1. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 Exploration of Wind Farm Power Output Using Meteorological Predictions Simon Lambert*, Maurice Dixon $ *, Julian Gallop*, and Richard Brownsword + *e-Science Centre STFC + Energy Research Unit STFC $ CISM Kingston University

2. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 2 Outline Background Data in this work Modelling Conclusions and further work

3. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 3 Background 1 Wind power is being integrated into the national electricity grid ~10 hours to ramp up/down conventional coal/gas generators Wind farms are intermittent generators Improvements of a few percent are worth having Although some regard wind power prediction as a solved problem there remain important problems –The effect of predicted wind direction –The evolution of parameters in time (yearly?)

4. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 4 Background 2 ~2 hours to make a forecast Meteorological forecasts are quite good for higher in the atmosphere Ground roughening effects are problematic –E.g. Pyrenees in Spain Turbines interfere with one another so use predicted wind speed rather than actual anemometer reading Aim: –Take meteorological prediction of wind speed and “correct” for individual site

5. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 5 Background 3 How good is the adaptive behaviour incorporated in the model? What local area adaptation needs to be made? –Direction (e.g. small hills, woodland which perturb the coarse-scale meteorological forecast) and time of day (e.g. because of local wind effects such as sea breezes) What turbine/turbine adaptation needs to be made (e.g. for shielding/turbulence)? Does the prediction error arise from the behaviour of the model or from the wind speed forecast? –There could be interest in when wind speed is unreliable for the model.

6. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 6 Background 4 General approaches: –Exploration of data through visualisation –Autoregression (linear and non-linear) Autoregression equations can be used of the form P*(t+k) = a k P(t) + b k + c k V*(t+k) + d k V* 2 (t+k) P(t) is the measure actual power output at time t P*(t+k) is the estimated power forecast k timesteps ahead V*(t+k) is the met-forecast windspeed a k, b k, c k, d k are model constants. Additional terms involving Cos( Θ ) and Sin( Θ ) are included for wind direction.

7. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 7 Data in this work 1 Commercial confidentiality means data has been normalised Meteorological data is every 6 hours One year of data at hourly recording intervals –Power output from wind farm –Meteorological prediction of wind speed –Meteorological prediction of wind direction –Time of day

8. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 8 Data in this work 2 Marked Region of Low Speed and High Power - Visualisation

9. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 9 Modelling 1 Linear Autoregression –Construct lagged data set m1=1hr, 2hr, 3hr lagging on Power, Direction, Speed –Use a forward stepping ordinary least squares –Add / remove variables based on variance –Square of correlation R 2 = 0.92 Power = –0.02843 + Powerm1 * 1.005 + Speed * 0.0432 – Powerm2 * 0.09765 – Speedm1 * 0.02981 + Dirm1 * 0.00007911 + Tod * 0.000769 Other lagged variables found not necessary

10. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 10 Modelling 2 Non-Linear Autoregression –Use same lagged data set m1=1hr, 2hr, 3hr lagging on Power, Direction, Speed –Use Neural Net with second output node for model to predict own error –Square of correlation R 2 = 0.91

11. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 11 Modelling 3 Comparison of Models: –Using paired t-test both the NN and OLS are unbiased estimators of the mean –Using F test both OLS and NN have variance marginally above the experimental data

12. 12 Modelling 4 Comparison of Models: Using 95% CI we find 96% of test data lie between NN_L&NN_U

13. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 13 Modelling 5 Multivariate Non-Linear Regression without Autoregression –Model Power and Power_Residual_Squared from current Meteorological estimates of Wind speed, Wind direction, Time of day. –Use Neural Net to predict own error –Square of correlation R 2 = 0.559 (R = 0.75) –Variances definitely differ –Model is unbiased estimator of mean –4.5% of independent test set data points lie outside the 95% confidence prediction interval

14. 14 Modelling 6 Prediction interval – multivariate non auto regression

15. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 15 Conclusions and further work 1 Both linear and non-linear autoregression models give good estimates of the Power time series for the wind farm. –This is to be expected as the previous Power value is included in the equations The multivariate regression without autoregression is much less well correlated Possible to predict error in models –Useful to know when there is uncertainty Visualisation techniques allowed to see that there are regions when high power can be obtained at low predicted wind speed

16. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 16 Conclusions and further work 2 How is the forecast is used? –Having obtained some model parameters, how frequently should they be reevaluated? –What is the basis of reevaluation (recent history or whole history)? Probably the parameters will change with the time of year. Comparison with wave power forecasting (not regarded as solved) –It may be possible to link forecasting methods used in both fields, so long as the different effects of time are taken into account (waves build over period of hours)

17. ERCIM Environmental Modelling WG meeting Paris, 27 May 2009 17 Questions? Simon.Lambert@stfc.ac.uk