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Wind Energy I Michael Hölling, WS 2010/2011 slide 1 Wind field characterization

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### Transcript of Wind energy I. Lesson 3. Wind field characterization

Wind Energy I

Michael Hölling, WS 2010/2011 slide 1

Wind field characterization

Wind Energy I

slideMichael Hölling, WS 2010/2011 2

Class content

4 Wind power

5 Wind turbines in general 6 Wind - blades

interaction

7 Π-theorem

8 Wind turbine characterization

9 Control strategies

10 Generator

11 Electrics / grid

3 Wind field characterization

2 Wind measurements

Wind Energy I

slideMichael Hölling, WS 2010/2011 3

Motivation

Why should we know anything about the wind field ?

Atmospheric boundary layer (ABL)

Wind Energy I

slideMichael Hölling, WS 2010/2011 3

Motivation

Why should we know anything about the wind field ?

Atmospheric boundary layer (ABL)

Wind Energy I

slideMichael Hölling, WS 2010/2011 3

Motivation

Why should we know anything about the wind field ?

Atmospheric boundary layer (ABL)

Wind Energy I

slideMichael Hölling, WS 2010/2011 4

http://www.ecogeneration.com.auhttp://www.wind-energy-the-facts.org

Enercon E-126 BARD 5.0

Motivation

Wind Energy I

slideMichael Hölling, WS 2010/2011 5

Motivation

GROWIAN - Große Windkraftanlage (Big Wind energy converter)

Wind Energy I

slideMichael Hölling, WS 2010/2011 6

Resource wind

Kinetic energy of wind: E =m

2· u2 =

! · V

2· u2 =

! · A · x

2· u2

Wind energy converter can NOT convert 100% of that energy ! Consequently the power of the wind energy converter is also smaller:

PWEC = cp · 12

· ! · A · u3 = cp · Pair

Corresponding power for constant velocity u : Pair =

d

dt

!! · A · x

2· u2

"

=12

· ! · A · u2 · dx

dt

=12

· ! · A · u3

Wind Energy I

slideMichael Hölling, WS 2010/2011 7

Resource wind

Power curve of wind energy converter - theory

0 10 20 300.0

0.4

0.8

1.2

1.6

2.0

u [m/s]

P(u

) [M

W]

P(u)

cut in

cut out

rated

Wind Energy I

slideMichael Hölling, WS 2010/2011 8

Power curve of wind energy converter - reality

Resource wind

Wind Energy I

slideMichael Hölling, WS 2010/2011 9

Resource wind

Annual mean wind speed taken from wind atlas

Wind Energy I

slideMichael Hölling, WS 2010/2011 10

Resource wind

Estimation of Annual Energy Production (AEP) based on annual mean wind speed from wind atlas:

0 10 20 300.0

0.4

0.8

1.2

1.6

2.0

u [m/s]

P(u

) [M

W]

P(u)

500kW!u"annual # 7m/s

Wind Energy I

slideMichael Hölling, WS 2010/2011 11

Resource wind

Is such a calculation realistic ? How does real wind behave ?

Wind velocity time series (20 days)

Wind Energy I

slideMichael Hölling, WS 2010/2011 12

Calculation of 10-minute averaged wind speed

Resource wind

Wind Energy I

slideMichael Hölling, WS 2010/2011 12

Calculation of 10-minute averaged wind speed

Resource wind

Wind Energy I

slideMichael Hölling, WS 2010/2011 13

Resource wind

Distribution of 10-minute averaged wind speeds (u

)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

E(u)

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

E(u)

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

E(u)

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

E(u)

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 14

Resource wind

Estimation of energy production based on wind distribution

E(u)

energy production:

E =N!

i=1

E(ui) =N!

i=1

counts(ui)/6 · P (ui)

(u)

Wind Energy I

slideMichael Hölling, WS 2010/2011 15

Resource wind

Comparison of energy production for mean wind speed and 10-minute averaged wind speed distribution (example based on data of 20 days):

!u" = 6.3m/s 244 kW

E = counts(< u >)[h] · P (< u >)= 24 · 20 · 244 = 117120kWh

Wind Energy I

slideMichael Hölling, WS 2010/2011 16

Resource wind

E(u)

E =N!

i=1

E(ui) =N!

i=1

counts(ui)/6 · P (ui) = 166, 920kWh

Wind Energy I

slideMichael Hölling, WS 2010/2011 17

Resource wind

Description of wind speed distribution (u

)

Wind Energy I

slideMichael Hölling, WS 2010/2011 18

Resource wind

Convert to probability density by normalization

Wind Energy I

slideMichael Hölling, WS 2010/2011 19

Distribution can be fitted by Weibull distribution

Resource wind

A = scaling parameter

k = form parameter

A = 7

k = 2.59

Wind Energy I

slideMichael Hölling, WS 2010/2011 20

Weibull distribution

Resource wind

u [m/s]

Wind Energy I

slideMichael Hölling, WS 2010/2011 21

Resource wind

Atmospheric boundary layer (ABL)

Wind speed variation with height

Wind Energy I

slideMichael Hölling, WS 2010/2011 22

logarithmic profile

roughness length for topographical effects

thermal effects

Wind field characterization

Meteorological approach:

International Electrotechnical Commission (IEC) approach:power law profile

standard for site assessment

Alternative approach: stochastic analysis

high frequency data for better understanding

Wind Energy I

slideMichael Hölling, WS 2010/2011 23

Meteorological approach

Wind speed u (mean values) as a function of height z:

Logarithmic profile:

u* = friction velocity (typically between 0.1m/s and 0.5m/s)

k = von Karman constant, about 0.4

z0 = surface roughness length

Wind Energy I

slideMichael Hölling, WS 2010/2011 24

Meteorological approach

classes 3

2

10

Wind Energy I

slideMichael Hölling, WS 2010/2011 25

Meteorological approach

classes 3

2

10

Wind Energy I

slideMichael Hölling, WS 2010/2011 26

Influence of friction velocity u* on profile

Meteorological approach

Wind Energy I

slideMichael Hölling, WS 2010/2011 27

Influence of friction velocity u* on profile

Meteorological approach

Wind Energy I

slideMichael Hölling, WS 2010/2011 28

Meteorological approach Meteorological approach

Thermal effects make ABL stable, neutral or unstableMonin Obukhov

length

Wind Energy I

slideMichael Hölling, WS 2010/2011 29

IEC approach

Wind speed u (mean values) as a function of height z:

z2

z1

Power law profile:

α needs to be fitted from data !

Commonly used for wind energy applications !

u(z) = u(z1) ·!

z

z1

"!

Velocity at height z can be determined by:

Wind Energy I

slideMichael Hölling, WS 2010/2011 30

What is the difference between the two approaches ?

Wind profile

Wind Energy I

slideMichael Hölling, WS 2010/2011 30

What is the difference between the two approaches ?

Wind profile

u(z1)

u(z2)

Wind Energy I

slideMichael Hölling, WS 2010/2011 31

Wind profile

What is the difference between the two approaches ?

u(z1)

u(z2)

Wind Energy I

slideMichael Hölling, WS 2010/2011 32

Site characterization / assessment

IEC demands information for site characterization:

annual mean wind velocity

parameters for Weibull distribution of 10-min averaged wind speeds

annual mean wind profile

turbulence intensity Ti =!<u>10min

< u >10min

Wind Energy I

slideMichael Hölling, WS 2010/2011 33

Alternative approach

What happens in reality ?

Wind Energy I

slideMichael Hölling, WS 2010/2011 34

What happens in reality ?

Alternative approach