Wind Resource Assessment

S.R.MohanrajanAmrita Wind Energy Centre

Department of Electrical and Electronics Engineering

Amrita Vishwa Vidyapeetham

Wind Resource Assessment

1. Wind Turbine– Power in the Wind

– Power Curve

2. Prospecting for Wind Farm– Tree Flagging

– Nearby weather stations

3. Preparation of Meteorological data– Wind Speed

– Air density( Pressure, temperature)

– Wind Direction

4. Estimation of Annual Energy Production– Wind Shear form Meteorological data

– Wind Regime Modeling

5. Calculate Utilization Index

Met Mast

Power in the Wind (Watts)

Density = P/(RxT) P - pressure (Pa) R - specific gas constant (287 J/kgK) T - air temperature (K)

= 1/2 x air density x swept rotor area x (wind speed)3

A V3

Area = r2 Instantaneous Speed(not mean speed)

kg/m3 m2 m/s

Power in the Wind• Wind Speed

– Wind energy increases with the cube of the wind speed

– 10% increase in wind speed translates into 30% more electricity

– 2X the wind speed translates into 8X the electricity

• Height

– Wind energy increases with height to the 1/7 power

– 2X the height translates into 10.4% more electricity• Air density

– Wind energy increases proportionally with air density– Humid climates have greater air density than dry climates– Lower elevations have greater air density than higher elevations– Wind energy in Denver about 6% less than at sea level

• Blade swept area– Wind energy increases proportionally with swept area of the blades

• Blades are shaped like airplane wings– 10% increase in swept diameter translates into 21% greater swept area– Longest blades up to 413 feet in diameter

• Resulting in 600 foot total height

• Betz Limit

– Theoretical maximum energy extraction from wind = 16/27 = 59.3%

– Undisturbed wind velocity reduced by 1/3

– Albert Betz (1928)

Wind Turbine Spec.

Rated

Cut-in

Location for Wind Turbine

Climatic data form Meteorological Mast

© 2007 AWS Truewind, LLC

Typical Met Mast

• Heights up to 120 m

• Tubular pole supported by guy wires

• Installed in ~ 2 days without foundation using 4-5 people

• Solar powered; cellular data communications

Wind Shear The change in horizontal wind speed with height

• A function of wind speed, surface roughness (may vary with wind direction), and atmospheric stability (changes from day to night)

• Wind shear exponents are higher at low wind speeds, above rough surfaces, and during stable conditions

• Typical exponent () values:– .10 - .15: water/beach

– .15 - .25: gently rolling farmland

– .25 - .40+: forests/mountains

= Log10 [V2/V1]

Log10 [Z2/Z1]

WindShearProfile

WindShearProfile

V2= 19.4 m/sV2= 19.4 m/s

V1 = 18.4 m/sV1 = 18.4 m/s

Z2= 70 mZ2= 70 m

Z1= 50 mZ1= 50 m

V2 = V1(Z2/Z1)

Wind speed, and available power, generallyincrease significantly with height

Hub

Wind Shear Calculation from Meteorological Data = Log10 [V2/V1]

Log10 [Z2/Z1]V2 = V1(Z2/Z1)

70m 50m α   80m 100m 78m 75m 90m 65m 60m 55m 44m

18.8 17.9 0.145796 19.16959 19.8035 19.09896 18.99006 19.50162 18.59797 18.38219 17.9 17.56948

18.9 17.9 0.161562 19.31217 20.02111 19.23334 19.11185 19.68319 18.67506 18.43511 17.9 17.5341

18.9 18 0.145005 19.26952 19.90322 19.19891 19.09003 19.60145 18.69799 18.48222 18 17.66942

18.9 18 0.145005 19.26952 19.90322 19.19891 19.09003 19.60145 18.69799 18.48222 18 17.66942

19 18 0.160689 19.41209 20.12077 19.33327 19.21181 19.78299 18.77508 18.53515 18 17.63403

19 18 0.160689 19.41209 20.12077 19.33327 19.21181 19.78299 18.77508 18.53515 18 17.63403

