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Time-series modelling of aggregate wind power output

Time-series modelling of aggregate wind power output. Alexander Sturt, Goran Strbac 17 March 2011. Introduction. Eastern Wind Integration and Transmission Study (EWITS) (2010). Wind datasets prepared by AWS Truewind over 9 month period

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Time-series modelling of aggregate wind power output

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  1. Time-series modelling of aggregate wind power output Alexander Sturt, Goran Strbac 17 March 2011

  2. 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?

  3. 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 iid N(0,1) n = number of data points per day

  4. Model calibration 1. Choose these to satisfy long-term distribution and diurnal variation, assuming X~N(0,1) X P W Σ μ

  5. Model calibration 2. Choose parameters of AR model to fit short-term transitional properties and N(0,1) asymptotic distribution X P W Σ μ

  6. 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

  7. 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

  8. GB2030 (untweaked): distribution and volatility Volatility curve Power output distribution

  9. GB2030 (untweaked):distribution of absolute power output changes 1 hr 4 hr 8 hr 24 hr

  10. GB2030: variation of 4hr volatility with power level W(x) x

  11. What about turbine cutout? Denmark, distribution of 4-hour changes (non-rolling window) 8 Jan 2005

  12. 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 => Reduce μ values by a factor of 4

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

  14. GB2030: Effect of tweak Volatility curve Power output distribution

  15. GB2030: Time history sample (“Turing test”) Wind output (GW) Poyry data Tweaked GB2030 synthetic winter data

  16. Conclusions • 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

  17. References • 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

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