how to determine the portfolio effect based on wind regime dependency: european examples
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How to determine the Portfolio Effect based on wind regime dependency: European examples. José Manuel Marco Circe Triviño Guillermo Gil. EWEC 09 Marseille, 18 March 2009. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
How to determine the Portfolio Effect based on wind regime
dependency: European examples
José Manuel MarcoCirce TriviñoGuillermo Gil
EWEC 09 Marseille, 18 March 2009
The wind industry has seen large players owning portfolios of wind farms spread across regions and countries
Financing portfolios of wind farms allows uncertainties associated with wind variability to be mitigated
We show a statistical and meteorological perspective with due consideration to the correlation of the wind regimes at the wind farm sites
This is a tool to determine the degree of dependency between wind regimes in order to analytically evaluate the “portfolio effect
Benefit from reductions in energy prediction uncertainty levels
Introduction
Wind Variability
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Month
Win
d S
peed Portugal
France
Spain
Average
IntroductionWhat do we mean with “Portfolio Effect”?Geographic spread Lower overall wind speed variability
Extreme wind conditions are balanced in average
Financing a portfolio of wind farms provides reduced risks due to reduced wind variability uncertainty
Introduction
Wind sites spread around
Production data or wind data as a proxy
We are able to add the wind variability
uncertainties as partially dependent (portfolio
effect) This allows mitigation of the wind variability
uncertainties and the overall portfolio
uncertainty associated to the energy production
estimation
With statistic techniques we find
a statistical relation
(dependency) between those wind regimes
(Pearson coefficient)
Definition of Uncertainty
• For the Wind Analysis: That associated with the prediction of the long-term annual average energy production, typically expressed as a standard deviation, σ.
• The estimation of the energy production defines the mean, and the uncertainty in the estimate, σ. A Gaussian distribution is the industry standard assumption.
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AnemometerWind shearCorrelation toreference
Periodrepresentative
of long-term
Frequencydistribution
Wind flowmodeling
Future 1-yrvariability
Uncertainty source
Un
cert
ain
ty [
% o
f n
et
en
erg
y]
Uncertainty Analysis - Sources
Technical uncertainties
Wind variability uncertainties
Uncertainty Analysis – Wind Variability
Our analysis focuses in the reduction of the uncertainty associated to the wind variability uncertainty sources of combined projects
Statistical basis - Parametric techniques (1)
When using Parametric Inferential Statistics , the correlation coefficient “r” is given together with a confidence interval,
which contains the value of the population parameter (with a concrete significance level) and, at the same time, this interval expresses how representative the sample is
Statistical basis - Parametric techniques (2)
• (1)Both the population and the sample must fit to a normal distribution.
• (2)Independency of the samples
Kolmogorov-Smirnov normality test
Ljung-Box test of autocorrelation
Loma Negra
Perc
ent
7500500025000-2500-5000
99.9
99
95
90
80706050403020
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5
1
0.1
Mean 9.734StDev 1724N 94AD 0.483P-Value 0.225
Normal - 95% CILoma Negra
Lag
Auto
corr
ela
tion
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Loma Negra
Portfolio Effect – Pearson matrix and confidence intervals
The correlation coefficient “r” is given together with a confidence interval, which contains the value of the population parameter, with a significance level of 95%.
The level of dependence between project uncertainty elements is described by the Pearson or correlation coefficient, r
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...
1...
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...1
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1
21
1112
m
i
mj
r
r
r
rrr
Pearson Matrix
Portfolio Effect – Uncertainty Matrix
A portfolio of m wind farms with its future wind uncertainties
...... m21
It is necessary to combine (add) the uncertainties with the correlation structure defined by the Pearson Matrix:
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...1
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21
1112
m
i
mj
r
r
r
rrr
m
...
...2
1
...... m21
Uncertainty Matrix
Portfolio Effect – Variance-Covariance matrix
The sum of all the elements in the above matrix is the portfolio variance, and its square root, the final uncertainty associated to the portfolio
Variance-Covariance Matrix
2
2
1111211221
...00
......
0
...0
22...2
m
i
mmjj rrr
Our case – European portfolio
Our portfolio consists of 75 wind farms distributed across Portugal, Spain, France and Germany
Our Pearson Matrix consists of 75x75 = 5625 Pearson coefficients
Since it is a symmetric matrix, we have analyzed 2775 coefficientsand its associated confidence interval, with a significance level of 95%,
in order to evaluate the statistical significance of Pearson and adjust it when necessary
Pearson Matrix
Pearson Coefficient
Number of pairs of the correlation
Interval (0.56 – 0.90)
95 % confidence
Statistical+Meteorological Analysis
Pearson = 0.29
Pearson = 0.49
Pearson = 0
Independency
Results of the Analysis- 1-year scenario
Energy prediction of the portfolio 3793 GWh/year Uncertainty without Portfolio Effect 651 GWh/year
Uncertainty considering Portfolio Effect 488 GWh/year
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GWh/year
No portfolio Effect
Portfolio Effect
Two different Gaussian distributions depending on the Uncertainty = σ
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GWh/year
Results of the Analysis – 1-year scenario
P50 = 3793
P75 = 3463
P75 = 3354
P90 = 3167
P90 = 2958
Lower uncertainties imply higher energy estimations for the same exceedance levels P75, P90
Summary and conclusions (1)
The analysis is carried out using real production data or monthly wind speed data as proxy, which have been used to state a level of dependency/independency between sites summarised by a Pearson coefficient matrix.
Combining this matrix with the individual uncertainties, it is possible to determine the “portfolio effect” associated with wind speed variability uncertainties.
The “portfolio effect” of the wind speed variability uncertainty of a portfolio made up of 75 wind farms in different geographical areas has been assessed in this presentation.
Summary and conclusions (2)
Estimated Energy Production
Overall uncertainty
1-year
[GWh] [GWh]
No “portfolio effect”
3793 651
“Portfolio effect”
3793 488
Benefit due to “portfolio effect” in the wind speed variability in a 1year
scenario25.0%
Summary and conclusions (3)The geographic and climatological dispersion intensifies the independency between wind regimes and therefore increases the observed “portfolio effect”
The scope of this study is to show the importance of considering and quantifying this effect when analysing portfolios rather than considering the wind farms as isolated entities
This feature is very important for investors and owners to mitigate wind risks by acquiring or developing a geographically distributed wind farm portfolio.
Thanks for your attention
[email protected]@garradhassan.comwww.garradhassan.com