Transcript Slide 1

Preliminary assessment of wind climate fluctuations
and
use of Dynamical Systems Theory for resource assessment
Wolf-Gerrit Früh
Christina Skittides
With support from SgurrEnergy
Questions
• How sensitive is the electricity production of a wind
farm to the local wind statistics
• How will climate change affect the electricity
production from wind farms?
• How large are inter-annual variations in the electricity
production due to weather fluctuations?
• How much can a large spatial distribution of wind
farms smooth electricity output
• Can we use dynamic information for an improved wind
resource assessment and prediction at potential
development sites?
2
Data used
• Land surface wind data from the MIDAS data
record provided by the British Atmospheric Data
Centre, maintained by NERC
– Hourly winds from weather stations all over the UK
– In particular from two stations in Edinburgh,
Gogarbank and Blackford Hill
– Data format
• Wind speed in knots at 10 m above sea level
• Wind direction in degrees
• Wind data converted to m/s at a typical turbine
hub
3
Assumptions
• Standard wind shear profile

U z  U0


log
z


log
z0

• Best-fit Weibull distribution
• Typical turbine performance
curve
• Ideal turbine response
• All generation exported for
use
4
From wind distribution to electricity
 Number of hours
during which the wind
was u: Φ(u) * T
 The output from a
turbine during that
time: P(u)
 The electricity
generated during those
hours:
E(u)= P(u) * Φ(u) * T
 Total output:
Etotal = Σ E(u)
5
Weibull and Rayleigh distributions
• Cumulative Weibull
– k: shape factor
• Weibull
u' k
 
