An examination of orthogonal expansions for estimating the wind power density function

The wind power density (WPD) function serves as an estimator of the power generation potential of wind turbines. One can formulate the WPD function indirectly as a nonlinear function of the wind speed probability density function (PDF). In such cases, the fidelity of WPD functions depends critically on the accurate estimation of wind speed PDFs from available data.

Scientists have traditionally estimated wind speed PDFs using parametric PDF models, including the Weibull, Rayleigh and Lognormal functions. The two parameter Weibull function enjoys broad acceptance in wind power literature as an adequate model for wind speed PDFs. However, wind speed does not always have a Weibull-like distribution and the WPD function can suffer from large errors when computed from imperfect Weibull approximations of the wind speed PDF.

This paper investigates a class of non-parametric techniques which may prove suitable for optimal non-parametric estimation of the WPD, specifically using orthogonal polynomial expansions. It also proposes a new formulation using orthogonal functions for direct estimation of WPD and evaluates the new formulation analytically and empirically.

Results indicate that the new method produces less bias and random error compared to traditional non-parametric methods.