1. Un-freezing the turbulence: improved wind field modelling for investigating Lidar-assisted wind turbine control
Ervin Bossanyi

2. Contents Possibility of Lidar-assisted control for wind turbines
Reasons for current interest
Simulation modelling including Lidar sensors
Taylor’s Frozen Turbulence hypothesis
Unfreezing the turbulence
Evolution of wind field
Modelling along-wind decorrelation
Example simulation results
Decorrelation effect
Enhancement of collective pitch control
Reducing extreme loads
Turbulence with embedded gusts
Conclusions

3. Possibility of Lidar-assisted control for wind turbines
Lidars now well developed for site assessment
Turbine-mounted Lidars could be cheaper
Laser beam points ahead of turbine
Doppler-shifted reflection from particles reveals ‘line-of-sight’ wind speed
Scanning or multiple beams sample the swept area
Significant potential for load reduction
Wind field preview circumvents delays in feedback control
Possibility to reduce both fatigue and extreme loads
Limited potential for direct increase in energy output
Reoptimisation of turbine design will lead to improved cost-effectiveness…
…perhaps enough to pay for the Lidar, at least on large turbines

4. Simulation modelling including Lidar sensors
Wind field is sampled at points along the beam line
Wind vector resolved in direction of beam
Samples averaged using a weighting function
Single scanning beam or multiple fixed beams
Single or multiple focal points along beam (pulsed or continuous-wave Lidar)
Existing simulation models assume Taylor’s Frozen Turbulence hypothesis: turbulent variations convect downwind at mean wind velocity
In reality, turbulence measured by the Lidar will evolve and change before it reaches the turbine.
Control action based on the measurement will be incorrect.

5. Unfreezing the turbulencey
x, or t = x/U
Frozen turbulence:
3-dimensional wind field
Evolution of the wind field z y t
x = x0
x = x0 + xi x
4-dimensional wind field

6. Modelling along-wind decorrelation
Kristensen model of turbulent eddy decay
Eddies decay with time constant (n): function of frequency n ( = U/)
P1 = probability of eddy surviving for time t, or for distance x = Ut
P1(n) = e- t/(n) = e - x/(U(n))
Transversal diffusion: P2 = probability that an eddy seen at the first point will actually pass through the second point x downstream without drifting sideways
Total probability is a measure of coherence:
P1P2 =
Assumptions: (axisymmetric Gaussian transversal diffusion, isoptropy and neutral lapse rate)
and G() = 2 ( + 1/121)0.5 / ( + 1/33)11/6

7. Modelling along-wind decorrelation
Turbulence modelled by Veers method:
Spectrum
Random phase (correlated between grid points to represent cross-wind coherence)
Use two uncorrelated realisations with i,1 and i,2 (different random number seeds).
First realisation might evolve into the second one an infinite distance upstream.
fi = f(ni) represents the extent to which eddies from realisation 1 have evolved into
realisation 2. fi = P1P2 =

8. Modelling along-wind decorrelation
Could also be used with “non-Veers” wind fields (e.g. Mann): just use FFT to decompose turbulence into Veers form first; store spectrum & phase for each grid point and each frequency
Length scale L calculated by integrating the autocorrelation function, calculated as FFT of the power spectrum.
Can use other coherence models than Kristensen: all we need is an expression for the coherence fi =
Applied similarly to other two components of turbulence: just use the appropriate spectrum and length scale.
Still no mass flow continuity

9. Example simulation results (1)
‘Ideal’ sensor measuring longitudinal component at a single point 150m ahead of the turbine
Low frequencies remain similar;
High frequencies evolve more towards second realisation

10. Example simulation results (2)
Two ‘Ideal’ sensors:
measuring lateral component at a single point 75m ahead of the turbine and 45m to the side
measuring vertical component at a single point 75m ahead of the turbine and 45m above centreline

11. Example: Lidar-assisted collective pitch control
Simple Lidar feed-forward results in tighter speed control
Feedback gains then reduced to restore speed control and reduce loads
Preview information results in smoother, calmer control action
CW Lidar, 75m range, circular scan with 30º half-angle giving scan circle radius 37.5m (60% of turbine radius)

12. Example: Lidar-assisted collective pitch control
Small effect of decorrelation, as high frequencies already filtered out:
Averaging along beam (with weighting function)
Averaging around the circular scan (50 points in 1 second)
Further averaging to remove high frequencies, so that frozen turbulence is not “cheating” (cut-off frequency U/min where min = 17.3m chosen where Kristensen coherence = 0.2)
No cheating with unfrozen turbulence, so we can remove that last filter if it’s helpful.

13. Example: Lidar-assisted collective pitch control. Time history
Example: Lidar-assisted collective pitch control Time history DEL for this simulation
Steel
Tower base DEL sensitive to random number seed due to light damping
DEL reduced by 18.7% with frozen turbulence; average 16.9% if unfrozen
DEL reduced by 26.2% if filter removed

14. Reducing extreme loads
What is an extreme gust???
Even if it doesn’t evolve, with what speed and direction does the gust convect between Lidar measurement and turbine?
Could an extreme gust sneak up from the side, undetected?

15. Turbulence with embedded gust?
Gust shape consistent with spectrum and coherence model
May not represent the worst real events:
Non-Gaussian extreme turbulence
Low-level jets
Thunderstorm down-draughts
Eddies from topography
May not even generate particularly severe loads
Here, pitch action follows gust
Tower loading actually reduces
Some increase in asymmetric
loads

16. Embedded gust with unfrozen turbulence
Line-of-sight velocity during passage of gust, as measured by a Lidar
Not much evolution over 75m

17. Conclusions
Method proposed to simulate evolution of turbulent wind field, avoiding the “idealism” of frozen turbulence
Implementation based on Kristensen/Veers is easily generalised
Very simple Lidar feed-forward scheme has significant potential to reduce fatigue loads
Result is affected by evolution of the turbulence
As the evolution is now modelled, low-pass filtering can be minimised, which leads to significant further reductions in fatigue loads
Whether Lidar can be relied on to reduce extreme loads depends on definition of extreme load cases (standard gusts not really valid)
Embedded gusts may be more realistic, but are they sufficiently extreme?

18. Thank you for your attention Feedback / criticism / questions / discussion?