 c 
uu'  e
k 1
– c: scale factor

k u 
u    e
c c 
u k
 
c 

6
Capacity factor vs c with k = 2
7
Sensitivity analysis
6
5
4
Example:
100 MW farm with expected
Capacity factor 30%:
Income £26.2 m
3
2
Actual Capacity factor 27%:
Income £23.6 m
8
Deficit: £ 2.4 m
Does the wind always blow somewhere?
Fraction of sites
not producing
Fraction of sites producing at part capacity
Fraction of sites producing at full capacity
9
National capacity factor
for first 1000 days in 2010
10
Has the wind changed?
Edinburgh Gogarbank
Ccap = 0.14 ± 0.06
11
Has the wind changed?
Edinburgh Blackford Hill
Ccap = 0.28 ± 0.08
12
Assessing resource from a short
measurement campaign
• Short time to measure potential site
– Does not give good statistics
• Are the measurements correlated to a site nearby
with existing longer record?
•  Use ‘MCP’
– Measure a short record
– Correlate with longer record
– Predict resource at location
with shorter record
•  Christina
13
Statistical Modelling of Wind
Energy Resource
Christina Skittides
Supervisor: Dr. Wolf G. Früh
17th March 2011
14
MCP Methods
• MCP goal: characterize wind speed
distribution and estimate the annual energy
capture of a wind farm
• MCP methods: model relationship between
wind speed and direction at two sites
Measurement period: a year or more
Input: wind speed and wind direction
Output: mapping from one site to other
Use: apply mapping to more data from reference
site
15
•
MCP
Methods
MCP invariants:
wind speed, direction
distance, eg. time of flight delays
effects of terrain on the flow, eg. local obstructions
large/small–scale weather, eg. atmospheric stability
Reference
Derrick
Woods &
Watson
“Variance
Ratio”
Method
Characterisation
typical MCP
method
refinement
of typical
method
alternative
Approach
wind speed
linear
regression fit
same wind
speed, binned
wind direction
relate
variances from
reference and
target site
16
Dynamical Systems Theory
• Dynamical systems involve differential
equations that depend on position and
momentum
• Phase space: describes the system’s variables
• Attractor: defines the solution of the system
• Orbit: the path the system follows during its
evolution
Method needed to define equivalent variables
to the phase space ones
Time-delay
17
Time-Delay/PCA Theory
Time-Delay:
• practical implementation of dynamical systems
• Results sensitive to choice of delays
PCA
PCA:
• non-parametric method to optimize phase space
reconstruction
• identifies number of needed time- delays
• gives picture of their shape
• reduces dimensions so as to extract useful information
18
PCA theory
Useful PCA outputs:
• Singular Vectors: represent the dimensions of
the phase space, describe optimum way of
reconstructing it
• Singular Values: measure total contribution of
each dimension to total variance
• Principal Components (PC): describe the
system’s time series, separate important
variables from noise
19
Pendulum Example
• Dynamical system with two inputs x,y
Case A (without noise):
x= 3sin(t/0.7)
y= x+0.4sin(t/π)
Case B (with noise):
x= 3sin(t/0.7)
y= x+0.4sin(t/π) + 0.6ε
20
Pendulum Example
1
-1
0
tarr[,2]
0
-1
-2
-2
-3
-3
-3
0
200
400
600
800
-2
-1
1000
0
1
2
0.005
0.010
3
tarr[,1]
0
0.000
-0.015
200
-0.010
400
-0.005
600
pc[, 2]
800
0.005
1000
0.010
1200
0.015
1400
time
lambda
signal2
1
2
2
3
3
Case A
0
10
20
30
40
Index
50
60
70
-0.015
-0.010
-0.005
0.000
pc[, 1]
0.015
21
Noisy Pendulum Example
2
-4
-4
-2
-2
0
tarr[, (2 + win)]
0
signal2
2
4
4
Case B
-4
-2
0
2
4
tarr[, (1 + win)]
0
200
400
600
800
1000
0.005
-0.015 -0.010 -0.005
0.000
pc[, 2]
800
600
400
200
0
lambda
1000
0.010
1200
0.015
1400
time
0
10
20
30
40
Index
50
60
70
-0.015
-0.010
-0.005
0.000
pc[, 1]
0.005
0.010
0.015
22
Conclusions
• PCA is robust and useful for time series of
multiple inputs
• Noisy or “clean”data: no significant differences
• Choice of time-delay length and gap of entries
in the matrix not important
23
Gogarbank Data
• 10 year (2000-2010) data taken from
Gogarbank station, Edinburgh
• Input variables: wind speed, direction,
pressure, temperature
• Apply PCA to different models:
 all variables
 wind speed, direction and pressure
 only wind speed and direction
hourly
every 3 hours
weekly
×
×
2 weeks
×
×
monthly
seasonal
×
daily
×
×
24
Gogarbank Data
0
50
100
150
200
250
-0.03 0.02
pc[, 2]
0 60
lambda
• Only wind speed and direction,
hourly measurements per week
300
-0.03
-0.02
-0.01
0.00
-0.02
-0.01
0.00
0.01
0.02
0.03
-0.03
-0.02
-0.01
100
150
200
250
300
0
50
100
4000
td
0.03
150
200
250
300
6000
8000
-0.03 0.02
pc[, 3]
2000
0.02
Index
-0.03 0.01
pc[, 1]
Index
0
0.01
-0.10 0.05
svec[, 3]
0.00
50
0.00
pc[, 3]
-0.08
svec[, 1]
pc[, 2]
0
0.03
-0.02 0.04
pc[, 4]
-0.03
0.02
pc[, 1]
-0.03 0.02
pc[, 3]
Index
0.01
0
2000
4000
td
6000
8000
25
Conclusions
• Gogarbank station wind: dynamic behaviour
found in structure of PCs and singular vectors
• Adding pressure
no significant difference
• Temperature changes results significantly
since PCs concentrate on seasonal cycle
• Cyclic behaviour over the year, more windy
around January and from SeptemberDecember
• Using 1 week or 2 weeks identifies weather
(typical predictability of weather ~ 14 days)
26
Following Steps
• Apply PCA to simultaneous data from two
weather stations (Gogarbank & Blackford Hill,
Edinburgh)
Application to a one-year segment
Using Gogarbank for other years to predict
Blackford Hill
Comparison with actual measurements from
Blackford Hill
27