wind power forecasting using non-linear armax models and...

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

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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

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A case study

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Google Earth Map

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Tararua Wind Farm (Panoramio, Alan Blackley)

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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

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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)

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Five Parameters Logistic Model

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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

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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

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Power Curves Fits

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Wind Speed in Two Weeks for One Turbine

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Power Prediction for One Turbine

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One to One Correspondance?

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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.

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Turbine Layout and Grid Points from Mesoscale Model

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Wind Speed Predictions from Mesoscale Model

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Power Predictions from Mesoscale Model Wind Speeds

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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

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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.

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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)

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Output from Neural Network

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Output from Neural Network

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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?

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THANK YOU FOR YOUR ATTENTION

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