19.1 18.1 0.159824 19.512 20.22043 19.43321 19.31178 19.88279 18.87511 18.63518 18.1 17.73395

19.1 18.1 0.159824 19.512 20.22043 19.43321 19.31178 19.88279 18.87511 18.63518 18.1 17.73395

19.2 18.1 0.175344 19.65485 20.43913 19.56779 19.43368 20.06499 18.95212 18.68799 18.1 17.69881

19.2 18.2 0.158969 19.61192 20.3201 19.53315 19.41174 19.98259 18.97513 18.73522 18.2 17.83388

19.2 18.2 0.158969 19.61192 20.3201 19.53315 19.41174 19.98259 18.97513 18.73522 18.2 17.83388

19.2 18.4 0.126488 19.52704 20.08604 19.46461 19.36829 19.82014 19.02086 18.82926 18.4 18.10488

19.4 18.4 0.157286 19.81176 20.51945 19.73302 19.61167 20.18221 19.17518 18.93529 18.4 18.03374

19.4 18.5 0.141178 19.76919 20.40189 19.69866 19.58988 20.10067 19.19809 18.98237 18.5 18.16912

Time variation of wind Velocity

Average wind speed

Wind speed distribution is a critical factor in wind resource assessment.

Site 2

Site 1

Site 1 will generate power throughout the day with 15m/s wind speed.

Site 2 the turbine will be idle throughout the day as the velocity is 30 m/s.

Frequency distribution of Wind Velocity in a month

Statistical models for wind data analysis

Weibull distribution1. The cumulative distribution

function

2. The probability density function

where,

V = wind speed in m/s

k = dimensionless weibull shape parameter

c=weibull scale parameter in m/s

1

( )

kk V

ck Vf V e

c c

0( ) 1 ( )

kV

vcF V e f V dv

Statistical models for wind data analysisProbability functions were fitted with the field data to identify suitable

statistical distributions for representing wind regimes.

Weibull probability density function

Weibull probability density function for c =8 m/s.

c

cc

ccc

Weibull probability density function for k= 2

Methods for determining Weibull parameters k and c

• Least square linearisation method

• Standard Deviation method

• World Meteorological Organisation (WMO) method

• Justus approximation method

• Maximum likelihood method

• Graphical method

Determining k and c using least square linearisation method

( ) 1

kV

cF V e

1

( ) ( )i

i jj

F V P V

Determining k and c using least square linearisation method

( ) 1 ...............(2)

kV

cF V e

1

( ) ( )...................(1)i

i jj

F V P V

1 ( ) ....................(3)

kV

cF V e

ln(1 ( )) ....................(4)k

VF V

c

ln[ ln(1 ( ))] ln ln .........(5)F V k V k c

......................(6)y ax b

ln[ ln(1 ( ))]

ln

ln

y F V

a k

x V

b k c

By equating eqn(5) and eqn(6)We get,

Determining k and c using least square linearisation method

2

1

2 2

1

1 1

( )( )( )

( )( )

1

w

i i ii

w

i ii

w w

i ii i

p V x x y ya

p V x x

ab y x

w w

bk

k a

c e

Where x and y are the mean values of xi

and yi respectively and w is the total number of pairs of values available.

Then the Weibull parameters are,

Annual Energy Production

Frequency of wind speed

Annual Energy Production

Where:Ei=Energy per wind speed

f(V)i=Frequency of wind speed

Pi =Power of WIG in a wind speed

( ) 8760i i iAEP E f V P

1

( )

kk V

ck Vf V e

c c

Wind Utilization Index (WUI)

Annual energy production by the WEG at the site

Annual energy content of wind regime at the siteWUI

•WUI is an index of site-machine matching

•Varies from 20% – 40% (study on 110 sites)

•The higher is WUI the lower is cost of generation

Better SiteBetter Site

References:

• Wind Energy - Gerhard J. Gerdes

• Wind Energy Fundamentals, Resource Analysis and Economics- Sathyajith Mathew

• Wind Energy-Cy Harbourt