Modelling Wind Farm Data and the Short Term Prediction of Wind - - PowerPoint PPT Presentation

Data Considerations Current Techniques and Models Data Investigation Conclusion

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

Data Considerations Current Techniques and Models Data Investigation Conclusion

Outline

1

Data Considerations Overview General Considerations

2

Current Techniques and Models Models

3

Data Investigation Wind Farm 1 Data

4

Conclusion Conclusions

Data Considerations Current Techniques and Models Data Investigation Conclusion Overview

Outline

1

Data Considerations Overview General Considerations

2

Current Techniques and Models Models

3

Data Investigation Wind Farm 1 Data

4

Conclusion Conclusions

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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?

10 20 30 40 50 5000 10000 15000

Direction Dependent Power Curve

Wind Speed Power Output 90 120 150 180 210 240

Data Considerations Current Techniques and Models Data Investigation Conclusion 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).

Data Considerations Current Techniques and Models Data Investigation Conclusion Models

Outline

1

Data Considerations Overview General Considerations

2

Current Techniques and Models Models

3

Data Investigation Wind Farm 1 Data

4

Conclusion Conclusions

Data Considerations Current Techniques and Models Data Investigation Conclusion 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. ˆ pt+k = pt. 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. ˆ pt+k = 1 N

N

• t=1

pt.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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: ˆ pt+k = akpt + (1 − ak)¯ p, where ak is the correlation coefficient between pt and pt+k, and ¯ p is the mean value of the series.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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,

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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

Data Considerations Current Techniques and Models Data Investigation Conclusion 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

SCADA.new Frequency 5 10 15 20 50 100 150 200 250 300 Weibull(2,7.4) Weibull(2,7.4) Weibull(2,7.4) Weibull(2,7.4)

The mean of the SCADA data here is 7.553096 ms−1, with a variance of 11.91252.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

5 10 15 20 7.0 7.5 8.0

Plot of Hourly Mean Wind Speeds

Hour of Day Hourly Means

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

5 10 15 20 5 10 15 20

Plot of Mean Squared Errors for New Reference Models

Forecast Horizon, +k hrs Mean Squared Error Original Data Hourly Adjusted Data Monthly Adjusted Data

Data Considerations Current Techniques and Models Data Investigation Conclusion 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. SCADA ∼ NWP + cos 2hrπ 24

• + sin

2hrπ 24

• +NWP ∗ cos

2hrπ 24

• + NWP ∗ sin

2hrπ 24

Data Considerations Current Techniques and Models Data Investigation Conclusion 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:

5 10 15 20 5 10 15 20

Plot of Mean Squared Errors for New Reference Models

Forecast Horizon, +k hrs Mean Squared Error Daily New Ref Model Linear Model

Data Considerations Current Techniques and Models Data Investigation Conclusion 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

• ●
• ●
• −3

−2 −1 1 2 3 −6 −4 −2 2 4 6

Sin and Cos Model Residuals

Theoretical Quantiles Sample Quantiles

• ●
• ● ●
• ●
• ●
• ●
• −3

−2 −1 1 2 3 −1.0 −0.5 0.0 0.5 1.0

Sin and Cos Sqrt Model Residuals

Theoretical Quantiles Sample Quantiles

Data Considerations Current Techniques and Models Data Investigation Conclusion Conclusions

Outline

1

Data Considerations Overview General Considerations

2

Current Techniques and Models Models

3

Data Investigation Wind Farm 1 Data

4

Conclusion Conclusions

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion 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.

Data Considerations Current Techniques and Models Data Investigation Conclusion Conclusions

Any questions?