.

• At each site, showed excellent agreement between the tower and Triton data in terms of correlation (Ravg = 0.975) and average wind speed

• Estimated alpha (power law exponent) using both the Triton and tower data

• Used both alphas to generate extrapolated wind shear profiles

• Calculated the theoretical power production with each wind shear profile and found the percent difference

19

Conclusions

• Extrapolating wind shear profiles, based on tower data, can lead to under or over estimation of wind speeds

• Error in theoretical power increases with rotor radius and, more drastically, with hub height

• SODARs (and other remote sensing devices) measure wind speed across the rotor diameter which reduces uncertainty in shear exponent estimation.