Mechanical Characterization and FE Modelling of a Hyperelastic ...
Characterization and modelling of the power output ... · Characterization and modelling of the ppp...
Transcript of Characterization and modelling of the power output ... · Characterization and modelling of the ppp...
![Page 1: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/1.jpg)
Characterization and modellinggof the power output variability of wind farms clusters
Hans Georg BeyerHans Georg BeyerDepartment of EngineeringUniversity of Agder, Grimstad
![Page 2: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/2.jpg)
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
![Page 3: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/3.jpg)
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
![Page 4: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/4.jpg)
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
![Page 5: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/5.jpg)
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
![Page 6: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/6.jpg)
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
![Page 7: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/7.jpg)
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
![Page 8: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/8.jpg)
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
![Page 9: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/9.jpg)
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
![Page 10: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/10.jpg)
smoothing effect of wind farm aggregationssmoothing effect of wind farm aggregations
10
![Page 11: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/11.jpg)
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
![Page 12: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/12.jpg)
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
![Page 13: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/13.jpg)
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:
![Page 14: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/14.jpg)
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
![Page 15: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/15.jpg)
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
![Page 16: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/16.jpg)
spectrum power output fluctuationscombined power output in a grid sectionmeasured and modelled
SS(f
)f·S
(
1/(24h)
1/(100s)
frequency [Hz]
![Page 17: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/17.jpg)
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 !
![Page 18: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/18.jpg)
Thanks !
18
![Page 19: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/19.jpg)
![Page 20: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/20.jpg)
total spectrum from a group of wind farms
SS
20
![Page 21: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/21.jpg)
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
![Page 22: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/22.jpg)
Modell Building → SimulationModell Building → Simulation
anticipating future scenarios
![Page 23: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/23.jpg)
Park effect::Wind farm efficiency (average for 12 farms)
![Page 24: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/24.jpg)
Estimation of power curves for future ‘average‘ turbine
![Page 25: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/25.jpg)
Estimation of power curve for wind farmEstimation of power curve for wind farm
![Page 26: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/26.jpg)
Perform ance of the modelPerform,ance of the model
Normalized power output : - data Germany 2007- modell 2007- modell 2020
![Page 27: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/27.jpg)
prob. distrubution averaged wind speedprob. distrubution averaged wind speed
power curve ‘Germany‘
![Page 28: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/28.jpg)
frequency distrubution total power outputfrequency distrubution total power output
occurence of power output changes
![Page 29: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/29.jpg)
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
![Page 30: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/30.jpg)
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
![Page 31: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/31.jpg)
)/x²(ln1²dP1 0model
²2
)/x²(lnexp
2x1
²x2²dP
exp2x
1dx)dP(elmod
0
0
31
![Page 32: Characterization and modelling of the power output ... · Characterization and modelling of the ppp yower output variability of wind farms clusters - examples are e.g. developed in](https://reader031.fdocuments.us/reader031/viewer/2022012003/609fc77d9ba781794511a43e/html5/thumbnails/32.jpg)
total spectrum from a group of wind farms
SS
32