Spectral Coherence Models for the
Wind Speed in Large Wind Farms
A. Vigueras-Rodrı́guez1 , P.E. Sørensen2 & A. Viedma1
avigueras. rodriguez@ upct. es
1 Fluids
and Thermal Engineering Department
Universidad Politécnica de Cartagena
2 Wind
Energy Department
Risø National Laboratory
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
Power Fluctuation in a Wind Turbine
General Sketch of the system
Power Fluctuation in a Wind Turbine
General Sketch of the system
Equivalent wind speed model for power fluctuation
Power Fluctuation in a Wind Farm
Sketch of the system
Power Fluctuation in a Wind Farm
Sketch of the system: Wind model
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
Wind park model
The wind model farm used in this work is based on a matrix of
crossed power spectral density. An example of wind farm simulator
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using this kind of model is WINDPARK
Crossed Power Spectral Density
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Sxx (f ) ⇒ Model of the variability of the wind speed in a
single point. Models based on experimental results like
Kaimal, Solari, . . .
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Sxy (f ) ⇒ represents the relation between the variation of the
wind in two different points.
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p
Sxy = γ(f , . . . ) Sxx (f ) · Syy (f )
Coherence function: γ(f ) ⇒ Defined by empirical models
based on Davenport’s model.
Davenport’s exponential model: |γ(f , dxy )| = e −axy
Decay factor: axy
dxy ·f
U
Decay Factor Models
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Decay factor: axy
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Davenport’s Model ⇒ constant value (axy = 7.5, corrected
afterwards by Frost).
Solari ⇒ the value is not constant, and he proposed a
d
stochastic model depending of some variables: axy = b zxyxy .
Schlez and Infield ⇒ 2 significantly different situations
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Longitudinal decay factor: axy ,long = (15 ± 5) · Iu
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Lateral decay factor: axy ,lat = (17.5 ± 5 s/m) · Iu U
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Intermediate
situations:
p
axy = (along cos αxy )2 + (alat sin αxy )2
Aim of this contribution
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Check the models previously described for the usual
characteristics in a large wind farm.
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Study the dependence of the coherence with variables like the
wind speed, distance, inflow angle and/or the wind direction.
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Check the model for different time scales useful for power
fluctuation analysis (minutes to hours).
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
Nysted Wind Park
Distribution of the windmills in the wind farm of Nysted
Pairs of wind turbines: segments
Segment 01: distance 482m.
Pairs of wind turbines: segments
Segment 02: distance 964m.
Pairs of wind turbines: segments
Segment 03: distance 1445m.
Proceeding of the calculations:
Main characteristics of selected 2-hour intervals
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75% of valid data in MM2
At least 7 of the 72 WT with the following conditions:
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90% of valid data
Holes smaller than 3 seconds
Wind turbine working in a “normal” state
Coherence in the 2-hour interval is calculated by averaging Sxx ,
Sxy and Syy in similar segments with the following condition
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At least 8 pairs of valid combinations for each “segment”.
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
Results
Segment (0,+1)
Coherence for three different inflow angle intervals
Results
Segment (0,+1)
Negative logarithm of the coherence for each inflow angle interval
Results
Segments (0,+1) → ’o’, (0,+2) → ’∗’ and (0,+3)→ ’x’
Negative logarithm of the coherence for each inflow angle interval
Results
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Significant dependence of the inflow angle
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Exponential shape
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Light dependence of the wind direction, once considered the
inflow angle (and mainly due to the wake in the mast)
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Low slope in the coherence for the longitudinal situation
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Greater influence of the distance for the longitudinal situation
Comparing the decay factor -axy Comparison of the lateral and longitudinal decay factor for the
Schlez & Infield Model and the values obtained in the Nysted and
Høvsøre experiments:
1 Introduction
2 Decay Factor: definition and models
3 Experimental data
4 Comparison with the empirical models
5 Conclusions
Conclusions & Open Problems
Conclusions:
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Difference between the Schlez & Infield’s Model and these
empirical results are due to the different distance scale
considered.
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It is necessary to patch that model for making it suitable
within a wind farm frame
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Lateral decay factor (axy ,lat ) gets lower as the distance rises.
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Longitudinal decay factor remains constant in Høvsøre data,
as well as in Nysted data axy ,long ≈ 4.
Conclusions & Open Problems
Open Problems:
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All segments are being included in the analysis
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It should be developed a model for axy ,lat and for different α
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The expression axy ,long should be checked using the rest of the
segments
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Different time scales (medium frequencies).
Thank you for your attention
Questions and comments