wind power forecasting using non-linear armax models and...
TRANSCRIPT
Frede Aakmann Tøgersen & Kim Emil AndersenWind & Site Competence Centre
Technology R & DVestas Wind Systems A/S
Wind Power Forecasting Using Non-Linear ARMAX
Models and Neural Networks
2 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Agenda
• Introducing a case study used in developing the forecast method• Explaining power curves for wind turbine generators• Fitting power curve model• Windspeed measured at turbine and power prediction• Numerical weather predictions models (NWP)• Correcting NWP data to turbine data using ARMAX models and NN• Future work
3 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
A case study
4 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Google Earth Map
5 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Tararua Wind Farm (Panoramio, Alan Blackley)
6 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Observed Power and Wind SpeedFrom physics the
power is related to the windspeed as given by the following formula.
Lower bound is 0 whereas upper bound is determined by components of the turbine
7 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Different Power Curves For Different Air Density
• Different theoretical power curves for different air densities.
• Mismatch is mostly due to the windspeed is measured behind rotor
• But can also be attributed to difficult climatic conditions (complex terrain)
8 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Five Parameters Logistic Model
9 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Other Variables Influencing Power Curves• TI: turbulence intensity,
coefficient of variation of windspeed
• Inflow angle: the angle between wind direction and rotor plane (depends on the orography of the site)
• Windshear: characterizes how fast windspeed increases with increasing height above ground
10 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
11 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Splitting Oberved Data After MET And CFD Data
From meteorological data:
• Wind speed, wind direction• Pressure, temperature, humidity giving air density• Turbulence kinetic energy (TKE), substitute for TI
From CFD (for each turbine)
Wind directions is split into usually 12 wind sectors
• Sectorwise wind shear• Sectorwise TI (if no TKE)• Sectorwise inflow angle
12 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Power Curves Fits
13 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
14 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Wind Speed in Two Weeks for One Turbine
15 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Power Prediction for One Turbine
16 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
One to One Correspondance?
17 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Weather Forecast
• Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to predict the weather. It usually operates on the scale of up to 1000 km.
• There exists numerous models, e.g. ETA, WRF, RAMS, MM5, ALADIN to mention a few
• Mesoscale meteorology is the study of weather systems smaller than synoptic scale systems but larger than microscale and storm- scale cumulus systems. Horizontal dimensions generally range from around 5 kilometers to several hundred kilometers.
18 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Turbine Layout and Grid Points from Mesoscale Model
19 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Wind Speed Predictions from Mesoscale Model
20 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Power Predictions from Mesoscale Model Wind Speeds
21 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
ARMAX modelsLinear model: ARMAX(p,q,b)
where
are the parameters of the autoregressive part of the model,
are the parameters of the moving average part of the model
are the parameters of the exogenous part of the model.
Standard statistical methods exist to estimate the parameters of the linear model
22 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Non-linear ARMAX models
• The model parameters depends on the functional form of
• No generic methods from the statistical community to estimate the parameters of the model.
• However neural network is able to approximate the model using non-linear activation functions at the nodes of the layers of the network.
23 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Output from Neural Network
• Forecasts is based on observed turbine data. These will not be available at prediction time but must be estimated by some iterative prediction method (not implemented yet)
24 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Output from Neural Network
25 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Output from Neural Network
26 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
Future work
• Implement a procedure for iterative predictions of future values of turbine data
• Other input variables to consider such as e.g. wind directions etc.• Explore how many training data is necessary for a good training and
reliable forecasts• How many mesoscale gridpoints is needed as input?• How do we find the optimal spatial resolution of the mesoscale
models?• How far into the future do we need or dare to forecast?• How often per day do we need to forecast?
27 | The 30th Annual International Symposium on Forecasting, June 21 – 23 2010
THANK YOU FOR YOUR ATTENTION
Copyright NoticeThe documents are created by Vestas Wind Systems A/S and contain copyrighted material, trademarks, and other proprietary information. All rights reserved. No part of the documents may be reproduced or copied in any form or by any means—such as graphic, electronic, or mechanical, including photocopying, taping, or information storage and retrieval systems without the prior written permission of Vestas Wind Systems A/S. The use of these documents by you, or anyone else authorized by you, is prohibited unless specifically permitted by Vestas Wind Systems A/S. You may not alter or remove any trademark, copyright or other notice from the documents. The documents are provided “as is” and Vestas Wind Systems A/S shall not have any responsibility or liability whatsoever for the results of use of the documents by you. Vestas wishes to acknowledge and respect all copyrights in connection with the illustrations used in this presentation. In case we have unintentionally violated copyrighted material, we want to be informed immediately in order to straighten things out and thus to honour any obligatory fees.