SYSTEMATIC QUANTIFICATION
OF WAKE MODEL UNCERTAINTY
And additional perspectives
Nicolai Gayle Nygaard
VindKaftNet, November 25 2015
How certain are modelled wake losses?
OR
What do the data tell us?
2
Example wind farm AEP losses
Fraction of
gross AEP
Relative
uncertainty
Electrical
3%
50%
WTG
unavailability
4%
50%
Substation
unavailability
0.5%
25%
Wakes
12%
50%
Grid availability
0.5%
25%
Blade
degradation
0.5%
25%
Loss
3
Uncertainty defines
68% confidence interval
(1 standard deviation)
Wake model uncertainty presumed high
4
Systematic quantification of wake model uncertainty
VALIDATION
Wake model
(this presentation: Jensen model)
Observed wake losses
No model fitting
Wake decay parameter k=0.04 for all wind farms
5
Wake model error
Uncertainty defines
68% confidence interval
(1 standard deviation)
True wake loss:
value realised
Wake model error:
Losstrue −Lossmodel
6
Bias
Uncertainty
Relative wake model error
Lossobs − Lossmodel
𝜀=
Lossobs
AEP conservative
AEP optimistic
𝜀
Model over-predicts
wake loss
7
0
Model under-predicts
wake loss
Wind farm production
N
N
E W
W
S
E
Wind speed/direction
S
SCADA
validation data
8
Bootstrapping SCADA data
Re-sampling
with replacement
Circular block
bootstrap samples
Wind farm production
N
N
E W
W
S
E
Wind speed/direction
S
SCADA
validation data
11
Bootstrapping SCADA data
Re-sampling
with replacement
Circular block
bootstrap samples
Wind farm production
N
N
E W
W
S
E
Wind speed/direction
S
SCADA
validation data
11
Bootstrapping SCADA data
Re-sampling
with replacement
Circular block
bootstrap samples
Wind farm production
N
N
E W
W
S
E
Wind speed/direction
S
SCADA
validation data
11
Bootstrapping SCADA data
Re-sampling
with replacement
Circular block
bootstrap samples
Wind farm production
N
N
E W
W
S
E
Wind speed/direction
S
SCADA
validation data
11
Bootstrapping SCADA data
Re-sampling
with replacement
Circular block
bootstrap samples
Bootstrap statistics
Bootstrap sample
net and gross power
Bootstrap
sample
wind climate
Lossobs −Lossmodel
Relative model error 𝜀 =
Lossobs
Input to
wake model
12
Modelled
wake loss
Observed
wake loss
Model error distribution
We define the uncertainty from 68% confidence interval
13
Wind farms – shapes and sizes
Walney 1+2
London Array
Burbo Bank
Barrow
Horns Rev 1
Gunfleet Sands
Anholt
Horns Rev 2
Nysted
14
Walney 1
Model AEP conservative
Very few
data after
filtering
Model AEP optimistic
Probability
Bootstrap
distributions of
relative model error
Example:
10% wake loss
15% uncertainty
Loss=10%±1.5%
Relative wake model error [%]
Wake model extrapolation uncertainty
New wind farms
 Worst case: bias not
predictable
 Consider distribution over
all wind farms
Portfolio estimate:
 Bias ≈ 0
 Uncertainty = 16%
16
Conclusions so far
• Applicable to any wake model
• Tested on Jensen wake model
• No model fitting
• Uncertainty well below common
industry estimate
17
Uncertainty [%]
• Systematic framework
40
16
Jensen
model
Industry
standard
Will the wake model still work
If turbines increase in size?
If wind farms get larger?
If there is a neighbour?
19
Does (turbine) size matter?
6 MW
D=154 m
2 MW
D=80 m
20
Does (turbine) size matter?
2 MW, 80 m rotor diameter
21
6 MW, 154 m rotor diameter
Does (wind farm) size matter?
Nygaard, J. Phys.: Conf. Series 524, 012162(2014)
22
Before neighbour wind farm
23
After neighbour wind farm
24
Neighbour mainly affects nearest turbines
25
Summary
Systematic uncertainty
quantification
Wake model uncertainty < 20%
Larger turbines, larger wind farms,
neighbours – no problem
26
Thank you for your attention
Backup slides
28
Observed wake loss
Observed gross power

Power of free stream turbines
 Scaled to N turbines
 Averaged over validation sample
Observed net power

Power of all operating turbines
 Scaled to N turbines
 Averaged over validation sample
Lossobs = 1 −
29
𝑃net
𝑃gross
Modelled wake loss
Modelled gross power

Validation sample wind climate
 Power curve
Modelled net power

Validation sample wind climate
 Power matrix – wind speed/direction
Lossmodel = 1 −
30
𝑃net
𝑃gross
Accounting for wind direction distribution
Equal model weighting in sector
31
Accounting for wind direction distribution
Model weighting based on actual distribution
32
Jensen model elements
33
Overlapping wakes
34