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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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

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ent

7500500025000-2500-5000

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99

95

90

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Mean 9.734StDev 1724N 94AD 0.483P-Value 0.225

Normal - 95% CILoma Negra

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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...

...

...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...

...

...1

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1

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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No portfolio Effect

Portfolio Effect

Two different Gaussian distributions depending on the Uncertainty = σ

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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

Jose.Marco@garradhassan.comCirce.Trivino@garradhassan.comwww.garradhassan.com