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
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- 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
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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
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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
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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)(
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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 !
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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
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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
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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])
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)/x²(ln1²dP1 0model
²2
)/x²(lnexp
2x1
²x2²dP
exp2x
1dx)dP(elmod
0
0
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total spectrum from a group of wind farms
SS
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