Modelling Wind Farm Data and the Short Term Prediction of Wind Speeds

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1 Modelling Wind Farm Data and the Short Term Prediction of Wind Speeds An Investigation into Wind Speed Data Sets Erin Mitchell Lancaster University 6th April 2011

2 Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

3 Overview Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

4 Overview Wind Speed Prediction Wind energy fast developing market, UK government aims to produce 20% of energy from wind by 2020; this figure was only at 1.8% in 2007, Accurate short term predictions of wind speeds vital in the development of wind energy, Error margins for predictions useful in the trade of energy.

5 General Considerations Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

6 General Considerations What to Consider? There are many different things to consider when making a wind speed or wind power prediction. These include: Model inputs, Type of model - physical or statistical? Prediction horizon, Single turbine/farm prediction or regional/national prediction? Confidence intervals.

7 General Considerations Model Inputs There are many different variables that can be considered when predicting Wind Speed and Wind Energy: Wind speed (SCADA) and NWP inputs, Wind direction, Air pressure, Air temperature, Season/time of day, Wind power production.

8 General Considerations Forecasting Horizons When predicting Wind Speeds we consider that different forecast horizons have different uses: Short-Term, 0-3hrs: monitoring of turbines, Short/Mid-Term, 1-48hrs: sale of wind energy to the market, Long-Term, 48hrs-7 days: for planning scheduled maintenance of turbines.

9 General Considerations Wind Power Transformation The transformation from wind speed to wind power is cubic. Should power be predicted directly, or be calculated from predicted wind speeds? Direction Dependent Power Curve Power Output Wind Speed

10 General Considerations Different Ways of Making a Forecast Wind Energy forecasting can be generally split into two fields: Physical Models - process wind speed data according to laws of physics in order to adjust data and make forecasts; best at longer term prediction. Statistical Models - look at finding statistical relationships between input variables in order to predict future wind profile based on these dependancies. Combinations of these two approaches are also popular, and it has been suggested that both approaches can be needed for successful forecasts (Project ANEMOS, 2003).

11 Models Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

12 Models The Persistence Model and Mean Value Model The most frequently used reference model is the persistence model: the forecast for all horizons is equal to the value of the most recent observation. ˆp t+k = p t. A second popular reference model is the mean value model: for all horizons, the prediction is the mean value of the data so far, or the mean of a training data set. ˆp t+k = 1 N N p t. t=1

13 Models The New Reference Model The persistence model and mean value model both have their benefits but also their weaknesses: Persistence Model strong at short horizons, Mean Value Model more accurate at longer horizons. The New Reference Model combines the two, assigning weights depending on the forecast horizon: ˆp t+k = a k p t + (1 a k ) p, where a k is the correlation coefficient between p t and p t+k, and p is the mean value of the series.

14 Models Physical Models Many models predict wind from a physical background, considering aspects such as: Geo Drag Law and Log Profile to transform wind to surface height estimations, Orographical effects at the site, Wake effects of the turbines, MOS correction for errors not modelled by the physical side of the model.

15 Models Statistical Models The second school of thought is that of statistical models, with techniques used including: ARIMA Models, Bayesian Model Averaging, Neural Networks, Kalman Filters, Model Output Statistics, Hidden Markov Models.

16 Models Auto-Regressive Models Auto-regressive models are a powerful prediction tool in time series analysis. Wind speed data is highly correlated, so regressing on previous observations is a natural tool to use. Time series models often considered for shorter prediction horizons, i.e. seconds, minutes, 1-3 hours, It has been found that an AR(2) model works well, both in terms of accuracy and simplicity,

17 Models Problems with AR Models There are some issues to be addressed when considering Auto-Regressive Models. Require a data training set in order to compute parameters, AR models assume stationarity but wind data is not stationary - use a time varying AR model to combat this feature, It can be considered desirable to model seasonal effects by using a different model for each month, but this requires a much longer data set on which to train the parameters.

18 Models Analysing Results There are different methods for assessing how well a model is performing, each giving information that may be useful in a slightly different way. Having a standard measure of error is useful for model comparisons, and the following statistics are recommended (ANEMOS D2.3): Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Normalised MAE and RMSE.

19 Wind Farm 1 Data Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

20 Wind Farm 1 Data SCADA Data The SCADA Data for Wind Farm 1 is distributed as shown below, with the curve of a Weibull approximation fitted: Histogram of SCADA.new Frequency Weibull(2,7.4) SCADA.new The mean of the SCADA data here is ms 1, with a variance of

21 Wind Farm 1 Data Daily and Monthy Variation It can be considered the wind speed data contains a daily or monthly trend. In order to investigate this hourly and monthly average wind speeds were calculated and compared. Plot of Hourly Mean Wind Speeds Hourly Means Hour of Day

22 Wind Farm 1 Data Daily and Monthy Variation The new reference model was fitted to the raw data, and to the data adjusted for daily and monthly correction. Plot of Mean Squared Errors for New Reference Models Mean Squared Error Original Data Hourly Adjusted Data Monthly Adjusted Data Forecast Horizon, +k hrs

23 Wind Farm 1 Data Linear Models Linear models were seen to be appropriate to model the relationship between the SCADA and NWP data. Different models were tested, including an hourly factor and a sinusiodal fit for daily variations. ( ) ( ) 2hrπ 2hrπ SCADA NWP + cos + sin ( ) ( ) 2hrπ 2hrπ +NWP cos + NWP sin 24 24

24 Wind Farm 1 Data Linear Model Improvement The MSEs of both the afore mentioned linear model and the new reference daily adjusted model are shown below: Plot of Mean Squared Errors for New Reference Models Mean Squared Error Daily New Ref Model Linear Model Forecast Horizon, +k hrs

25 Wind Farm 1 Data Square Root Transformation In order to stabilise the variance, a square root transformation was applied to the data. The QQ plot of the residuals of the following model is shown below: SCADA NWP + cos ( 2hrπ 24 ) + sin ( 2hrπ 24 ) Sin and Cos Model Residuals Theoretical Quantiles Sample Quantiles Sin and Cos Sqrt Model Residuals Theoretical Quantiles Sample Quantiles

26 Conclusions Outline 1 Data Considerations Overview General Considerations 2 Current Techniques and Models Models 3 Data Investigation Wind Farm 1 Data 4 Conclusion Conclusions

27 Conclusions Summary Both physical and statistical models should be considered - does a prediction need to use both fields to obtain the most successful results? Wind speeds do not follow a Gaussian distribution, Daily effect is strong; monthly effect not so prevalent, Square root transformation could be appropriate, SCADA data useful for short term predictions; NWP data more accurate at longer forecast horizons.

28 Conclusions Future Work Continue to analyse wind farm 1 data, Repeat investigation of data for a second wind farm, Consider whether or not wind farm data is similar across different farms, Implement dynamic linear models in order to predict wind speeds, Include the extra variables of wind direction, air pressure, and temperature, Look to improve accuracy of predictions at longer horizons - combine SCADA and NWP methods.

29 Conclusions Any questions?