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

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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

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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

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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.

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

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Modelling along-wind decorrelation Kristensen model of turbulent eddy decay Eddies decay with time constant (n): function of frequency n ( = U/ ) P 1 = probability of eddy surviving for time t, or for distance x = U t P 1 (n) = e - t/ (n) = e - x/(U (n)) Transversal diffusion: P 2 = 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: P 1 P 2 = Assumptions: (axisymmetric Gaussian transversal diffusion, isoptropy and neutral lapse rate) and G( ) = 2 ( + 1/121) 0.5 / ( + 1/33) 11/6

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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. f i = f(n i ) represents the extent to which eddies from realisation 1 have evolved into realisation 2. f i = P 1 P 2 =

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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 f i = Applied similarly to other two components of turbulence: just use the appropriate spectrum and length scale. Still no mass flow continuity

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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

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Example simulation results (2) Two ‘Ideal’ sensors: 1.measuring lateral component at a single point 75m ahead of the turbine and 45m to the side 2.measuring vertical component at a single point 75m ahead of the turbine and 45m above centreline

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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)

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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.

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Example: Lidar-assisted collective pitch control Time history DEL for this simulation 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 Steel

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Reducing extreme loads 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? What is an extreme gust???

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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

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

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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?

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

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