Time-series modelling of aggregate wind power output

Time-series modelling of aggregate wind power output

Alexander Sturt, Goran Strbac17 March 2011

Introduction

Eastern Wind Integration and Transmission Study (EWITS) (2010)

• Wind datasets prepared by AWS Truewind over 9 month period

• Created by simulation using mesoscale Numerical Weather Prediction (NWP) model

• 3 years of synthetic data, 1326 sites (freely available online)

• Hardware used: 80 x dual CPU quad core penguin workstations (640 cores)

• Run time per year of simulation: 21 days (in theory...)

What if this level of detail isn’t needed?What if we need a model of aggregated wind output?What if we need to understand the statistical properties?

Modelling strategy

• Univariate model for aggregate wind power, not wind speed• Autoregressive driver: AR(p), hourly (or half-hourly) timesteps

• Include diurnal variation with periodic additive term:

• Fit to long-term distribution with transformation function:

• Use different models for the different seasons

kkkk XXX ...2211 iid N(0,1)

nkkk XX mod

kk XP W

n = number of data points per day

Model calibration

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1. Choose these to satisfy long-term distribution and diurnal variation, assuming X~N(0,1)

Model calibration

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2. Choose parameters of AR model to fit short-term transitional properties and N(0,1) asymptotic distribution

Case study: GB2030 model

• 6 years of hourly wind speed data taken from MIDAS dataset by Olmos (2009)

• 116 sites (onshore only)• 10m anemometer data extrapolated to hub-height and

converted to wind power using turbine curve• Regional weightings chosen to match core 2030 buildout

scenario used by Poyry (2009); offshore capacity mapped to nearest onshore regions

Olmos Poyry

GB2030: modelling strategy

• Weighted regional power output aggregated to produce a univariate time series

• Split into four seasons• For each season, calibrate model to reproduce

asymptotic distribution, diurnal variation and short-term volatility, using AR(2) model

• Tweak to approximate effect of offshore component

GB2030 (untweaked): distribution and volatility

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Power output bucket (p.u.)

Sim Upper Sim LowerSim Mean Hist2001-2Hist2002-3 Hist2003-4Hist2004-5 Hist2005-6Hist2006-7 Hist Av

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Time horizon (hr)

Sim Upper Sim LowerSim Mean Hist2001-2Hist2002-3 Hist2003-4Hist2004-5 Hist2005-6Hist2006-7 HistAv

Power output distribution Volatility curve

GB2030 (untweaked):distribution of absolute power output changes

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Power output change bucket (p.u.)


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1 hr 4 hr

8 hr 24 hr

GB2030: variation of 4hr volatility with power level

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What about turbine cutout?

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Sim Upper Sim LowerSim Mean Hist2003-4Hist2004-5 Hist2005-6Hist2006-7 Hist2007-8Hist2008-9

8 Jan 2005

Denmark, distribution of 4-hour changes (non-rolling window)

GB2030: tweaking strategy (1)

Diurnal variation is too great• Lunchtime wind speed peak at hub height is less pronounced

than at anemometer height (insolation reduces stability)

• Offshore component has no diurnality

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Mea

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Olmos Summer

Olmos Winter

NG Summer

NG Winter

=> Reduce μ values by a factor of 4

GB2030: tweaking strategy (2)

Offshore component increases mean capacity factor (28% -> 33%)=> Stretch W function so as to match duration curves shown in Poyry (2009). Use same AR parameters as untweaked model

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Poyry 2030 data (43GW capacity) Synthetic data from tweaked GB2030 model

GB2030: Effect of tweak

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Power output distribution Volatility curve

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01-Dec-08 11-Dec-08 21-Dec-08 31-Dec-08 10-Jan-09 20-Jan-09 30-Jan-09

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)GB2030: Time history sample (“Turing test”)

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Poyry data

Tweaked GB2030 synthetic winter data

• Non-Gaussian wind power time series can be transformed to a Gaussian (X) domain and modelled with a Gaussian time series model

• Synthetic time series reproduce the important long-term and transitional properties (for power system simulation)

• Simplicity of model makes it possible to write down formulae for any desired statistic

• Transformation to Gaussian domain simplifies modelling of correlated RVs:

• Forecast errors (anti-correlated with wind realisation to prevent forecast biasing)

• Multi-bus models• Combined demand / wind model

Conclusions

• Sturt, A. and Strbac, G. “Time series modelling of power output for large-scale wind fleets”, Wind Energy, 2011 (to be published)

• Enernex Corporation “Eastern Wind Integration and Transmission Study”, 2010 http://www.nrel.gov/wind/systemsintegration/ewits.html

• Olmos, P. “Probability distribution of wind power during peak demand”, MSc dissertation, University of Edinburgh, 2009

• Olmos, P.E., Dent, C., Harrison, G.P. and Bialek, J.W. “Realistic calculation of wind generation capacity credits”, CIGRE/IEEE Symposium on integration of wide-scale renewable resources into the power delivery system, Calgary, 2009

• Poyry Energy Consulting, “Impact of intermittency: how wind variability could change the shape of the British and Irish electricity markets: summary report”, 2009 http://www.poyry.com

• Sturt, A. and Strbac, G. “A time series model for the aggregate GB wind output circa 2030”, 2011http://www.ee.ic.ac.uk/%20alexander.sturt07/GB2030SOM.pdf

References

http://www.nrel.gov/wind/systemsintegration/ewits.html



http://www.poyry.com/

http://www.ee.ic.ac.uk/%20alexander.sturt07/GB2030SOM.pdf

Time-series modelling of aggregate wind power output

Documents

wind datasets

diurnal variation

power levelwxxwhat

longterm distribution

model calibrationxwp2

parameters of ar model

greatlunchtime wind

years of synthetic data