Characterization and modellinggof the power output variability of wind farms clusters

Hans Georg BeyerHans Georg BeyerDepartment of EngineeringUniversity of Agder, Grimstad

Characterization and modellingof the power output variability of wind farms clustersp p y

- increasing contribution of di t h bl ( bl )non-dispatchable (renewable) power

calls for new strategies of system operation, unit dispatchand storage management

- for the design of the new strategies, detailed knowledge on the characteristics of the renewable power flows is nececessary

Characterization and modelling of the power output variability of wind farms clustersp p y

- detailed knowledge on the characteristics of the renewable power flowsthe characteristics of the renewable power flows is necessary

examples are e g developed in Germanyexamples are e.g. developed in Germany where regional shares of wind energy may amount up to ~50%

Source: DEWI 2010

Characterization and modelling of the power output variability of wind farms clustersp p y

- detailed knowledge on the characteristics of the renewable power flowsthe characteristics of the renewable power flows is necessary

examples are e g developed in Germanyexamples are e.g. developed in Germany

- for day-to day operation:schemes for wind power forecasting are in operational use

- for planning of capacity extension and grid reinforcement:tools for the characterization of the power output variabilityhad bee set up

Characterization and modelling of the power output variability of wind farms clustersp p y

- examples are e.g. developed in Germany

- for planning of capacity extension and grid reinforcement:tools for the characterization of the power output variabilityhad been set uphad been set up

e.g. Quintero et al. DEWEK 2008 Knorr et al. EWEC 2009coop. with Fraunhofer IWES, Kassel, Germany

following:

- approaches usedapp oac es used

- outlook: how to extend to the Norwegian offshore environment

Characterisation output variability / exampleCharacterisation output variability / example Germany

wind power ofwhole Germany

group of wind farmsgroup of wind farms

single wind turbine

Increasing size of aggregation lower variabilitySmoothing effect:6

approaches for characterisationapproaches for characterisationAim: Quantification of smoothing effect

Statistical Approach• Aggregation of Power Output• Probability Density Function• Modeling

Spectral Approach• Power Spectral Density

• Low Frequency Range• High Frequency Range

• Coherence FunctionCoherence Function• Total Spectrum

7

aggregation of power output / exampleaggregation of power output / example

60 wind farms:- distributed over whole

Germany - 1 hour mean values of

wind power & prediction- recorded in 2005

Aggregation 1 = Wind farm 1 34 MW

Aggregation 2 = Wind farm 1 Wi d f 2 126 MW

Aggregation 60 = Wind farm 1 + … + Wind farm 60 2057 MW

+ Wind farm 2 126 MW

randomlychosen

8

- wind power increments dP

probability density functionsprobability density functions

daily (0.4%)

once in a

hourly increments of wind power dP [% of Pn]

year (0.01%)

20% of dP between -1% and 0% of Pnnot Gaussian but intermittent distributed

74% of dP between -5% and 5% of Pnnot Gaussian, but intermittent distributed

9

smoothing effect of wind farm aggregationssmoothing effect of wind farm aggregations

10

approaches for characterisationapproaches for characterisation

Aim: Quantification of smoothing effect

Statistical Approach

Aim: Quantification of smoothing effect

• Aggregation of Power Output• Probability Density Function• Modeling• Modeling

Spectral Approachp pp• Power Spectral Density

• Low Frequency RangeHi h F R• High Frequency Range

• Coherence Function• Total Spectrum

11

spectral approachspectral approach

S S

fS(f

) power spectral densityaverage

S S4 wind turbinesresolution: 0.1s

f1h-1 15min-1 1min-1

S S

20 wind farmsresolution: 1min

(f

)

coherence

f SS

averagetotal spectrum of group of wind farms

S

12

power spectral density: low frequency rangepower spectral density: low frequency range

1E-7Fit im Frequenzbereich 10-5 bis 10-3 Hzf f 105 10 3f f 1 1 1 1

Average of 20 wind farms spektrum

1E-8

Fit im Frequenzbereich 10bis 10 HzFit in frequency range from 10-5 up to 10-3 HzFit in frequency range from 1h-1 up to 15min-1

1E-9

S(f)

1E-10

f

1E-11

1E-7 1E-6 1E-5 1E-4 1E-3 0,01

frequency [Hz]

556,0131061,7 ffSf13

approach:

power spectral density: high frequency rangepower spectral density: high frequency range

Average of 4 wind turbines spektrumFit i f f 15 i 1 t 15 i 1

1E-7Fit in frequency range from 15min-1 up to 15min-1

1E-8

f S(f)

1E-9

f

1E 3 0 01 0 1 1 10 1001E-10

5

fafSf Kaimal – Spectruma = 0,00003

1E-3 0,01 0,1 1 10 100frequency [Hz]

approach:

35

1 fbff

Kaimal Spectrum

+ extensions (Risø)b = 557

14

coherence between wind farms

)(2

fS

Definition

coherence between wind farms

)()(

)()(2

fSfS

fSf

yyxx

xyxy

Fit

Calculated+

distance = 30 km

Fit

Calculated+

distance = 30 km

Theoretic Expectation

fdc

ji

jiedc

fd

)(

,2

2)(

),(f

jijiedc )(

,1,2)(

15

spectrum power output fluctuationscombined power output in a grid sectionmeasured and modelled

SS(f

)f·S

(

1/(24h)

1/(100s)

frequency [Hz]

how to extend to the Norwegian offshore environment ?

application of the schemes presented

how to extend to the Norwegian offshore environment ?EWEA 2010

-> requires adaption model parametersf N i i d li tfor Norwegian wind climate-> requires data

[max wich][max. wich]wind speed and power output- with temporal resolution 1a – 1swith temporal resolution 1a 1s- at a station networkwith interstation distances500m (turbine spacing in farm)several 10km – 100km (spacing of farms)

17 every contribution to data sets welcome !

Thanks !

18

total spectrum from a group of wind farms

SS

20

conclusion

- development of model of PDF of

conclusion

d fitwind power gradients

depending on installed capacity spatial distribution

good fit

depending on installed capacity

- approach to model the PSD of wind farmsfor low frequency range

pshould be integrated

exponential functionfor low frequency rangeand high frequency range

exponential functionKaimal spektrum

- analysis of coherence model needsimprovements

further development

21

further development

Modell Building → SimulationModell Building → Simulation

anticipating future scenarios

Park effect::Wind farm efficiency (average for 12 farms)

Estimation of power curves for future ‘average‘ turbine

Estimation of power curve for wind farmEstimation of power curve for wind farm

Perform ance of the modelPerform,ance of the model

Normalized power output : - data Germany 2007- modell 2007- modell 2020

prob. distrubution averaged wind speedprob. distrubution averaged wind speed

power curve ‘Germany‘

frequency distrubution total power outputfrequency distrubution total power output

occurence of power output changes

Characterization and Modeling of the Variabilityof Power Output from Aggregated Wind Farms

DEWK 2008

C. Quintero, K.Knorr, B. Lange, H.G. Beyer

Simulation and Analysis of Future Wind Power Scenarios

EWEC 2009

K. Knorr, C.A. Quintero Marrone, D. Callies, B. Lange, K. Rohrig, H.G. Beyer

29

model development

²2)/²(lnexp

21

²2²exp

21)(mod 0

0

x

xxdP

xdxdPel

model of intermittent distributions:(modified after [Castaing 1990])

model development

(modified after [Castaing, 1990])

30

)/x²(ln1²dP1 0model

²2

)/x²(lnexp

2x1

²x2²dP

exp2x

1dx)dP(elmod

0

0

31

total spectrum from a group of wind farms

SS

32