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

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

Model calibration Σ X μ W P 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 OlmosPoyry

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 Power output distribution Volatility curve

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

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

What about turbine cutout? 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 => 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 Poyry 2030 data (43GW capacity) Synthetic data from tweaked GB2030 model

GB2030: Effect of tweak Power output distribution Volatility curve

GB2030: Time history sample (“Turing test”) Wind output (GW) 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”, 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”, Sturt, A. and Strbac, G. “A time series model for the aggregate GB wind output circa 2030”, References