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Local linear regression with adaptive orthogonal fitting for the wind power application

Abstract

Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve, owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assumption is relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those which minimize a weighted Total Least Squares (TLS) criterion. An adaptive estimation method is introduced in order to accommodate nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented covariance matrix. A robustification of the estimation method is also proposed. Simulations on semi-artificial datasets (for which the true power curve is available) underline the properties of the proposed regression and related estimation methods. An important result is the significantly higher ability of local polynomial regression with orthogonal fit to accurately approximate the target regression, even though it may hardly be visible when calculating error criteria against corrupted data.

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Correspondence to Pierre Pinson.

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Pinson, P., Nielsen, H.A., Madsen, H. et al. Local linear regression with adaptive orthogonal fitting for the wind power application. Stat Comput 18, 59–71 (2008). https://doi.org/10.1007/s11222-007-9038-7

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Keywords

  • Wind power
  • Modelling
  • Forecasting
  • Nonparametric regression
  • Local linear regression
  • Total least squares
  • Adaptive estimation
  • Robust estimation