Power curves in Swedish conditions with

typical forest wind veer/shear and

turbulence

Matthias Mohr

Energiforsk - Tema Vindresurs

Wind turbine power curve

• Usually measured in coastal Northern Germany/Denmark (low

wind shear, little turbulence, no forest!Inner range conditions)

Figure from Enercon: E-141 EP4: 4.2 MW turbine

Østerild, Høvsøre, Emden Test

Site Or calculated for turbulent flow (with specified TI

and wind shear/veer across rotor):

Forest effects on power curves

Figure from Peter Stuart (RES Group) head of Power Curve Working Group

Power curve for laminar flow

Inner/outer range conditions

Can we estimate effects of this?

Inner/outer range:

Frequency & Energy Production

Outer range dominating for Swedish forest

sites!!!

BUT: Does it really matter for AEP? Should this be included in resource maps?

Wind turbine

1. Feels wind over whole rotor

(Rotor Equivalent Wind Speed)

2. Is affected by turbulence

Normal distribution

defined by 𝜎𝑢

Turbulent wind Real world distribution

Hub height (through rotor) wind speed in 10 minute interval

Rotor Equivalent Wind Speed

(REWS)

• Definition:

where Φi = wind angle between

area Ai and hub height.

𝑈𝑒𝑞𝑢𝑖𝑣 = (𝑈𝑖cos(𝜙𝑖))3 ∙𝐴𝑖𝐴

𝑖

1/3

However: Should another power curve

be used with REWS?

Rotor Equivalent Wind Speed vs

Hub Height Wind Speed

Histogram of differences (REWS - HHWS)

Difference in calculated AEP

Enercon E-126 EP4 4.2 MW turbine:

126 m rotor diameter, 100 m hub height

Using same power curve, but either HHWS or REWS

• From laminar power curve, turbulent power curves can be

constructed for different turbulent intensities 𝑇𝐼 =𝜎𝑈

𝑈

• Calculate frequency distribution for momentaneous

through-rotor wind speed U

• Multiply frequencies of this distribution

with power from laminar power curve

• Sum it up to get 10-minute average

power (𝑃 ) for every 𝑈 = 0, 1, 2, 3, 4, 5,… , 25 m/s for different TI-values

Turbulent power curve vs

Laminar power curve

Power = f(Turbulence intensity)

Assumptions:

U’ at hub height

Hub height wind speed (m/s)

Difference in calculated AEP

Generic 126 m 3.6 MW IEC class IIB turbine (from Teknikgruppen):

126 m rotor diameter, 100 m hub height

Using either power curve for 8% TI or TI-dependent power curves

Power production wind farm in

forest = f(Turbulence Intensity)

Turbulence

intensity (TI)

Hub height wind speed

and TI from nacelle

anemometer

Power production wind farm in

forest = f(Turbulence Intensity)

Same as before, but

binned averages!

Turbulence

intensity (TI)

Conclusions (Implications for

forests and Swedish sites)

• Forest characterised by sometimes high wind shear/veer

and high turbulence

• Stable conditions very frequent (characterised by high

wind shear and veer as well as low turbulence)

• “Outer range” power curve conditions seem to dominate

• REWS generally agrees well with hub height wind speeds

• AEP based upon

– REWS within roughly ± 1% of AEP based on hub

height wind speed only

– TI-dependent power curves within roughly ± 1% of

AEP based on standard power curve only

• Power curve from real forest wind farm = f(TI)

Thank you for your attention!

And thanks to our sponsors…

References

[1] M. Mohr, J. Arnqvist, H. Abedio, H. Alfredsson, M. Baltscheffsky, I. Carlén, L. Davidsson, A. Segalini,

S. Söderberg (2018): Wind power in forests II - Project Forestwind, Energiforsk report, to be published

Nov. 2018.

[2] ENERCON E-141 EP4 4.2 MW turbine power curve [Available from Enercon

https://www.enercon.de/en/products/ep-4/e-141-ep4/]

[3] Wagner, R. et al. (2009): The Influence of the Wind Speed Profile on Wind Turbine Performance

Measurements, Wind Energy, 12:348-362.

[4] Antoniou et al. (2013): Rotor Average wind speed for power curve performance. Proceedings of

Power Curve Working Group, 2nd meeting, 12 March 2013, Remisen Brande, Denmark. [Available at

http://www.pcwg.org/proceedings/2013-03-12/02-Rotor-Average-wind-speed-for-power-curve-performance-I-Antoniou-J-Cleve-

A-Piperas-SWP.pdf ]

[5] Stuart, P., 2014b: Overview of the Power Curve Working Group. Proceedings from Power Curve

Working Group, 8th meeting, 6 October 2014, Vaisala, Louisville, Colorado. [Available at

https://pcwg.org/proceedings/2014-10-06/01-Overview-of-the-Power-Curve-Working-Group-Peter-Stuart-RES.ppt ]

[6] Rivera Lamata, R. and D. Pollack, 2014: Turbulence Intensity measurements offshore for power curve

verification and wind resource assessment. Proceedings from Power Curve Working Group, 8th meeting,

6 October 2014, Vaisala, Louisville, Colorado. [Available at https://pcwg.org/proceedings/2014-10-06/06-

Turbulence-Intensity-measmnts-offshore-4-PC-verification-wind-res-assmt-R-RiveraLamatA-D-Pollack-Dong.pptx ]

Laminar flow power curve for

generic turbine

Shear exponent distributions

ca 60 - 150 m höjd

Shear exponent distributions

From Sodar

70 - 250 m höjd

Shear exponent versus wind speed

Hornamossen

Wind veer distributions

ca 60 - 150 m höjd

Wind veer verus wind speed

Hornamossen